TSTP Solution File: ANA009-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% 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 19:14:29 EDT 2022
% Result : Unsatisfiable 0.17s 0.33s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 37 ( 5 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_lb(V_U),v_f(V_U),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
cnf(refute_0_0,plain,
( ~ c_lessequals(v_lb(V_U),v_f(V_U),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| c_lessequals(c_plus(v_lb(V_U),X_9,t_b),c_plus(v_f(V_U),X_9,t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Oadd__le__cancel__right_1:[bind(T_a,$fot(t_b)),bind(V_a,$fot(v_lb(V_U))),bind(V_b,$fot(v_f(V_U))),bind(V_c,$fot(X_9))]]) ).
cnf(refute_0_1,plain,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| c_lessequals(c_plus(v_lb(V_U),X_9,t_b),c_plus(v_f(V_U),X_9,t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(v_lb(V_U),v_f(V_U),t_b) )],[cls_conjecture_0,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_37:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_3,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_2]) ).
cnf(refute_0_4,plain,
c_lessequals(c_plus(v_lb(V_U),X_9,t_b),c_plus(v_f(V_U),X_9,t_b),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b),
inference(subst,[],[refute_0_4:[bind(V_U,$fot(X_10)),bind(X_9,$fot(c_uminus(v_lb(X_10),t_b)))]]) ).
cnf(refute_0_6,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,$fot(t_b))]]) ).
cnf(refute_0_7,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| c_plus(X_4,c_uminus(X_4,t_b),t_b) = c_0 ),
inference(subst,[],[cls_OrderedGroup_Oright__minus_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_4))]]) ).
cnf(refute_0_9,plain,
c_plus(X_4,c_uminus(X_4,t_b),t_b) = c_0,
inference(resolve,[$cnf( class_OrderedGroup_Oab__group__add(t_b) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b) = c_0,
inference(subst,[],[refute_0_9:[bind(X_4,$fot(v_lb(X_10)))]]) ).
cnf(refute_0_11,plain,
( c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b) != c_0
| ~ c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b)
| c_lessequals(c_0,c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) ),[0],$fot(c_0)]]) ).
cnf(refute_0_12,plain,
( ~ c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b)
| c_lessequals(c_0,c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_0) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
c_lessequals(c_0,c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_plus(v_lb(X_10),c_uminus(v_lb(X_10),t_b),t_b),c_plus(v_f(X_10),c_uminus(v_lb(X_10),t_b),t_b),t_b) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(subst,[],[refute_0_13:[bind(X_10,$fot(v_x))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b) )],[refute_0_14,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Fri Jul 8 04:16:42 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.33
% 0.17/0.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.17/0.33
%------------------------------------------------------------------------------