TSTP Solution File: ANA030-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 19:14:44 EDT 2022
% Result : Unsatisfiable 62.14s 62.39s
% Output : CNFRefutation 62.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 25
% Syntax : Number of clauses : 91 ( 40 unt; 0 nHn; 46 RR)
% Number of literals : 159 ( 85 equ; 70 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 141 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| c_HOL_Oabs(V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Ocompare__rls__1_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ominus__add__distrib_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ).
cnf(cls_Orderings_Ole__maxI2_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| c_lessequals(V_x,V_z,T_b) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
cnf(refute_0_0,plain,
~ c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(v_c))]]) ).
cnf(refute_0_1,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Olinorder(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_33:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_2,plain,
class_Orderings_Olinorder(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_lessequals(X_11,c_Orderings_Omax(X_10,X_11,t_b),t_b) ),
inference(subst,[],[cls_Orderings_Ole__maxI2_0:[bind(T_b,$fot(t_b)),bind(V_x,$fot(X_10)),bind(V_y,$fot(X_11))]]) ).
cnf(refute_0_4,plain,
c_lessequals(X_11,c_Orderings_Omax(X_10,X_11,t_b),t_b),
inference(resolve,[$cnf( class_Orderings_Olinorder(t_b) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
c_lessequals(c_0,c_Orderings_Omax(X_10,c_0,t_b),t_b),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(c_0))]]) ).
cnf(refute_0_6,plain,
( ~ c_lessequals(c_0,c_Orderings_Omax(X_10,c_0,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_HOL_Oabs(c_Orderings_Omax(X_10,c_0,t_b),t_b) = c_Orderings_Omax(X_10,c_0,t_b) ),
inference(subst,[],[cls_OrderedGroup_Oabs__of__nonneg_0:[bind(T_a,$fot(t_b)),bind(V_y,$fot(c_Orderings_Omax(X_10,c_0,t_b)))]]) ).
cnf(refute_0_7,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_HOL_Oabs(c_Orderings_Omax(X_10,c_0,t_b),t_b) = c_Orderings_Omax(X_10,c_0,t_b) ),
inference(resolve,[$cnf( c_lessequals(c_0,c_Orderings_Omax(X_10,c_0,t_b),t_b) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_50:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_9,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_8]) ).
cnf(refute_0_10,plain,
c_HOL_Oabs(c_Orderings_Omax(X_10,c_0,t_b),t_b) = c_Orderings_Omax(X_10,c_0,t_b),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b) = c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),
inference(subst,[],[refute_0_10:[bind(X_10,$fot(c_minus(v_f(V_U),v_g(V_U),t_b)))]]) ).
cnf(refute_0_12,plain,
( c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b) != c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b)
| ~ c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
| c_lessequals(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),[0],$fot(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b))]]) ).
cnf(refute_0_13,plain,
( ~ c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
| c_lessequals(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) )],[cls_conjecture_1,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ c_lessequals(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(V_U),v_g(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
inference(subst,[],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0:[bind(T_b,$fot(t_b)),bind(V_x,$fot(c_minus(v_f(V_U),v_g(V_U),t_b))),bind(V_y,$fot(c_0)),bind(V_z,$fot(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b)))]]) ).
cnf(refute_0_16,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(V_U),v_g(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
c_lessequals(c_minus(v_f(V_U),v_g(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(resolve,[$cnf( class_Orderings_Olinorder(t_b) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ c_lessequals(c_minus(v_f(V_U),v_g(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(v_f(V_U),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Ocompare__rls__8_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(v_f(V_U))),bind(V_b,$fot(v_g(V_U))),bind(V_c,$fot(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b)))]]) ).
cnf(refute_0_19,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(v_f(V_U),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_minus(v_f(V_U),v_g(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Oab__group__add(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_4:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_21,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| c_uminus(c_uminus(X_7,t_b),t_b) = X_7 ),
inference(subst,[],[cls_OrderedGroup_Ominus__minus_0:[bind(T_a,$fot(t_b)),bind(V_y,$fot(X_7))]]) ).
cnf(refute_0_23,plain,
c_uminus(c_uminus(X_7,t_b),t_b) = X_7,
inference(resolve,[$cnf( class_OrderedGroup_Oab__group__add(t_b) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
c_uminus(c_uminus(c_plus(X_46,X_47,t_b),t_b),t_b) = c_plus(X_46,X_47,t_b),
inference(subst,[],[refute_0_23:[bind(X_7,$fot(c_plus(X_46,X_47,t_b)))]]) ).
cnf(refute_0_25,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| c_uminus(c_plus(X_44,X_45,t_b),t_b) = c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Ominus__add__distrib_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_44)),bind(V_b,$fot(X_45))]]) ).
cnf(refute_0_26,plain,
c_uminus(c_plus(X_44,X_45,t_b),t_b) = c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Oab__group__add(t_b) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| c_uminus(c_minus(X_22,X_23,t_b),t_b) = c_minus(X_23,X_22,t_b) ),
inference(subst,[],[cls_OrderedGroup_Ominus__diff__eq_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_22)),bind(V_b,$fot(X_23))]]) ).
cnf(refute_0_28,plain,
c_uminus(c_minus(X_22,X_23,t_b),t_b) = c_minus(X_23,X_22,t_b),
inference(resolve,[$cnf( class_OrderedGroup_Oab__group__add(t_b) )],[refute_0_21,refute_0_27]) ).
cnf(refute_0_29,plain,
c_uminus(c_minus(X_24,c_uminus(X_7,t_b),t_b),t_b) = c_minus(c_uminus(X_7,t_b),X_24,t_b),
inference(subst,[],[refute_0_28:[bind(X_22,$fot(X_24)),bind(X_23,$fot(c_uminus(X_7,t_b)))]]) ).
cnf(refute_0_30,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| c_plus(X_15,c_uminus(X_16,t_b),t_b) = c_minus(X_15,X_16,t_b) ),
inference(subst,[],[cls_OrderedGroup_Ocompare__rls__1_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_15)),bind(V_b,$fot(X_16))]]) ).
cnf(refute_0_31,plain,
c_plus(X_15,c_uminus(X_16,t_b),t_b) = c_minus(X_15,X_16,t_b),
inference(resolve,[$cnf( class_OrderedGroup_Oab__group__add(t_b) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
c_plus(X_17,c_uminus(c_uminus(X_7,t_b),t_b),t_b) = c_minus(X_17,c_uminus(X_7,t_b),t_b),
inference(subst,[],[refute_0_31:[bind(X_15,$fot(X_17)),bind(X_16,$fot(c_uminus(X_7,t_b)))]]) ).
cnf(refute_0_33,plain,
( c_plus(X_17,c_uminus(c_uminus(X_7,t_b),t_b),t_b) != c_minus(X_17,c_uminus(X_7,t_b),t_b)
| c_uminus(c_uminus(X_7,t_b),t_b) != X_7
| c_plus(X_17,X_7,t_b) = c_minus(X_17,c_uminus(X_7,t_b),t_b) ),
introduced(tautology,[equality,[$cnf( $equal(c_plus(X_17,c_uminus(c_uminus(X_7,t_b),t_b),t_b),c_minus(X_17,c_uminus(X_7,t_b),t_b)) ),[0,1],$fot(X_7)]]) ).
cnf(refute_0_34,plain,
( c_plus(X_17,c_uminus(c_uminus(X_7,t_b),t_b),t_b) != c_minus(X_17,c_uminus(X_7,t_b),t_b)
| c_plus(X_17,X_7,t_b) = c_minus(X_17,c_uminus(X_7,t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_uminus(c_uminus(X_7,t_b),t_b),X_7) )],[refute_0_23,refute_0_33]) ).
cnf(refute_0_35,plain,
c_plus(X_17,X_7,t_b) = c_minus(X_17,c_uminus(X_7,t_b),t_b),
inference(resolve,[$cnf( $equal(c_plus(X_17,c_uminus(c_uminus(X_7,t_b),t_b),t_b),c_minus(X_17,c_uminus(X_7,t_b),t_b)) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
c_plus(X_24,X_7,t_b) = c_minus(X_24,c_uminus(X_7,t_b),t_b),
inference(subst,[],[refute_0_35:[bind(X_17,$fot(X_24))]]) ).
cnf(refute_0_37,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_38,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_39,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( c_plus(X_24,X_7,t_b) != c_minus(X_24,c_uminus(X_7,t_b),t_b)
| c_minus(X_24,c_uminus(X_7,t_b),t_b) = c_plus(X_24,X_7,t_b) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(c_plus(X_24,X_7,t_b))),bind(Y,$fot(c_minus(X_24,c_uminus(X_7,t_b),t_b)))]]) ).
cnf(refute_0_41,plain,
c_minus(X_24,c_uminus(X_7,t_b),t_b) = c_plus(X_24,X_7,t_b),
inference(resolve,[$cnf( $equal(c_plus(X_24,X_7,t_b),c_minus(X_24,c_uminus(X_7,t_b),t_b)) )],[refute_0_36,refute_0_40]) ).
cnf(refute_0_42,plain,
( c_minus(X_24,c_uminus(X_7,t_b),t_b) != c_plus(X_24,X_7,t_b)
| c_uminus(c_minus(X_24,c_uminus(X_7,t_b),t_b),t_b) != c_minus(c_uminus(X_7,t_b),X_24,t_b)
| c_uminus(c_plus(X_24,X_7,t_b),t_b) = c_minus(c_uminus(X_7,t_b),X_24,t_b) ),
introduced(tautology,[equality,[$cnf( $equal(c_uminus(c_minus(X_24,c_uminus(X_7,t_b),t_b),t_b),c_minus(c_uminus(X_7,t_b),X_24,t_b)) ),[0,0],$fot(c_plus(X_24,X_7,t_b))]]) ).
cnf(refute_0_43,plain,
( c_uminus(c_minus(X_24,c_uminus(X_7,t_b),t_b),t_b) != c_minus(c_uminus(X_7,t_b),X_24,t_b)
| c_uminus(c_plus(X_24,X_7,t_b),t_b) = c_minus(c_uminus(X_7,t_b),X_24,t_b) ),
inference(resolve,[$cnf( $equal(c_minus(X_24,c_uminus(X_7,t_b),t_b),c_plus(X_24,X_7,t_b)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
c_uminus(c_plus(X_24,X_7,t_b),t_b) = c_minus(c_uminus(X_7,t_b),X_24,t_b),
inference(resolve,[$cnf( $equal(c_uminus(c_minus(X_24,c_uminus(X_7,t_b),t_b),t_b),c_minus(c_uminus(X_7,t_b),X_24,t_b)) )],[refute_0_29,refute_0_43]) ).
cnf(refute_0_45,plain,
( c_uminus(c_plus(X_24,X_7,t_b),t_b) != c_minus(c_uminus(X_7,t_b),X_24,t_b)
| c_minus(c_uminus(X_7,t_b),X_24,t_b) = c_uminus(c_plus(X_24,X_7,t_b),t_b) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(c_uminus(c_plus(X_24,X_7,t_b),t_b))),bind(Y,$fot(c_minus(c_uminus(X_7,t_b),X_24,t_b)))]]) ).
cnf(refute_0_46,plain,
c_minus(c_uminus(X_7,t_b),X_24,t_b) = c_uminus(c_plus(X_24,X_7,t_b),t_b),
inference(resolve,[$cnf( $equal(c_uminus(c_plus(X_24,X_7,t_b),t_b),c_minus(c_uminus(X_7,t_b),X_24,t_b)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
c_minus(c_uminus(X_44,t_b),X_45,t_b) = c_uminus(c_plus(X_45,X_44,t_b),t_b),
inference(subst,[],[refute_0_46:[bind(X_24,$fot(X_45)),bind(X_7,$fot(X_44))]]) ).
cnf(refute_0_48,plain,
c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b) = c_minus(c_uminus(X_44,t_b),X_45,t_b),
inference(subst,[],[refute_0_31:[bind(X_15,$fot(c_uminus(X_44,t_b))),bind(X_16,$fot(X_45))]]) ).
cnf(refute_0_49,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_50,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_39,refute_0_49]) ).
cnf(refute_0_51,plain,
( c_minus(c_uminus(X_44,t_b),X_45,t_b) != c_uminus(c_plus(X_45,X_44,t_b),t_b)
| c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b) != c_minus(c_uminus(X_44,t_b),X_45,t_b)
| c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b) = c_uminus(c_plus(X_45,X_44,t_b),t_b) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b))),bind(Y,$fot(c_minus(c_uminus(X_44,t_b),X_45,t_b))),bind(Z,$fot(c_uminus(c_plus(X_45,X_44,t_b),t_b)))]]) ).
cnf(refute_0_52,plain,
( c_minus(c_uminus(X_44,t_b),X_45,t_b) != c_uminus(c_plus(X_45,X_44,t_b),t_b)
| c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b) = c_uminus(c_plus(X_45,X_44,t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b),c_minus(c_uminus(X_44,t_b),X_45,t_b)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b) = c_uminus(c_plus(X_45,X_44,t_b),t_b),
inference(resolve,[$cnf( $equal(c_minus(c_uminus(X_44,t_b),X_45,t_b),c_uminus(c_plus(X_45,X_44,t_b),t_b)) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
( c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b) != c_uminus(c_plus(X_45,X_44,t_b),t_b)
| c_uminus(c_plus(X_44,X_45,t_b),t_b) != c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b)
| c_uminus(c_plus(X_44,X_45,t_b),t_b) = c_uminus(c_plus(X_45,X_44,t_b),t_b) ),
introduced(tautology,[equality,[$cnf( $equal(c_uminus(c_plus(X_44,X_45,t_b),t_b),c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b)) ),[1],$fot(c_uminus(c_plus(X_45,X_44,t_b),t_b))]]) ).
cnf(refute_0_55,plain,
( c_uminus(c_plus(X_44,X_45,t_b),t_b) != c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b)
| c_uminus(c_plus(X_44,X_45,t_b),t_b) = c_uminus(c_plus(X_45,X_44,t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b),c_uminus(c_plus(X_45,X_44,t_b),t_b)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
c_uminus(c_plus(X_44,X_45,t_b),t_b) = c_uminus(c_plus(X_45,X_44,t_b),t_b),
inference(resolve,[$cnf( $equal(c_uminus(c_plus(X_44,X_45,t_b),t_b),c_plus(c_uminus(X_44,t_b),c_uminus(X_45,t_b),t_b)) )],[refute_0_26,refute_0_55]) ).
cnf(refute_0_57,plain,
c_uminus(c_plus(X_46,X_47,t_b),t_b) = c_uminus(c_plus(X_47,X_46,t_b),t_b),
inference(subst,[],[refute_0_56:[bind(X_44,$fot(X_46)),bind(X_45,$fot(X_47))]]) ).
cnf(refute_0_58,plain,
( c_uminus(c_plus(X_46,X_47,t_b),t_b) != c_uminus(c_plus(X_47,X_46,t_b),t_b)
| c_uminus(c_uminus(c_plus(X_46,X_47,t_b),t_b),t_b) != c_plus(X_46,X_47,t_b)
| c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b) = c_plus(X_46,X_47,t_b) ),
introduced(tautology,[equality,[$cnf( $equal(c_uminus(c_uminus(c_plus(X_46,X_47,t_b),t_b),t_b),c_plus(X_46,X_47,t_b)) ),[0,0],$fot(c_uminus(c_plus(X_47,X_46,t_b),t_b))]]) ).
cnf(refute_0_59,plain,
( c_uminus(c_uminus(c_plus(X_46,X_47,t_b),t_b),t_b) != c_plus(X_46,X_47,t_b)
| c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b) = c_plus(X_46,X_47,t_b) ),
inference(resolve,[$cnf( $equal(c_uminus(c_plus(X_46,X_47,t_b),t_b),c_uminus(c_plus(X_47,X_46,t_b),t_b)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b) = c_plus(X_46,X_47,t_b),
inference(resolve,[$cnf( $equal(c_uminus(c_uminus(c_plus(X_46,X_47,t_b),t_b),t_b),c_plus(X_46,X_47,t_b)) )],[refute_0_24,refute_0_59]) ).
cnf(refute_0_61,plain,
c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b) = c_plus(X_47,X_46,t_b),
inference(subst,[],[refute_0_23:[bind(X_7,$fot(c_plus(X_47,X_46,t_b)))]]) ).
cnf(refute_0_62,plain,
( c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b) != c_plus(X_46,X_47,t_b)
| c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b) != c_plus(X_47,X_46,t_b)
| c_plus(X_47,X_46,t_b) = c_plus(X_46,X_47,t_b) ),
introduced(tautology,[equality,[$cnf( $equal(c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b),c_plus(X_46,X_47,t_b)) ),[0],$fot(c_plus(X_47,X_46,t_b))]]) ).
cnf(refute_0_63,plain,
( c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b) != c_plus(X_46,X_47,t_b)
| c_plus(X_47,X_46,t_b) = c_plus(X_46,X_47,t_b) ),
inference(resolve,[$cnf( $equal(c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b),c_plus(X_47,X_46,t_b)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
c_plus(X_47,X_46,t_b) = c_plus(X_46,X_47,t_b),
inference(resolve,[$cnf( $equal(c_uminus(c_uminus(c_plus(X_47,X_46,t_b),t_b),t_b),c_plus(X_46,X_47,t_b)) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( c_plus(X_47,X_46,t_b) != c_plus(X_46,X_47,t_b)
| c_plus(X_46,X_47,t_b) = c_plus(X_47,X_46,t_b) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(c_plus(X_47,X_46,t_b))),bind(Y,$fot(c_plus(X_46,X_47,t_b)))]]) ).
cnf(refute_0_66,plain,
c_plus(X_46,X_47,t_b) = c_plus(X_47,X_46,t_b),
inference(resolve,[$cnf( $equal(c_plus(X_47,X_46,t_b),c_plus(X_46,X_47,t_b)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b) = c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
inference(subst,[],[refute_0_66:[bind(X_46,$fot(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b))),bind(X_47,$fot(v_g(V_U)))]]) ).
cnf(refute_0_68,plain,
( c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b) != c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)
| ~ c_lessequals(v_f(V_U),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b),t_b)
| c_lessequals(v_f(V_U),c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( c_lessequals(v_f(V_U),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b),t_b) ),[1],$fot(c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b))]]) ).
cnf(refute_0_69,plain,
( ~ c_lessequals(v_f(V_U),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b),t_b)
| c_lessequals(v_f(V_U),c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b),c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(v_f(V_U),c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(v_f(V_U),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),v_g(V_U),t_b),t_b) )],[refute_0_19,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(subst,[],[clsrel_OrderedGroup_Olordered__ab__group__abs_1:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_72,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_9,refute_0_71]) ).
cnf(refute_0_73,plain,
c_lessequals(v_f(V_U),c_plus(v_g(V_U),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Opordered__ab__group__add(t_b) )],[refute_0_72,refute_0_70]) ).
cnf(refute_0_74,plain,
c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b),
inference(subst,[],[refute_0_73:[bind(V_U,$fot(v_x(v_c)))]]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( c_lessequals(v_f(v_x(v_c)),c_plus(v_g(v_x(v_c)),c_times(v_c,c_HOL_Oabs(v_h(v_x(v_c)),t_b),t_b),t_b),t_b) )],[refute_0_74,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 05:59:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 62.14/62.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.14/62.39
% 62.14/62.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 62.14/62.39
%------------------------------------------------------------------------------