TSTP Solution File: ANA014-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA014-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 19:14:33 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of clauses : 99 ( 37 unt; 15 nHn; 58 RR)
% Number of literals : 181 ( 122 equ; 73 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 116 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
v_c != c_0 ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a) ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_times(c_1,V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ) ).
cnf(clsrel_Ring__and__Field_Ofield_12,axiom,
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Oordered__idom(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_58,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ) ).
cnf(refute_0_0,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Oordered__idom(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__field_34:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_1,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__field(t_a) )],[tfree_tcs,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| c_HOL_Oabs(c_times(X_16,X_17,t_a),t_a) = c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(X_17,t_a),t_a) ),
inference(subst,[],[cls_Ring__and__Field_Oabs__mult_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_16)),bind(V_b,$fot(X_17))]]) ).
cnf(refute_0_3,plain,
c_HOL_Oabs(c_times(X_16,X_17,t_a),t_a) = c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(X_17,t_a),t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_a) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( c_HOL_Oabs(c_times(X_16,X_17,t_a),t_a) != c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(X_17,t_a),t_a)
| c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(X_17,t_a),t_a) = c_HOL_Oabs(c_times(X_16,X_17,t_a),t_a) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(c_HOL_Oabs(c_times(X_16,X_17,t_a),t_a))),bind(Y,$fot(c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(X_17,t_a),t_a)))]]) ).
cnf(refute_0_8,plain,
c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(X_17,t_a),t_a) = c_HOL_Oabs(c_times(X_16,X_17,t_a),t_a),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(X_16,X_17,t_a),t_a),c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(X_17,t_a),t_a)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a) = c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),
inference(subst,[],[refute_0_8:[bind(X_16,$fot(v_c)),bind(X_17,$fot(v_f(v_x(V_U))))]]) ).
cnf(refute_0_10,plain,
c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) = c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),
introduced(tautology,[refl,[$fot(c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a))]]) ).
cnf(refute_0_11,plain,
( c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) != c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a)
| c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a) != c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a)
| c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) = c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a)) ),[1,1],$fot(c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a))]]) ).
cnf(refute_0_12,plain,
( c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a) != c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a)
| c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) = c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) = c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a) != c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a) ),[1],$fot(c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a))]]) ).
cnf(refute_0_15,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U)),t_a),t_a),t_a),t_a),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a) )],[refute_0_15,cls_conjecture_1]) ).
cnf(refute_0_17,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a),
inference(subst,[],[refute_0_16:[bind(V_U,$fot(c_HOL_Oabs(X_16,t_a)))]]) ).
cnf(refute_0_18,plain,
c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a) = c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),
inference(subst,[],[refute_0_3:[bind(X_17,$fot(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a)))]]) ).
cnf(refute_0_19,plain,
( c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a) != c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a)
| c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a) = c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a))),bind(Y,$fot(c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a)))]]) ).
cnf(refute_0_20,plain,
c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a) = c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a) != c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a) ),[1],$fot(c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a))]]) ).
cnf(refute_0_22,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_HOL_Oabs(c_times(X_16,c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),c_times(c_HOL_Oabs(X_16,t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X_16,t_a))),t_a),t_a),t_a),t_a) )],[refute_0_22,refute_0_17]) ).
cnf(refute_0_24,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a),t_a),
inference(subst,[],[refute_0_23:[bind(X_16,$fot(c_HOL_Oinverse(v_c,t_a)))]]) ).
cnf(refute_0_25,plain,
c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_times(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a),c_HOL_Oabs(X_17,t_a),t_a),
inference(subst,[],[refute_0_3:[bind(X_16,$fot(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a)))]]) ).
cnf(refute_0_26,plain,
c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a) = c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a),
inference(subst,[],[refute_0_3:[bind(X_16,$fot(c_HOL_Oinverse(X_19,t_a))),bind(X_17,$fot(X_19))]]) ).
cnf(refute_0_27,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__field_0:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_28,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__field(t_a) )],[tfree_tcs,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| X_13 = c_0
| c_times(c_HOL_Oinverse(X_13,t_a),X_13,t_a) = c_1 ),
inference(subst,[],[cls_Ring__and__Field_Ofield__class_Oaxioms__1_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_13))]]) ).
cnf(refute_0_30,plain,
( X_13 = c_0
| c_times(c_HOL_Oinverse(X_13,t_a),X_13,t_a) = c_1 ),
inference(resolve,[$cnf( class_Ring__and__Field_Ofield(t_a) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( X_19 = c_0
| c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a) = c_1 ),
inference(subst,[],[refute_0_30:[bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_32,plain,
( c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a) != c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a)
| c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a) != c_1
| c_HOL_Oabs(c_1,t_a) = c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a),c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a)) ),[0,0],$fot(c_1)]]) ).
cnf(refute_0_33,plain,
( c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a) != c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a)
| X_19 = c_0
| c_HOL_Oabs(c_1,t_a) = c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),c_1) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( X_19 = c_0
| c_HOL_Oabs(c_1,t_a) = c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a),c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a)) )],[refute_0_26,refute_0_33]) ).
cnf(refute_0_35,plain,
c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a),
inference(subst,[],[refute_0_8:[bind(X_16,$fot(c_HOL_Oinverse(X_19,t_a))),bind(X_17,$fot(X_19))]]) ).
cnf(refute_0_36,plain,
( c_HOL_Oabs(c_1,t_a) != c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a)
| c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a) != c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a)
| c_HOL_Oabs(c_1,t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a)) ),[0],$fot(c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a))]]) ).
cnf(refute_0_37,plain,
( c_HOL_Oabs(c_1,t_a) != c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a)
| c_HOL_Oabs(c_1,t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( X_19 = c_0
| c_HOL_Oabs(c_1,t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_19,t_a),X_19,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_1,t_a),c_times(c_HOL_Oabs(c_HOL_Oinverse(X_19,t_a),t_a),c_HOL_Oabs(X_19,t_a),t_a)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( X_22 = c_0
| c_HOL_Oabs(c_1,t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a) ),
inference(subst,[],[refute_0_38:[bind(X_19,$fot(X_22))]]) ).
cnf(refute_0_40,plain,
( c_HOL_Oabs(c_1,t_a) != c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a)
| c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a) = c_HOL_Oabs(c_1,t_a) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(c_HOL_Oabs(c_1,t_a))),bind(Y,$fot(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a)))]]) ).
cnf(refute_0_41,plain,
( X_22 = c_0
| c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a) = c_HOL_Oabs(c_1,t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a) != c_HOL_Oabs(c_1,t_a)
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_times(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a),c_HOL_Oabs(X_17,t_a),t_a)
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_times(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a),c_HOL_Oabs(X_17,t_a),t_a)) ),[1,0],$fot(c_HOL_Oabs(c_1,t_a))]]) ).
cnf(refute_0_43,plain,
( c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_times(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a),c_HOL_Oabs(X_17,t_a),t_a)
| X_22 = c_0
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a),c_HOL_Oabs(c_1,t_a)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( X_22 = c_0
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_times(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),t_a),c_HOL_Oabs(X_17,t_a),t_a)) )],[refute_0_25,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| class_OrderedGroup_Omonoid__mult(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Ofield_12:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_46,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Ofield(t_a) )],[refute_0_28,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ class_OrderedGroup_Omonoid__mult(t_a)
| c_times(c_1,X_10,t_a) = X_10 ),
inference(subst,[],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0:[bind(T_a,$fot(t_a)),bind(V_y,$fot(X_10))]]) ).
cnf(refute_0_48,plain,
c_times(c_1,X_10,t_a) = X_10,
inference(resolve,[$cnf( class_OrderedGroup_Omonoid__mult(t_a) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
c_times(c_1,X_17,t_a) = X_17,
inference(subst,[],[refute_0_48:[bind(X_10,$fot(X_17))]]) ).
cnf(refute_0_50,plain,
c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a) = c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a),
introduced(tautology,[refl,[$fot(c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a))]]) ).
cnf(refute_0_51,plain,
( c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a) != c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a)
| c_times(c_1,X_17,t_a) != X_17
| c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a),c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a)) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_52,plain,
( c_times(c_1,X_17,t_a) != X_17
| c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a),c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a),
inference(resolve,[$cnf( $equal(c_times(c_1,X_17,t_a),X_17) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) = c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a),
inference(subst,[],[refute_0_8:[bind(X_16,$fot(c_1))]]) ).
cnf(refute_0_55,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_56,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_6,refute_0_55]) ).
cnf(refute_0_57,plain,
( c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a) != c_HOL_Oabs(X_17,t_a)
| c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) != c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a)
| c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
inference(subst,[],[refute_0_56:[bind(X,$fot(c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a))),bind(Y,$fot(c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a))),bind(Z,$fot(c_HOL_Oabs(X_17,t_a)))]]) ).
cnf(refute_0_58,plain,
( c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a) != c_HOL_Oabs(X_17,t_a)
| c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a),c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a)) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_1,X_17,t_a),t_a),c_HOL_Oabs(X_17,t_a)) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
( c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a)
| c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a) != c_HOL_Oabs(X_17,t_a)
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_HOL_Oabs(X_17,t_a)) ),[0],$fot(c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a))]]) ).
cnf(refute_0_61,plain,
( c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a)
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a),c_HOL_Oabs(X_17,t_a)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( X_22 = c_0
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_times(c_HOL_Oabs(c_1,t_a),c_HOL_Oabs(X_17,t_a),t_a)) )],[refute_0_44,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| class_OrderedGroup_Osemigroup__mult(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Ofield_21:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_64,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Ofield(t_a) )],[refute_0_28,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_a)
| c_times(c_times(X_26,X_27,t_a),X_28,t_a) = c_times(X_26,c_times(X_27,X_28,t_a),t_a) ),
inference(subst,[],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_26)),bind(V_b,$fot(X_27)),bind(V_c,$fot(X_28))]]) ).
cnf(refute_0_66,plain,
c_times(c_times(X_26,X_27,t_a),X_28,t_a) = c_times(X_26,c_times(X_27,X_28,t_a),t_a),
inference(resolve,[$cnf( class_OrderedGroup_Osemigroup__mult(t_a) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a) = c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),
inference(subst,[],[refute_0_66:[bind(X_26,$fot(c_HOL_Oinverse(X_22,t_a))),bind(X_27,$fot(X_22)),bind(X_28,$fot(X_17))]]) ).
cnf(refute_0_68,plain,
c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),
introduced(tautology,[refl,[$fot(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a))]]) ).
cnf(refute_0_69,plain,
( c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a)
| c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a) != c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a)
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a)) ),[1,0],$fot(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a))]]) ).
cnf(refute_0_70,plain,
( c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a) != c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a)
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) = c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a),
inference(resolve,[$cnf( $equal(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_HOL_Oabs(X_17,t_a)
| c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a)
| c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_HOL_Oabs(X_17,t_a)) ),[0],$fot(c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a))]]) ).
cnf(refute_0_73,plain,
( c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a) != c_HOL_Oabs(X_17,t_a)
| c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( X_22 = c_0
| c_HOL_Oabs(c_times(c_HOL_Oinverse(X_22,t_a),c_times(X_22,X_17,t_a),t_a),t_a) = c_HOL_Oabs(X_17,t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_times(c_HOL_Oinverse(X_22,t_a),X_22,t_a),X_17,t_a),t_a),c_HOL_Oabs(X_17,t_a)) )],[refute_0_62,refute_0_73]) ).
cnf(refute_0_75,plain,
( c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a) = c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a)
| v_c = c_0 ),
inference(subst,[],[refute_0_74:[bind(X_17,$fot(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))))),bind(X_22,$fot(v_c))]]) ).
cnf(refute_0_76,plain,
( c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a) != c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a),t_a) ),[1],$fot(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a))]]) ).
cnf(refute_0_77,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| v_c = c_0
| c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| v_c = c_0 ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),c_times(v_c,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a),t_a) )],[refute_0_77,refute_0_24]) ).
cnf(refute_0_79,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Orderings_Oorder(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__field_58:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_80,plain,
class_Orderings_Oorder(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__field(t_a) )],[tfree_tcs,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(X_6,X_6,t_a) ),
inference(subst,[],[cls_Orderings_Oorder__class_Oaxioms__1_0:[bind(T_a,$fot(t_a)),bind(V_x,$fot(X_6))]]) ).
cnf(refute_0_82,plain,
c_lessequals(X_6,X_6,t_a),
inference(resolve,[$cnf( class_Orderings_Oorder(t_a) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),
inference(subst,[],[refute_0_82:[bind(X_6,$fot(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a)))]]) ).
cnf(refute_0_84,plain,
v_c = c_0,
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a) )],[refute_0_83,refute_0_78]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(v_c,c_0) )],[refute_0_84,cls_conjecture_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA014-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 06:01:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------