TSTP Solution File: ANA025-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA025-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 19:14:41 EDT 2022
% Result : Unsatisfiable 2.50s 2.70s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 15 unt; 4 nHn; 33 RR)
% Number of literals : 83 ( 0 equ; 39 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
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_Olinorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ) ).
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_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_conjecture_2,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_LOrder_Ojoin__semilorder(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_50,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
cnf(refute_0_0,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,$fot(t_b))]]) ).
cnf(refute_0_1,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(X_5,t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Oabs__ge__zero_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_5))]]) ).
cnf(refute_0_3,plain,
c_lessequals(c_0,c_HOL_Oabs(X_5,t_b),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
c_lessequals(c_0,c_HOL_Oabs(X_425,t_b),t_b),
inference(subst,[],[refute_0_3:[bind(X_5,$fot(X_425))]]) ).
cnf(refute_0_5,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,$fot(t_b))]]) ).
cnf(refute_0_6,plain,
class_Orderings_Olinorder(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_less(X_9,X_8,t_b)
| c_lessequals(X_8,X_9,t_b) ),
inference(subst,[],[cls_Orderings_Olinorder__not__le_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(X_8)),bind(V_y,$fot(X_9))]]) ).
cnf(refute_0_8,plain,
( c_less(X_9,X_8,t_b)
| c_lessequals(X_8,X_9,t_b) ),
inference(resolve,[$cnf( class_Orderings_Olinorder(t_b) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) ),
inference(subst,[],[refute_0_8:[bind(X_8,$fot(c_0)),bind(X_9,$fot(c_minus(v_k(v_x),v_g(v_x),t_b)))]]) ).
cnf(refute_0_10,plain,
c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(resolve,[$cnf( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) )],[refute_0_9,cls_conjecture_2]) ).
cnf(refute_0_11,plain,
( ~ c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(subst,[],[cls_Orderings_Oorder__less__imp__le_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(c_minus(v_k(v_x),v_g(v_x),t_b))),bind(V_y,$fot(c_0))]]) ).
cnf(refute_0_12,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(resolve,[$cnf( c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ class_LOrder_Ojoin__semilorder(t_b)
| class_Orderings_Oorder(t_b) ),
inference(subst,[],[clsrel_LOrder_Ojoin__semilorder_1:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_14,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| class_LOrder_Ojoin__semilorder(t_b) ),
inference(subst,[],[clsrel_OrderedGroup_Olordered__ab__group__abs_15:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_15,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[$cnf( class_LOrder_Ojoin__semilorder(t_b) )],[refute_0_15,refute_0_13]) ).
cnf(refute_0_17,plain,
c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(resolve,[$cnf( class_Orderings_Oorder(t_b) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( ~ c_lessequals(c_0,X_32,t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X_32,t_b) ),
inference(subst,[],[cls_Orderings_Oorder__class_Oorder__trans_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(c_minus(v_k(v_x),v_g(v_x),t_b))),bind(V_y,$fot(c_0)),bind(V_z,$fot(X_32))]]) ).
cnf(refute_0_19,plain,
( ~ c_lessequals(c_0,X_32,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X_32,t_b) ),
inference(resolve,[$cnf( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ c_lessequals(c_0,X_32,t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X_32,t_b) ),
inference(resolve,[$cnf( class_Orderings_Oorder(t_b) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(X_5,t_b),t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(X_5,t_b),t_b) ),
inference(subst,[],[refute_0_20:[bind(X_32,$fot(c_HOL_Oabs(X_5,t_b)))]]) ).
cnf(refute_0_22,plain,
c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(X_5,t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_0,c_HOL_Oabs(X_5,t_b),t_b) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ c_lessequals(X_128,c_HOL_Oabs(X_5,t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(X_5,t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),X_128,t_b),c_HOL_Oabs(X_5,t_b),t_b) ),
inference(subst,[],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2:[bind(T_b,$fot(t_b)),bind(V_x,$fot(c_minus(v_k(v_x),v_g(v_x),t_b))),bind(V_y,$fot(X_128)),bind(V_z,$fot(c_HOL_Oabs(X_5,t_b)))]]) ).
cnf(refute_0_24,plain,
( ~ c_lessequals(X_128,c_HOL_Oabs(X_5,t_b),t_b)
| ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),X_128,t_b),c_HOL_Oabs(X_5,t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(X_5,t_b),t_b) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ c_lessequals(X_128,c_HOL_Oabs(X_5,t_b),t_b)
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),X_128,t_b),c_HOL_Oabs(X_5,t_b),t_b) ),
inference(resolve,[$cnf( class_Orderings_Olinorder(t_b) )],[refute_0_6,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(X_425,t_b),t_b)
| c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(X_425,t_b),t_b) ),
inference(subst,[],[refute_0_25:[bind(X_128,$fot(c_0)),bind(X_5,$fot(X_425))]]) ).
cnf(refute_0_27,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(X_425,t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_0,c_HOL_Oabs(X_425,t_b),t_b) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(subst,[],[refute_0_27:[bind(X_425,$fot(c_minus(v_f(v_x),v_g(v_x),t_b)))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) )],[refute_0_28,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA025-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 06:48:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.50/2.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.50/2.70
% 2.50/2.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.50/2.70
%------------------------------------------------------------------------------