TSTP Solution File: ANA023-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA023-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 19:28:49 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ifeq2(u,u,v,w),v),
file('ANA023-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ifeq(u,u,v,w),v),
file('ANA023-10.p',unknown),
[] ).
cnf(3,axiom,
equal(ifeq2(class_OrderedGroup_Ocomm__monoid__add(u),true__dfg,c_plus(c_0,v,u),v),v),
file('ANA023-10.p',unknown),
[] ).
cnf(4,axiom,
equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(u),true__dfg,ifeq(c_lessequals(v,c_minus(w,x,u),u),true__dfg,c_lessequals(c_plus(v,x,u),w,u),true__dfg),true__dfg),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(5,axiom,
equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(u),true__dfg,ifeq(c_lessequals(c_plus(v,w,u),x,u),true__dfg,c_lessequals(v,c_minus(x,w,u),u),true__dfg),true__dfg),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(6,axiom,
equal(ifeq(class_Orderings_Oorder(u),true__dfg,ifeq(c_lessequals(v,w,u),true__dfg,ifeq(c_lessequals(w,x,u),true__dfg,c_lessequals(v,x,u),true__dfg),true__dfg),true__dfg),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(7,axiom,
equal(ifeq(class_Orderings_Olinorder(u),true__dfg,class_Orderings_Oorder(u),true__dfg),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(8,axiom,
equal(ifeq(class_Ring__and__Field_Oordered__idom(u),true__dfg,class_OrderedGroup_Ocomm__monoid__add(u),true__dfg),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(9,axiom,
equal(ifeq(class_Ring__and__Field_Oordered__idom(u),true__dfg,class_Orderings_Olinorder(u),true__dfg),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(10,axiom,
equal(ifeq(class_Ring__and__Field_Oordered__idom(u),true__dfg,class_OrderedGroup_Opordered__ab__group__add(u),true__dfg),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(11,axiom,
equal(c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(12,axiom,
equal(c_lessequals(v_k(v_x),v(v_x),t_b),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(13,axiom,
~ equal(c_lessequals(c_0,c_minus(v(v_x),v_g(v_x),t_b),t_b),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(14,axiom,
equal(class_Ring__and__Field_Oordered__idom(t_b),true__dfg),
file('ANA023-10.p',unknown),
[] ).
cnf(20,plain,
equal(ifeq(true__dfg,true__dfg,class_OrderedGroup_Opordered__ab__group__add(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpR:14.0,10.0')] ).
cnf(21,plain,
equal(class_OrderedGroup_Opordered__ab__group__add(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,20]),
[iquote('0:Rew:2.0,20.0')] ).
cnf(26,plain,
equal(ifeq(true__dfg,true__dfg,class_Orderings_Olinorder(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[14,9]),
[iquote('0:SpR:14.0,9.0')] ).
cnf(27,plain,
equal(class_Orderings_Olinorder(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,26]),
[iquote('0:Rew:2.0,26.0')] ).
cnf(32,plain,
equal(ifeq(true__dfg,true__dfg,class_OrderedGroup_Ocomm__monoid__add(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[14,8]),
[iquote('0:SpR:14.0,8.0')] ).
cnf(33,plain,
equal(class_OrderedGroup_Ocomm__monoid__add(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,32]),
[iquote('0:Rew:2.0,32.0')] ).
cnf(35,plain,
equal(ifeq(true__dfg,true__dfg,class_Orderings_Oorder(t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[27,7]),
[iquote('0:SpR:27.0,7.0')] ).
cnf(36,plain,
equal(class_Orderings_Oorder(t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,35]),
[iquote('0:Rew:2.0,35.0')] ).
cnf(45,plain,
equal(ifeq2(true__dfg,true__dfg,c_plus(c_0,u,t_b),u),u),
inference(spr,[status(thm),theory(equality)],[33,3]),
[iquote('0:SpR:33.0,3.0')] ).
cnf(46,plain,
equal(c_plus(c_0,u,t_b),u),
inference(rew,[status(thm),theory(equality)],[1,45]),
[iquote('0:Rew:1.0,45.0')] ).
cnf(52,plain,
equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true__dfg,ifeq(c_lessequals(u,v,t_b),true__dfg,c_lessequals(c_0,c_minus(v,u,t_b),t_b),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[46,5]),
[iquote('0:SpR:46.0,5.0')] ).
cnf(55,plain,
equal(ifeq(c_lessequals(u,v,t_b),true__dfg,c_lessequals(c_0,c_minus(v,u,t_b),t_b),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,52,21]),
[iquote('0:Rew:2.0,52.0,21.0,52.0')] ).
cnf(66,plain,
equal(ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true__dfg,ifeq(true__dfg,true__dfg,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[11,4]),
[iquote('0:SpR:11.0,4.0')] ).
cnf(68,plain,
equal(c_lessequals(v_g(v_x),v_k(v_x),t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,66,21,46]),
[iquote('0:Rew:2.0,66.0,21.0,66.0,2.0,66.0,46.0,66.0')] ).
cnf(120,plain,
equal(ifeq(class_Orderings_Oorder(t_b),true__dfg,ifeq(true__dfg,true__dfg,ifeq(c_lessequals(v_k(v_x),u,t_b),true__dfg,c_lessequals(v_g(v_x),u,t_b),true__dfg),true__dfg),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[68,6]),
[iquote('0:SpR:68.0,6.0')] ).
cnf(123,plain,
equal(ifeq(c_lessequals(v_k(v_x),u,t_b),true__dfg,c_lessequals(v_g(v_x),u,t_b),true__dfg),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,120,36]),
[iquote('0:Rew:2.0,120.0,36.0,120.0,2.0,120.0')] ).
cnf(144,plain,
equal(ifeq(true__dfg,true__dfg,c_lessequals(v_g(v_x),v(v_x),t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[12,123]),
[iquote('0:SpR:12.0,123.0')] ).
cnf(145,plain,
equal(c_lessequals(v_g(v_x),v(v_x),t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,144]),
[iquote('0:Rew:2.0,144.0')] ).
cnf(147,plain,
equal(ifeq(true__dfg,true__dfg,c_lessequals(c_0,c_minus(v(v_x),v_g(v_x),t_b),t_b),true__dfg),true__dfg),
inference(spr,[status(thm),theory(equality)],[145,55]),
[iquote('0:SpR:145.0,55.0')] ).
cnf(154,plain,
equal(c_lessequals(c_0,c_minus(v(v_x),v_g(v_x),t_b),t_b),true__dfg),
inference(rew,[status(thm),theory(equality)],[2,147]),
[iquote('0:Rew:2.0,147.0')] ).
cnf(155,plain,
$false,
inference(mrr,[status(thm)],[154,13]),
[iquote('0:MRR:154.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA023-10 : TPTP v8.1.0. Released v7.5.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.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 05:44:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 86 clauses, backtracked 0 clauses, performed 0 splits and kept 55 clauses.
% 0.20/0.43 SPASS allocated 63357 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.43 0:00:00.04 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.02 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 4, length 35 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : ifeq_axiom ifeq_axiom_001 cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 cls_OrderedGroup_Ocompare__rls__9_0 cls_OrderedGroup_Ocompare__rls__9_1 cls_Orderings_Oorder__class_Oorder__trans_0 clsrel_Orderings_Olinorder_4 clsrel_Ring__and__Field_Oordered__idom_23 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_54 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 tfree_tcs
% 0.20/0.43
%------------------------------------------------------------------------------