TSTP Solution File: ANA019-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 19:14:36 EDT 2022
% Result : Unsatisfiable 3.46s 3.65s
% Output : CNFRefutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 26
% Syntax : Number of clauses : 84 ( 24 unt; 13 nHn; 67 RR)
% Number of literals : 164 ( 72 equ; 72 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
v_f(c_0) = c_0 ).
cnf(cls_conjecture_1,negated_conjecture,
c_less(c_0,v_x,t_a) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U)),t_a),c_times(V_U,c_HOL_Oabs(v_h(v_xa(V_U)),t_a),t_a),t_a)
| ~ c_less(c_0,V_U,t_a) ) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a) ).
cnf(cls_NatBin_OSuc__pred_H_0,axiom,
( ~ c_less(c_0,V_x,tc_nat)
| V_x = c_Suc(c_minus(V_x,c_1,tc_nat)) ) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( c_less(c_0,V_n,tc_nat)
| V_n = c_0 ) ).
cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(c_0,T_a) = c_0 ) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_LOrder_Ojoin__semilorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(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_less(c_0,v_x,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a) ),
inference(subst,[],[cls_conjecture_3:[bind(V_U,$fot(v_x))]]) ).
cnf(refute_0_1,plain,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),t_a),t_a),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(c_minus(X_8,c_1,tc_nat)))]]) ).
cnf(refute_0_2,plain,
( X_7 = c_0
| c_less(c_0,X_7,tc_nat) ),
inference(subst,[],[cls_Nat_Onot__gr0_0:[bind(V_n,$fot(X_7))]]) ).
cnf(refute_0_3,plain,
( ~ c_less(c_0,X_7,tc_nat)
| X_7 = c_Suc(c_minus(X_7,c_1,tc_nat)) ),
inference(subst,[],[cls_NatBin_OSuc__pred_H_0:[bind(V_x,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
( X_7 = c_0
| X_7 = c_Suc(c_minus(X_7,c_1,tc_nat)) ),
inference(resolve,[$cnf( c_less(c_0,X_7,tc_nat) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( X_8 = c_0
| X_8 = c_Suc(c_minus(X_8,c_1,tc_nat)) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(X_8))]]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( X_8 != c_Suc(c_minus(X_8,c_1,tc_nat))
| c_Suc(c_minus(X_8,c_1,tc_nat)) = X_8 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_8)),bind(Y,$fot(c_Suc(c_minus(X_8,c_1,tc_nat))))]]) ).
cnf(refute_0_10,plain,
( X_8 = c_0
| c_Suc(c_minus(X_8,c_1,tc_nat)) = X_8 ),
inference(resolve,[$cnf( $equal(X_8,c_Suc(c_minus(X_8,c_1,tc_nat))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( c_Suc(c_minus(X_8,c_1,tc_nat)) != X_8
| ~ c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_8),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),t_a),t_a) ),[1,1,0,0],$fot(X_8)]]) ).
cnf(refute_0_12,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),t_a),t_a)
| X_8 = c_0
| c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_8),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_Suc(c_minus(X_8,c_1,tc_nat)),X_8) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( X_8 = c_0
| c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_8),t_a),t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(c_minus(X_8,c_1,tc_nat))),t_a),t_a),t_a) )],[refute_0_1,refute_0_12]) ).
cnf(refute_0_14,plain,
( X_13 = c_0
| c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_13,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a) ),
inference(subst,[],[refute_0_13:[bind(X_8,$fot(X_13))]]) ).
cnf(refute_0_15,plain,
( X_13 = c_0
| X_13 = c_Suc(c_minus(X_13,c_1,tc_nat)) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(X_13))]]) ).
cnf(refute_0_16,plain,
( X_13 != c_Suc(c_minus(X_13,c_1,tc_nat))
| c_Suc(c_minus(X_13,c_1,tc_nat)) = X_13 ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_13)),bind(Y,$fot(c_Suc(c_minus(X_13,c_1,tc_nat))))]]) ).
cnf(refute_0_17,plain,
( X_13 = c_0
| c_Suc(c_minus(X_13,c_1,tc_nat)) = X_13 ),
inference(resolve,[$cnf( $equal(X_13,c_Suc(c_minus(X_13,c_1,tc_nat))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( c_Suc(c_minus(X_13,c_1,tc_nat)) != X_13
| ~ c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_13,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(X_13),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_13,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a) ),[0,0,0],$fot(X_13)]]) ).
cnf(refute_0_19,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_13,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a)
| X_13 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X_13),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_Suc(c_minus(X_13,c_1,tc_nat)),X_13) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( X_13 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X_13),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_13,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X_13),t_a),t_a),t_a) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
( v_xa(v_x) = c_0
| c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a) ),
inference(subst,[],[refute_0_20:[bind(X_13,$fot(v_xa(v_x)))]]) ).
cnf(refute_0_22,plain,
( ~ c_less(c_0,v_x,t_a)
| v_xa(v_x) = c_0 ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a) )],[refute_0_21,refute_0_0]) ).
cnf(refute_0_23,plain,
v_xa(v_x) = c_0,
inference(resolve,[$cnf( c_less(c_0,v_x,t_a) )],[cls_conjecture_1,refute_0_22]) ).
cnf(refute_0_24,plain,
( v_xa(v_x) != c_0
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a) ),[1,1,0,0],$fot(c_0)]]) ).
cnf(refute_0_25,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(v_xa(v_x),c_0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a) )],[refute_0_25,refute_0_0]) ).
cnf(refute_0_27,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_50:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_28,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_a) )],[tfree_tcs,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_HOL_Oabs(c_0,t_a) = c_0 ),
inference(subst,[],[cls_OrderedGroup_Oabs__eq__0_1:[bind(T_a,$fot(t_a))]]) ).
cnf(refute_0_30,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_a) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
v_f(v_xa(v_x)) = v_f(v_xa(v_x)),
introduced(tautology,[refl,[$fot(v_f(v_xa(v_x)))]]) ).
cnf(refute_0_32,plain,
( v_f(v_xa(v_x)) != v_f(v_xa(v_x))
| v_xa(v_x) != c_0
| v_f(v_xa(v_x)) = v_f(c_0) ),
introduced(tautology,[equality,[$cnf( $equal(v_f(v_xa(v_x)),v_f(v_xa(v_x))) ),[1,0],$fot(c_0)]]) ).
cnf(refute_0_33,plain,
( v_xa(v_x) != c_0
| v_f(v_xa(v_x)) = v_f(c_0) ),
inference(resolve,[$cnf( $equal(v_f(v_xa(v_x)),v_f(v_xa(v_x))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
v_f(v_xa(v_x)) = v_f(c_0),
inference(resolve,[$cnf( $equal(v_xa(v_x),c_0) )],[refute_0_23,refute_0_33]) ).
cnf(refute_0_35,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_8,refute_0_35]) ).
cnf(refute_0_37,plain,
( v_f(c_0) != c_0
| v_f(v_xa(v_x)) != v_f(c_0)
| v_f(v_xa(v_x)) = c_0 ),
inference(subst,[],[refute_0_36:[bind(X,$fot(v_f(v_xa(v_x)))),bind(Y,$fot(v_f(c_0))),bind(Z,$fot(c_0))]]) ).
cnf(refute_0_38,plain,
( v_f(c_0) != c_0
| v_f(v_xa(v_x)) = c_0 ),
inference(resolve,[$cnf( $equal(v_f(v_xa(v_x)),v_f(c_0)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
v_f(v_xa(v_x)) = c_0,
inference(resolve,[$cnf( $equal(v_f(c_0),c_0) )],[cls_conjecture_0,refute_0_38]) ).
cnf(refute_0_40,plain,
c_HOL_Oabs(v_f(v_xa(v_x)),t_a) = c_HOL_Oabs(v_f(v_xa(v_x)),t_a),
introduced(tautology,[refl,[$fot(c_HOL_Oabs(v_f(v_xa(v_x)),t_a))]]) ).
cnf(refute_0_41,plain,
( c_HOL_Oabs(v_f(v_xa(v_x)),t_a) != c_HOL_Oabs(v_f(v_xa(v_x)),t_a)
| v_f(v_xa(v_x)) != c_0
| c_HOL_Oabs(v_f(v_xa(v_x)),t_a) = c_HOL_Oabs(c_0,t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_HOL_Oabs(v_f(v_xa(v_x)),t_a)) ),[1,0],$fot(c_0)]]) ).
cnf(refute_0_42,plain,
( v_f(v_xa(v_x)) != c_0
| c_HOL_Oabs(v_f(v_xa(v_x)),t_a) = c_HOL_Oabs(c_0,t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_HOL_Oabs(v_f(v_xa(v_x)),t_a)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
c_HOL_Oabs(v_f(v_xa(v_x)),t_a) = c_HOL_Oabs(c_0,t_a),
inference(resolve,[$cnf( $equal(v_f(v_xa(v_x)),c_0) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( c_HOL_Oabs(c_0,t_a) != c_0
| c_HOL_Oabs(v_f(v_xa(v_x)),t_a) != c_HOL_Oabs(c_0,t_a)
| c_HOL_Oabs(v_f(v_xa(v_x)),t_a) = c_0 ),
inference(subst,[],[refute_0_36:[bind(X,$fot(c_HOL_Oabs(v_f(v_xa(v_x)),t_a))),bind(Y,$fot(c_HOL_Oabs(c_0,t_a))),bind(Z,$fot(c_0))]]) ).
cnf(refute_0_45,plain,
( c_HOL_Oabs(c_0,t_a) != c_0
| c_HOL_Oabs(v_f(v_xa(v_x)),t_a) = c_0 ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_HOL_Oabs(c_0,t_a)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
c_HOL_Oabs(v_f(v_xa(v_x)),t_a) = c_0,
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_0,t_a),c_0) )],[refute_0_30,refute_0_45]) ).
cnf(refute_0_47,plain,
( c_HOL_Oabs(v_f(v_xa(v_x)),t_a) != c_0
| ~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),[0],$fot(c_0)]]) ).
cnf(refute_0_48,plain,
( ~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_0) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) )],[refute_0_48,refute_0_26]) ).
cnf(refute_0_50,plain,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(resolve,[$cnf( c_less(c_0,v_x,t_a) )],[cls_conjecture_1,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(X_10,t_a),t_a) ),
inference(subst,[],[cls_OrderedGroup_Oabs__ge__zero_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_10))]]) ).
cnf(refute_0_52,plain,
c_lessequals(c_0,c_HOL_Oabs(X_10,t_a),t_a),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_a) )],[refute_0_28,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_x,t_a) ),
inference(subst,[],[cls_Orderings_Oorder__less__imp__le_0:[bind(T_a,$fot(t_a)),bind(V_x,$fot(c_0)),bind(V_y,$fot(v_x))]]) ).
cnf(refute_0_54,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_x,t_a) ),
inference(resolve,[$cnf( c_less(c_0,v_x,t_a) )],[cls_conjecture_1,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ class_LOrder_Ojoin__semilorder(t_a)
| class_Orderings_Oorder(t_a) ),
inference(subst,[],[clsrel_LOrder_Ojoin__semilorder_1:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_56,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_LOrder_Ojoin__semilorder(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_35:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_57,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_a) )],[tfree_tcs,refute_0_56]) ).
cnf(refute_0_58,plain,
class_Orderings_Oorder(t_a),
inference(resolve,[$cnf( class_LOrder_Ojoin__semilorder(t_a) )],[refute_0_57,refute_0_55]) ).
cnf(refute_0_59,plain,
c_lessequals(c_0,v_x,t_a),
inference(resolve,[$cnf( class_Orderings_Oorder(t_a) )],[refute_0_58,refute_0_54]) ).
cnf(refute_0_60,plain,
( ~ c_lessequals(c_0,X_29,t_a)
| ~ c_lessequals(c_0,v_x,t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| c_lessequals(c_0,c_times(v_x,X_29,t_a),t_a) ),
inference(subst,[],[cls_Ring__and__Field_Omult__nonneg__nonneg_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(v_x)),bind(V_b,$fot(X_29))]]) ).
cnf(refute_0_61,plain,
( ~ c_lessequals(c_0,X_29,t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| c_lessequals(c_0,c_times(v_x,X_29,t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(c_0,v_x,t_a) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_40:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_63,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_a) )],[tfree_tcs,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ c_lessequals(c_0,X_29,t_a)
| c_lessequals(c_0,c_times(v_x,X_29,t_a),t_a) ),
inference(resolve,[$cnf( class_Ring__and__Field_Opordered__cancel__semiring(t_a) )],[refute_0_63,refute_0_61]) ).
cnf(refute_0_65,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(X_10,t_a),t_a)
| c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(X_10,t_a),t_a),t_a) ),
inference(subst,[],[refute_0_64:[bind(X_29,$fot(c_HOL_Oabs(X_10,t_a)))]]) ).
cnf(refute_0_66,plain,
c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(X_10,t_a),t_a),t_a),
inference(resolve,[$cnf( c_lessequals(c_0,c_HOL_Oabs(X_10,t_a),t_a) )],[refute_0_52,refute_0_65]) ).
cnf(refute_0_67,plain,
c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(v_h(c_0)))]]) ).
cnf(refute_0_68,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) )],[refute_0_67,refute_0_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.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
% 0.12/0.34 % DateTime : Fri Jul 8 02:56:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.46/3.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.46/3.65
% 3.46/3.65 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.46/3.66
%------------------------------------------------------------------------------