TSTP Solution File: ANA034-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA034-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 19:28:56 EDT 2022
% Result : Unsatisfiable 0.45s 0.63s
% Output : Refutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 11 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq2(u,u,v,w),v),
file('ANA034-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(u,u,v,w),v),
file('ANA034-10.p',unknown),
[] ).
cnf(3,axiom,
equal(ifeq2(class_Ring__and__Field_Oordered__idom(u),true__dfg,c_times(c_HOL_Oabs(v,u),c_HOL_Oabs(w,u),u),c_HOL_Oabs(c_times(v,w,u),u)),c_HOL_Oabs(c_times(v,w,u),u)),
file('ANA034-10.p',unknown),
[] ).
cnf(4,axiom,
equal(ifeq(c_lessequals(c_0,u,v),true__dfg,ifeq(c_lessequals(c_0,w,v),true__dfg,ifeq(c_lessequals(x,u,v),true__dfg,ifeq(c_lessequals(w,y,v),true__dfg,ifeq(class_Ring__and__Field_Opordered__semiring(v),true__dfg,c_lessequals(c_times(x,w,v),c_times(u,y,v),v),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(5,axiom,
equal(ifeq(class_Ring__and__Field_Opordered__cancel__semiring(u),true__dfg,ifeq(c_lessequals(c_0,v,u),true__dfg,ifeq(c_lessequals(c_0,w,u),true__dfg,c_lessequals(c_0,c_times(v,w,u),u),true__dfg),true__dfg),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(6,axiom,
equal(ifeq(c_less(u,v,w),true__dfg,ifeq(class_Orderings_Oorder(w),true__dfg,c_lessequals(u,v,w),true__dfg),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(7,axiom,
equal(ifeq(class_OrderedGroup_Olordered__ab__group__abs(u),true__dfg,c_lessequals(c_0,c_HOL_Oabs(v,u),u),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(8,axiom,
equal(ifeq(class_OrderedGroup_Olordered__ab__group__abs(u),true__dfg,class_Orderings_Oorder(u),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(9,axiom,
equal(ifeq(class_Ring__and__Field_Oordered__idom(u),true__dfg,class_Ring__and__Field_Opordered__cancel__semiring(u),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(10,axiom,
equal(ifeq(class_Ring__and__Field_Oordered__idom(u),true__dfg,class_Ring__and__Field_Opordered__semiring(u),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(11,axiom,
equal(ifeq(class_Ring__and__Field_Oordered__idom(u),true__dfg,class_OrderedGroup_Olordered__ab__group__abs(u),true__dfg),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(12,axiom,
equal(c_less(c_0,v_c,t_b),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(13,axiom,
equal(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),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(14,axiom,
equal(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),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(15,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('ANA034-10.p',unknown),
[] ).
cnf(16,axiom,
~ equal(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),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(17,axiom,
equal(class_Ring__and__Field_Oordered__idom(t_b),true__dfg),
file('ANA034-10.p',unknown),
[] ).
cnf(23,plain,
equal(ifeq(true__dfg,true__dfg,class_OrderedGroup_Olordered__ab__group__abs(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.0,11.0')] ).
cnf(24,plain,
equal(class_OrderedGroup_Olordered__ab__group__abs(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,23]),
[iquote('0:Rew:2.0,23.0')] ).
cnf(29,plain,
equal(ifeq(true__dfg,true__dfg,class_Ring__and__Field_Opordered__semiring(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[17,10]),
[iquote('0:SpR:17.0,10.0')] ).
cnf(30,plain,
equal(class_Ring__and__Field_Opordered__semiring(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,29]),
[iquote('0:Rew:2.0,29.0')] ).
cnf(35,plain,
equal(ifeq(true__dfg,true__dfg,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[17,9]),
[iquote('0:SpR:17.0,9.0')] ).
cnf(36,plain,
equal(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,35]),
[iquote('0:Rew:2.0,35.0')] ).
cnf(38,plain,
equal(ifeq(true__dfg,true__dfg,class_Orderings_Oorder(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[24,8]),
[iquote('0:SpR:24.0,8.0')] ).
cnf(39,plain,
equal(class_Orderings_Oorder(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,38]),
[iquote('0:Rew:2.0,38.0')] ).
cnf(47,plain,
equal(ifeq(true__dfg,true__dfg,c_lessequals(c_0,c_HOL_Oabs(u,t_b),t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[24,7]),
[iquote('0:SpR:24.0,7.0')] ).
cnf(48,plain,
equal(c_lessequals(c_0,c_HOL_Oabs(u,t_b),t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,47]),
[iquote('0:Rew:2.0,47.0')] ).
cnf(59,plain,
equal(ifeq(true__dfg,true__dfg,ifeq(class_Orderings_Oorder(t_b),true__dfg,c_lessequals(c_0,v_c,t_b),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[12,6]),
[iquote('0:SpR:12.0,6.0')] ).
cnf(60,plain,
equal(c_lessequals(c_0,v_c,t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,59,39]),
[iquote('0:Rew:2.0,59.0,2.0,59.0,39.0,59.0')] ).
cnf(70,plain,
equal(ifeq2(true__dfg,true__dfg,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)),c_HOL_Oabs(c_times(u,v,t_b),t_b)),
inference(spr,[status(thm),theory(equality)],[17,3]),
[iquote('0:SpR:17.0,3.0')] ).
cnf(71,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(rew,[status(thm),theory(equality)],[1,70]),
[iquote('0:Rew:1.0,70.0')] ).
cnf(92,plain,
equal(ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true__dfg,ifeq(true__dfg,true__dfg,ifeq(c_lessequals(c_0,u,t_b),true__dfg,c_lessequals(c_0,c_times(v_c,u,t_b),t_b),true__dfg),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[60,5]),
[iquote('0:SpR:60.0,5.0')] ).
cnf(94,plain,
equal(ifeq(c_lessequals(c_0,u,t_b),true__dfg,c_lessequals(c_0,c_times(v_c,u,t_b),t_b),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,92,36]),
[iquote('0:Rew:2.0,92.0,36.0,92.0,2.0,92.0')] ).
cnf(102,plain,
equal(ifeq(true__dfg,true__dfg,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(u,t_b),t_b),t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[48,94]),
[iquote('0:SpR:48.0,94.0')] ).
cnf(106,plain,
equal(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(u,t_b),t_b),t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,102]),
[iquote('0:Rew:2.0,102.0')] ).
cnf(190,plain,
equal(ifeq(c_lessequals(c_0,u,t_b),true__dfg,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true__dfg,ifeq(c_lessequals(v,u,t_b),true__dfg,ifeq(true__dfg,true__dfg,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true__dfg,c_lessequals(c_times(v,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(u,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[14,4]),
[iquote('0:SpR:14.0,4.0')] ).
cnf(247,plain,
equal(ifeq(c_lessequals(c_0,u,t_b),true__dfg,ifeq(c_lessequals(v,u,t_b),true__dfg,c_lessequals(c_times(v,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(u,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true__dfg),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,190,48,30]),
[iquote('0:Rew:2.0,190.0,48.0,190.0,2.0,190.0,2.0,190.0,30.0,190.0')] ).
cnf(545,plain,
equal(ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v(v_x),t_b),t_b),t_b),true__dfg,ifeq(true__dfg,true__dfg,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),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),t_b),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[13,247]),
[iquote('0:SpR:13.0,247.0')] ).
cnf(589,plain,
equal(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),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,545,106,71,15]),
[iquote('0:Rew:2.0,545.0,106.0,545.0,2.0,545.0,71.0,545.0,15.0,545.0')] ).
cnf(590,plain,
$false,
inference(mrr,[status(thm)],[589,16]),
[iquote('0:MRR:589.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA034-10 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 03:44:14 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.45/0.63
% 0.45/0.63 SPASS V 3.9
% 0.45/0.63 SPASS beiseite: Proof found.
% 0.45/0.63 % SZS status Theorem
% 0.45/0.63 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.63 SPASS derived 329 clauses, backtracked 0 clauses, performed 0 splits and kept 238 clauses.
% 0.45/0.63 SPASS allocated 64892 KBytes.
% 0.45/0.63 SPASS spent 0:00:00.26 on the problem.
% 0.45/0.63 0:00:00.04 for the input.
% 0.45/0.63 0:00:00.00 for the FLOTTER CNF translation.
% 0.45/0.63 0:00:00.01 for inferences.
% 0.45/0.63 0:00:00.00 for the backtracking.
% 0.45/0.63 0:00:00.18 for the reduction.
% 0.45/0.63
% 0.45/0.63
% 0.45/0.63 Here is a proof with depth 3, length 40 :
% 0.45/0.63 % SZS output start Refutation
% See solution above
% 0.45/0.63 Formulae used in the proof : ifeq_axiom ifeq_axiom_001 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
% 0.45/0.63
%------------------------------------------------------------------------------