%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA023-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 19:14:40 EDT 2022
% Result : Unsatisfiable 0.60s 0.77s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 43 ( 15 unt; 0 nHn; 39 RR)
% Number of literals : 83 ( 7 equ; 41 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_plus(c_0,V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ).
cnf(clsrel_Orderings_Olinorder_4,axiom,
( ~ class_Orderings_Olinorder(T)
| class_Orderings_Oorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__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_54,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
cnf(refute_0_0,plain,
( ~ c_lessequals(c_plus(c_0,X_13,t_b),X_14,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(X_14,X_13,t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Ocompare__rls__9_1:[bind(T_a,$fot(t_b)),bind(V_a,$fot(c_0)),bind(V_b,$fot(X_13)),bind(V_c,$fot(X_14))]]) ).
cnf(refute_0_1,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Ocomm__monoid__add(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_23:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_2,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| c_plus(c_0,X_5,t_b) = X_5 ),
inference(subst,[],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0:[bind(T_a,$fot(t_b)),bind(V_y,$fot(X_5))]]) ).
cnf(refute_0_4,plain,
c_plus(c_0,X_5,t_b) = X_5,
inference(resolve,[$cnf( class_OrderedGroup_Ocomm__monoid__add(t_b) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
c_plus(c_0,X_13,t_b) = X_13,
inference(subst,[],[refute_0_4:[bind(X_5,$fot(X_13))]]) ).
cnf(refute_0_6,plain,
( c_plus(c_0,X_13,t_b) != X_13
| ~ c_lessequals(X_13,X_14,t_b)
| c_lessequals(c_plus(c_0,X_13,t_b),X_14,t_b) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_plus(c_0,X_13,t_b),X_14,t_b) ),[0],$fot(X_13)]]) ).
cnf(refute_0_7,plain,
( ~ c_lessequals(X_13,X_14,t_b)
| c_lessequals(c_plus(c_0,X_13,t_b),X_14,t_b) ),
inference(resolve,[$cnf( $equal(c_plus(c_0,X_13,t_b),X_13) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ c_lessequals(X_13,X_14,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(X_14,X_13,t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_plus(c_0,X_13,t_b),X_14,t_b) )],[refute_0_7,refute_0_0]) ).
cnf(refute_0_9,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_54:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_10,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ c_lessequals(X_13,X_14,t_b)
| c_lessequals(c_0,c_minus(X_14,X_13,t_b),t_b) ),
inference(resolve,[$cnf( class_OrderedGroup_Opordered__ab__group__add(t_b) )],[refute_0_10,refute_0_8]) ).
cnf(refute_0_12,plain,
( ~ c_lessequals(v_g(v_x),v_f(v_x),t_b)
| c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
inference(subst,[],[refute_0_11:[bind(X_13,$fot(v_g(v_x))),bind(X_14,$fot(v_f(v_x)))]]) ).
cnf(refute_0_13,plain,
( ~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) ),
inference(subst,[],[cls_OrderedGroup_Ocompare__rls__9_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(c_0)),bind(V_b,$fot(v_g(v_x))),bind(V_c,$fot(v_k(v_x)))]]) ).
cnf(refute_0_14,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) )],[cls_conjecture_1,refute_0_13]) ).
cnf(refute_0_15,plain,
c_plus(c_0,v_g(v_x),t_b) = v_g(v_x),
inference(subst,[],[refute_0_4:[bind(X_5,$fot(v_g(v_x)))]]) ).
cnf(refute_0_16,plain,
( c_plus(c_0,v_g(v_x),t_b) != v_g(v_x)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b)
| c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) ),[0],$fot(v_g(v_x))]]) ).
cnf(refute_0_17,plain,
( ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b)
| c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(resolve,[$cnf( $equal(c_plus(c_0,v_g(v_x),t_b),v_g(v_x)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Opordered__ab__group__add(t_b) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ c_lessequals(v_g(v_x),v_k(v_x),t_b)
| ~ c_lessequals(v_k(v_x),X_20,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_g(v_x),X_20,t_b) ),
inference(subst,[],[cls_Orderings_Oorder__class_Oorder__trans_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(v_g(v_x))),bind(V_y,$fot(v_k(v_x))),bind(V_z,$fot(X_20))]]) ).
cnf(refute_0_21,plain,
( ~ c_lessequals(v_k(v_x),X_20,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_g(v_x),X_20,t_b) ),
inference(resolve,[$cnf( c_lessequals(v_g(v_x),v_k(v_x),t_b) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ class_Orderings_Olinorder(t_b)
| class_Orderings_Oorder(t_b) ),
inference(subst,[],[clsrel_Orderings_Olinorder_4:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_23,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Orderings_Olinorder(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_33:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_24,plain,
class_Orderings_Olinorder(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_23]) ).
cnf(refute_0_25,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[$cnf( class_Orderings_Olinorder(t_b) )],[refute_0_24,refute_0_22]) ).
cnf(refute_0_26,plain,
( ~ c_lessequals(v_k(v_x),X_20,t_b)
| c_lessequals(v_g(v_x),X_20,t_b) ),
inference(resolve,[$cnf( class_Orderings_Oorder(t_b) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
( ~ c_lessequals(v_k(v_x),v_f(v_x),t_b)
| c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
inference(subst,[],[refute_0_26:[bind(X_20,$fot(v_f(v_x)))]]) ).
cnf(refute_0_28,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolve,[$cnf( c_lessequals(v_k(v_x),v_f(v_x),t_b) )],[cls_conjecture_2,refute_0_27]) ).
cnf(refute_0_29,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(v_g(v_x),v_f(v_x),t_b) )],[refute_0_28,refute_0_12]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) )],[refute_0_29,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA023-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 05:14:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.77
% 0.60/0.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.77
%------------------------------------------------------------------------------