%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 19:14:50 EDT 2022
% Result : Unsatisfiable 0.60s 0.76s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 34 ( 14 unt; 0 nHn; 20 RR)
% Number of literals : 64 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a) ).
cnf(cls_OrderedGroup_Oabs__ge__self_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) ) ).
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__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_Ring__and__Field_Opordered__semiring__class_Omult__right__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_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a) ) ).
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_44,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(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(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),X_16,t_a)
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),X_16,t_a) ),
inference(subst,[],[cls_Orderings_Oorder__class_Oorder__trans_0:[bind(T_a,$fot(t_a)),bind(V_x,$fot(c_HOL_Oabs(v_h(V_U),t_a))),bind(V_y,$fot(c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a))),bind(V_z,$fot(X_16))]]) ).
cnf(refute_0_1,plain,
( ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),X_16,t_a)
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),X_16,t_a) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) )],[cls_conjecture_0,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_44:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_3,plain,
class_Orderings_Oorder(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_a) )],[tfree_tcs,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),X_16,t_a)
| c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),X_16,t_a) ),
inference(resolve,[$cnf( class_Orderings_Oorder(t_a) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
( ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) ),
inference(subst,[],[refute_0_4:[bind(X_16,$fot(c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(V_U),t_a),t_a)))]]) ).
cnf(refute_0_6,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_50:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_7,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_a) )],[tfree_tcs,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(X_8,t_a),t_a) ),
inference(subst,[],[cls_OrderedGroup_Oabs__ge__zero_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_8))]]) ).
cnf(refute_0_9,plain,
c_lessequals(c_0,c_HOL_Oabs(X_8,t_a),t_a),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_a) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(X_5,c_HOL_Oabs(X_5,t_a),t_a) ),
inference(subst,[],[cls_OrderedGroup_Oabs__ge__self_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_5))]]) ).
cnf(refute_0_11,plain,
c_lessequals(X_5,c_HOL_Oabs(X_5,t_a),t_a),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_a) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
c_lessequals(X_176,c_HOL_Oabs(X_176,t_a),t_a),
inference(subst,[],[refute_0_11:[bind(X_5,$fot(X_176))]]) ).
cnf(refute_0_13,plain,
( ~ c_lessequals(X_176,c_HOL_Oabs(X_176,t_a),t_a)
| ~ c_lessequals(c_0,X_178,t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| c_lessequals(c_times(X_176,X_178,t_a),c_times(c_HOL_Oabs(X_176,t_a),X_178,t_a),t_a) ),
inference(subst,[],[cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_176)),bind(V_b,$fot(c_HOL_Oabs(X_176,t_a))),bind(V_c,$fot(X_178))]]) ).
cnf(refute_0_14,plain,
( ~ c_lessequals(c_0,X_178,t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| c_lessequals(c_times(X_176,X_178,t_a),c_times(c_HOL_Oabs(X_176,t_a),X_178,t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(X_176,c_HOL_Oabs(X_176,t_a),t_a) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_42:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_16,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_a) )],[tfree_tcs,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ c_lessequals(c_0,X_178,t_a)
| c_lessequals(c_times(X_176,X_178,t_a),c_times(c_HOL_Oabs(X_176,t_a),X_178,t_a),t_a) ),
inference(resolve,[$cnf( class_Ring__and__Field_Opordered__semiring(t_a) )],[refute_0_16,refute_0_14]) ).
cnf(refute_0_18,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(X_8,t_a),t_a)
| c_lessequals(c_times(X_179,c_HOL_Oabs(X_8,t_a),t_a),c_times(c_HOL_Oabs(X_179,t_a),c_HOL_Oabs(X_8,t_a),t_a),t_a) ),
inference(subst,[],[refute_0_17:[bind(X_176,$fot(X_179)),bind(X_178,$fot(c_HOL_Oabs(X_8,t_a)))]]) ).
cnf(refute_0_19,plain,
c_lessequals(c_times(X_179,c_HOL_Oabs(X_8,t_a),t_a),c_times(c_HOL_Oabs(X_179,t_a),c_HOL_Oabs(X_8,t_a),t_a),t_a),
inference(resolve,[$cnf( c_lessequals(c_0,c_HOL_Oabs(X_8,t_a),t_a) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
inference(subst,[],[refute_0_19:[bind(X_179,$fot(v_c)),bind(X_8,$fot(v_f(V_U)))]]) ).
cnf(refute_0_21,plain,
c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
inference(resolve,[$cnf( c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a) )],[refute_0_20,refute_0_5]) ).
cnf(refute_0_22,plain,
c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(subst,[],[refute_0_21:[bind(V_U,$fot(v_x))]]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) )],[refute_0_22,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.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 06:00:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.76
% 0.60/0.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.76
%------------------------------------------------------------------------------