TSTP Solution File: ANA010-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA010-2 : 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 19:14:30 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 42 ( 21 unt; 0 nHn; 29 RR)
% Number of literals : 73 ( 20 equ; 36 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| c_HOL_Oabs(V_y,T_a) = V_y ) ).
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_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_conjecture_0,negated_conjecture,
c_lessequals(c_0,v_f(V_U),t_b) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(v_f(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(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(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
cnf(refute_0_0,plain,
~ c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(c_HOL_Oabs(X_12,t_b)))]]) ).
cnf(refute_0_1,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| c_HOL_Oabs(c_times(X_9,X_10,t_b),t_b) = c_times(c_HOL_Oabs(X_9,t_b),c_HOL_Oabs(X_10,t_b),t_b) ),
inference(subst,[],[cls_Ring__and__Field_Oabs__mult_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_9)),bind(V_b,$fot(X_10))]]) ).
cnf(refute_0_2,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,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_1]) ).
cnf(refute_0_3,plain,
c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b) = c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),
inference(subst,[],[refute_0_2:[bind(X_10,$fot(v_g(v_x(c_HOL_Oabs(X_12,t_b))))),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b) != c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b)
| c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b) = c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b))),bind(Y,$fot(c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b)))]]) ).
cnf(refute_0_8,plain,
c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b) = c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b) != c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b)
| ~ c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b) ),[1],$fot(c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b))]]) ).
cnf(refute_0_10,plain,
( ~ c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b)
| c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
~ c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_HOL_Oabs(c_times(X_12,v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(v_f(v_x(c_HOL_Oabs(X_12,t_b))),c_times(c_HOL_Oabs(X_12,t_b),c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(X_12,t_b))),t_b),t_b),t_b) )],[refute_0_10,refute_0_0]) ).
cnf(refute_0_12,plain,
~ c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),t_b),
inference(subst,[],[refute_0_11:[bind(X_12,$fot(v_c))]]) ).
cnf(refute_0_13,plain,
( ~ c_lessequals(c_0,c_times(v_c,v_g(X_81),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_HOL_Oabs(c_times(v_c,v_g(X_81),t_b),t_b) = c_times(v_c,v_g(X_81),t_b) ),
inference(subst,[],[cls_OrderedGroup_Oabs__of__nonneg_0:[bind(T_a,$fot(t_b)),bind(V_y,$fot(c_times(v_c,v_g(X_81),t_b)))]]) ).
cnf(refute_0_14,plain,
c_lessequals(c_0,v_f(X_79),t_b),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(X_79))]]) ).
cnf(refute_0_15,plain,
( ~ c_lessequals(X_72,v_f(V_U),t_b)
| ~ c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(X_72,c_times(v_c,v_g(V_U),t_b),t_b) ),
inference(subst,[],[cls_Orderings_Oorder__class_Oorder__trans_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(X_72)),bind(V_y,$fot(v_f(V_U))),bind(V_z,$fot(c_times(v_c,v_g(V_U),t_b)))]]) ).
cnf(refute_0_16,plain,
( ~ c_lessequals(X_72,v_f(V_U),t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(X_72,c_times(v_c,v_g(V_U),t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b) )],[cls_conjecture_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| class_Orderings_Oorder(t_b) ),
inference(subst,[],[clsrel_OrderedGroup_Olordered__ab__group__abs_17:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_18,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,$fot(t_b))]]) ).
cnf(refute_0_19,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_18]) ).
cnf(refute_0_20,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_19,refute_0_17]) ).
cnf(refute_0_21,plain,
( ~ c_lessequals(X_72,v_f(V_U),t_b)
| c_lessequals(X_72,c_times(v_c,v_g(V_U),t_b),t_b) ),
inference(resolve,[$cnf( class_Orderings_Oorder(t_b) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
( ~ c_lessequals(c_0,v_f(X_79),t_b)
| c_lessequals(c_0,c_times(v_c,v_g(X_79),t_b),t_b) ),
inference(subst,[],[refute_0_21:[bind(V_U,$fot(X_79)),bind(X_72,$fot(c_0))]]) ).
cnf(refute_0_23,plain,
c_lessequals(c_0,c_times(v_c,v_g(X_79),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_0,v_f(X_79),t_b) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
c_lessequals(c_0,c_times(v_c,v_g(X_81),t_b),t_b),
inference(subst,[],[refute_0_23:[bind(X_79,$fot(X_81))]]) ).
cnf(refute_0_25,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_HOL_Oabs(c_times(v_c,v_g(X_81),t_b),t_b) = c_times(v_c,v_g(X_81),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_0,c_times(v_c,v_g(X_81),t_b),t_b) )],[refute_0_24,refute_0_13]) ).
cnf(refute_0_26,plain,
c_HOL_Oabs(c_times(v_c,v_g(X_81),t_b),t_b) = c_times(v_c,v_g(X_81),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Olordered__ab__group__abs(t_b) )],[refute_0_19,refute_0_25]) ).
cnf(refute_0_27,plain,
c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b) = c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),
inference(subst,[],[refute_0_26:[bind(X_81,$fot(v_x(c_HOL_Oabs(v_c,t_b))))]]) ).
cnf(refute_0_28,plain,
( c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b) != c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b)
| ~ c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b)
| c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),t_b) ),[1],$fot(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b))]]) ).
cnf(refute_0_29,plain,
( ~ c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b)
| c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
~ c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_HOL_Oabs(c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),t_b) )],[refute_0_29,refute_0_12]) ).
cnf(refute_0_31,plain,
c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(v_x(c_HOL_Oabs(v_c,t_b))))]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b) )],[refute_0_31,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 03:47:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.44
%------------------------------------------------------------------------------