TSTP Solution File: ANA034-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA034-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 19:28:57 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 34 ( 14 unt; 0 nHn; 34 RR)
% Number of literals : 76 ( 0 equ; 51 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| equal(c_times(c_HOL_Oabs(v,u),c_HOL_Oabs(w,u),u),c_HOL_Oabs(c_times(v,w,u),u)) ),
file('ANA034-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(x,y,u)
| ~ c_lessequals(c_0,w,u)
| ~ c_lessequals(c_0,x,u)
| c_lessequals(c_times(v,x,u),c_times(w,y,u),u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(u)
| ~ c_lessequals(c_0,v,u)
| ~ c_lessequals(c_0,w,u)
| c_lessequals(c_0,c_times(v,w,u),u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| c_lessequals(v,w,u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(c_0,c_HOL_Oabs(v,u),u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| class_Orderings_Oorder(u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__semiring(u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA034-2.p',unknown),
[] ).
cnf(10,axiom,
c_less(c_0,v_c,t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(11,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(12,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(13,axiom,
equal(c_times(c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v(v_x),v_g(v_x),t_b),t_b),t_b)),
file('ANA034-2.p',unknown),
[] ).
cnf(14,axiom,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(15,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA034-2.p',unknown),
[] ).
cnf(16,plain,
equal(c_times(c_HOL_Oabs(u,t_b),c_HOL_Oabs(v,t_b),t_b),c_HOL_Oabs(c_times(u,v,t_b),t_b)),
inference(res,[status(thm),theory(equality)],[15,1]),
[iquote('0:Res:15.0,1.0')] ).
cnf(17,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(res,[status(thm),theory(equality)],[15,7]),
[iquote('0:Res:15.0,7.0')] ).
cnf(18,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(res,[status(thm),theory(equality)],[15,8]),
[iquote('0:Res:15.0,8.0')] ).
cnf(19,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[15,9]),
[iquote('0:Res:15.0,9.0')] ).
cnf(20,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_c,t_b) ),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.0,4.1')] ).
cnf(26,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,v_c,t_b) ),
inference(sor,[status(thm)],[20,6]),
[iquote('0:SoR:20.0,6.1')] ).
cnf(27,plain,
c_lessequals(c_0,v_c,t_b),
inference(ssi,[status(thm)],[26,15,18,17,19]),
[iquote('0:SSi:26.0,15.0,18.0,17.0,19.0')] ).
cnf(58,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(u,t_b),v,t_b)
| ~ c_lessequals(c_HOL_Oabs(w,t_b),x,t_b)
| ~ c_lessequals(c_0,v,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(w,t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(u,w,t_b),t_b),c_times(v,x,t_b),t_b) ),
inference(spr,[status(thm),theory(equality)],[16,2]),
[iquote('0:SpR:16.0,2.5')] ).
cnf(61,plain,
( ~ c_lessequals(c_HOL_Oabs(u,t_b),v,t_b)
| ~ c_lessequals(c_HOL_Oabs(w,t_b),x,t_b)
| ~ c_lessequals(c_0,v,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(w,t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(u,w,t_b),t_b),c_times(v,x,t_b),t_b) ),
inference(ssi,[status(thm)],[58,15,18,17,19]),
[iquote('0:SSi:58.0,15.0,18.0,17.0,19.0')] ).
cnf(71,plain,
( ~ c_lessequals(c_HOL_Oabs(u,t_b),c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v,t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(u,v,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(spr,[status(thm),theory(equality)],[13,61]),
[iquote('0:SpR:13.0,61.4')] ).
cnf(270,plain,
( ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[71,14]),
[iquote('0:Res:71.4,14.0')] ).
cnf(271,plain,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(mrr,[status(thm)],[270,11,12]),
[iquote('0:MRR:270.0,270.1,11.0,12.0')] ).
cnf(272,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_0,v_c,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v(v_x),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[3,271]),
[iquote('0:Res:3.3,271.0')] ).
cnf(275,plain,
( ~ c_lessequals(c_0,v_c,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v(v_x),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(ssi,[status(thm)],[272,15,18,17,19]),
[iquote('0:SSi:272.0,15.0,18.0,17.0,19.0')] ).
cnf(276,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v(v_x),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(mrr,[status(thm)],[275,27]),
[iquote('0:MRR:275.0,27.0')] ).
cnf(277,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v(v_x),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[5,276]),
[iquote('0:Res:5.1,276.1')] ).
cnf(279,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v(v_x),t_b),t_b),
inference(ssi,[status(thm)],[277,15,18,17,19]),
[iquote('0:SSi:277.0,15.0,18.0,17.0,19.0')] ).
cnf(280,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[5,279]),
[iquote('0:Res:5.1,279.0')] ).
cnf(282,plain,
$false,
inference(ssi,[status(thm)],[280,15,18,17,19]),
[iquote('0:SSi:280.0,15.0,18.0,17.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA034-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 05:22:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 221 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.19/0.52 SPASS allocated 76262 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.02 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.08 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 7, length 34 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : cls_Ring__and__Field_Oabs__mult_0 cls_Ring__and__Field_Omult__mono_0 cls_Ring__and__Field_Omult__nonneg__nonneg_0 cls_Orderings_Oorder__less__imp__le_0 cls_OrderedGroup_Oabs__ge__zero_0 clsrel_OrderedGroup_Olordered__ab__group__abs_17 clsrel_Ring__and__Field_Oordered__idom_40 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5 tfree_tcs
% 0.19/0.52
%------------------------------------------------------------------------------