TSTP Solution File: ANA017-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 19:14:35 EDT 2022
% Result : Unsatisfiable 0.45s 0.63s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 44 ( 20 unt; 0 nHn; 25 RR)
% Number of literals : 76 ( 19 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 67 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(V_U)),t_b),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
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_OrderedGroup_Omult__ac__1_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_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_Opordered__semiring__class_Omult__left__mono_0,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__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_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(c_times(X_41,X_42,t_b)))]]) ).
cnf(refute_0_1,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_21:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_2,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| c_times(c_times(X_38,X_39,t_b),X_40,t_b) = c_times(X_38,c_times(X_39,X_40,t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Omult__ac__1_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_38)),bind(V_b,$fot(X_39)),bind(V_c,$fot(X_40))]]) ).
cnf(refute_0_4,plain,
c_times(c_times(X_38,X_39,t_b),X_40,t_b) = c_times(X_38,c_times(X_39,X_40,t_b),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Osemigroup__mult(t_b) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b) = c_times(X_41,c_times(X_42,c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b),
inference(subst,[],[refute_0_4:[bind(X_38,$fot(X_41)),bind(X_39,$fot(X_42)),bind(X_40,$fot(c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b)))]]) ).
cnf(refute_0_6,plain,
( c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b) != c_times(X_41,c_times(X_42,c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(X_41,c_times(X_42,c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b) ),[1],$fot(c_times(X_41,c_times(X_42,c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b))]]) ).
cnf(refute_0_7,plain,
( ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(X_41,c_times(X_42,c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(X_41,c_times(X_42,c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(X_41,c_times(X_42,c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),c_times(c_times(X_41,X_42,t_b),c_HOL_Oabs(v_f(v_x(c_times(X_41,X_42,t_b))),t_b),t_b),t_b) )],[refute_0_7,refute_0_0]) ).
cnf(refute_0_9,plain,
~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),v_ca,t_b))),t_b),t_b),c_times(c_HOL_Oabs(v_c,t_b),c_times(v_ca,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),v_ca,t_b))),t_b),t_b),t_b),t_b),
inference(subst,[],[refute_0_8:[bind(X_41,$fot(c_HOL_Oabs(v_c,t_b))),bind(X_42,$fot(v_ca))]]) ).
cnf(refute_0_10,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,$fot(t_b))]]) ).
cnf(refute_0_11,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(X_6,t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Oabs__ge__zero_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_6))]]) ).
cnf(refute_0_13,plain,
c_lessequals(c_0,c_HOL_Oabs(X_6,t_b),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ c_lessequals(c_0,X_129,t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(X_129,c_HOL_Oabs(v_b(V_U),t_b),t_b),c_times(X_129,c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b),t_b) ),
inference(subst,[],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(c_HOL_Oabs(v_b(V_U),t_b))),bind(V_b,$fot(c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b))),bind(V_c,$fot(X_129))]]) ).
cnf(refute_0_15,plain,
( ~ c_lessequals(c_0,X_129,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(X_129,c_HOL_Oabs(v_b(V_U),t_b),t_b),c_times(X_129,c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b) )],[cls_conjecture_0,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_42:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_17,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ c_lessequals(c_0,X_129,t_b)
| c_lessequals(c_times(X_129,c_HOL_Oabs(v_b(V_U),t_b),t_b),c_times(X_129,c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b),t_b) ),
inference(resolve,[$cnf( class_Ring__and__Field_Opordered__semiring(t_b) )],[refute_0_17,refute_0_15]) ).
cnf(refute_0_19,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(X_6,t_b),t_b)
| c_lessequals(c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b) ),
inference(subst,[],[refute_0_18:[bind(V_U,$fot(X_167)),bind(X_129,$fot(c_HOL_Oabs(X_6,t_b)))]]) ).
cnf(refute_0_20,plain,
c_lessequals(c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_0,c_HOL_Oabs(X_6,t_b),t_b) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b) = c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b) ),
inference(subst,[],[cls_Ring__and__Field_Oabs__mult_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_9)),bind(V_b,$fot(X_10))]]) ).
cnf(refute_0_22,plain,
c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b) = c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_21]) ).
cnf(refute_0_23,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_24,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_25,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b) != c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b)
| c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b) = c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b))),bind(Y,$fot(c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b)))]]) ).
cnf(refute_0_27,plain,
c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b) = c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b),c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b) = c_HOL_Oabs(c_times(X_6,v_b(X_167),t_b),t_b),
inference(subst,[],[refute_0_27:[bind(X_10,$fot(v_b(X_167))),bind(X_9,$fot(X_6))]]) ).
cnf(refute_0_29,plain,
( c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b) != c_HOL_Oabs(c_times(X_6,v_b(X_167),t_b),t_b)
| ~ c_lessequals(c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(X_6,v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b) ),[0],$fot(c_HOL_Oabs(c_times(X_6,v_b(X_167),t_b),t_b))]]) ).
cnf(refute_0_30,plain,
( ~ c_lessequals(c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(X_6,v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b),c_HOL_Oabs(c_times(X_6,v_b(X_167),t_b),t_b)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
c_lessequals(c_HOL_Oabs(c_times(X_6,v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_times(c_HOL_Oabs(X_6,t_b),c_HOL_Oabs(v_b(X_167),t_b),t_b),c_times(c_HOL_Oabs(X_6,t_b),c_times(v_ca,c_HOL_Oabs(v_f(X_167),t_b),t_b),t_b),t_b) )],[refute_0_20,refute_0_30]) ).
cnf(refute_0_32,plain,
c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),v_ca,t_b))),t_b),t_b),c_times(c_HOL_Oabs(v_c,t_b),c_times(v_ca,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),v_ca,t_b))),t_b),t_b),t_b),t_b),
inference(subst,[],[refute_0_31:[bind(X_167,$fot(v_x(c_times(c_HOL_Oabs(v_c,t_b),v_ca,t_b)))),bind(X_6,$fot(v_c))]]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),v_ca,t_b))),t_b),t_b),c_times(c_HOL_Oabs(v_c,t_b),c_times(v_ca,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),v_ca,t_b))),t_b),t_b),t_b),t_b) )],[refute_0_32,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 04:01:28 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.45/0.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.63
% 0.45/0.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.45/0.63
%------------------------------------------------------------------------------