TSTP Solution File: ANA018-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA018-2 : 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 19:14:36 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 43 ( 18 unt; 0 nHn; 35 RR)
% Number of literals : 81 ( 5 equ; 40 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b) ).
cnf(cls_conjecture_2,negated_conjecture,
c_less(c_0,v_ca,t_b) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) ).
cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,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_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_Ring__and__Field_Opordered__semiring__class_Omult__left__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_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_LOrder_Ojoin__semilorder(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ) ).
cnf(refute_0_0,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_21:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_1,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| c_times(c_times(X_12,X_13,t_b),X_14,t_b) = c_times(X_12,c_times(X_13,X_14,t_b),t_b) ),
inference(subst,[],[cls_OrderedGroup_Omult__ac__1_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_12)),bind(V_b,$fot(X_13)),bind(V_c,$fot(X_14))]]) ).
cnf(refute_0_3,plain,
c_times(c_times(X_12,X_13,t_b),X_14,t_b) = c_times(X_12,c_times(X_13,X_14,t_b),t_b),
inference(resolve,[$cnf( class_OrderedGroup_Osemigroup__mult(t_b) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b) = c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(subst,[],[refute_0_3:[bind(X_12,$fot(v_ca)),bind(X_13,$fot(v_c)),bind(X_14,$fot(c_HOL_Oabs(v_g(v_xa),t_b)))]]) ).
cnf(refute_0_5,plain,
( c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b) != c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) ),[1],$fot(c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b))]]) ).
cnf(refute_0_6,plain,
( ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) ),
inference(resolve,[$cnf( $equal(c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b) )],[refute_0_6,cls_conjecture_4]) ).
cnf(refute_0_8,plain,
( ~ c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b)
| ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),X_21,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),X_21,t_b) ),
inference(subst,[],[cls_Orderings_Oorder__class_Oorder__trans_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(c_HOL_Oabs(v_x(V_U),t_b))),bind(V_y,$fot(c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b))),bind(V_z,$fot(X_21))]]) ).
cnf(refute_0_9,plain,
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),X_21,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),X_21,t_b) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b) )],[cls_conjecture_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ class_LOrder_Ojoin__semilorder(t_b)
| class_Orderings_Oorder(t_b) ),
inference(subst,[],[clsrel_LOrder_Ojoin__semilorder_1:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_11,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_LOrder_Ojoin__semilorder(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_35:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_12,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_11]) ).
cnf(refute_0_13,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[$cnf( class_LOrder_Ojoin__semilorder(t_b) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),X_21,t_b)
| c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),X_21,t_b) ),
inference(resolve,[$cnf( class_Orderings_Oorder(t_b) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X_42),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X_42),t_b),t_b),t_b),t_b)
| c_lessequals(c_HOL_Oabs(v_x(X_42),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X_42),t_b),t_b),t_b),t_b) ),
inference(subst,[],[refute_0_14:[bind(V_U,$fot(X_42)),bind(X_21,$fot(c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X_42),t_b),t_b),t_b)))]]) ).
cnf(refute_0_16,plain,
( ~ c_less(c_0,v_ca,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_ca,t_b) ),
inference(subst,[],[cls_Orderings_Oorder__less__imp__le_0:[bind(T_a,$fot(t_b)),bind(V_x,$fot(c_0)),bind(V_y,$fot(v_ca))]]) ).
cnf(refute_0_17,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_ca,t_b) ),
inference(resolve,[$cnf( c_less(c_0,v_ca,t_b) )],[cls_conjecture_2,refute_0_16]) ).
cnf(refute_0_18,plain,
c_lessequals(c_0,v_ca,t_b),
inference(resolve,[$cnf( class_Orderings_Oorder(t_b) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ c_lessequals(X_34,X_35,t_b)
| ~ c_lessequals(c_0,v_ca,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(v_ca,X_34,t_b),c_times(v_ca,X_35,t_b),t_b) ),
inference(subst,[],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0:[bind(T_a,$fot(t_b)),bind(V_a,$fot(X_34)),bind(V_b,$fot(X_35)),bind(V_c,$fot(v_ca))]]) ).
cnf(refute_0_20,plain,
( ~ c_lessequals(X_34,X_35,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(v_ca,X_34,t_b),c_times(v_ca,X_35,t_b),t_b) ),
inference(resolve,[$cnf( c_lessequals(c_0,v_ca,t_b) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__idom_42:[bind(T,$fot(t_b))]]) ).
cnf(refute_0_22,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__idom(t_b) )],[tfree_tcs,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ c_lessequals(X_34,X_35,t_b)
| c_lessequals(c_times(v_ca,X_34,t_b),c_times(v_ca,X_35,t_b),t_b) ),
inference(resolve,[$cnf( class_Ring__and__Field_Opordered__semiring(t_b) )],[refute_0_22,refute_0_20]) ).
cnf(refute_0_24,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b)
| c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),t_b) ),
inference(subst,[],[refute_0_23:[bind(X_34,$fot(c_HOL_Oabs(v_f(V_U),t_b))),bind(X_35,$fot(c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b)))]]) ).
cnf(refute_0_25,plain,
c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b) )],[cls_conjecture_1,refute_0_24]) ).
cnf(refute_0_26,plain,
c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X_42),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X_42),t_b),t_b),t_b),t_b),
inference(subst,[],[refute_0_25:[bind(V_U,$fot(X_42))]]) ).
cnf(refute_0_27,plain,
c_lessequals(c_HOL_Oabs(v_x(X_42),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X_42),t_b),t_b),t_b),t_b),
inference(resolve,[$cnf( c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(X_42),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(X_42),t_b),t_b),t_b),t_b) )],[refute_0_26,refute_0_15]) ).
cnf(refute_0_28,plain,
c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(subst,[],[refute_0_27:[bind(X_42,$fot(v_xa))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b) )],[refute_0_28,refute_0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ANA018-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 03:00:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------