TSTP Solution File: ANA025-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA025-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 19:28:51 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 9 unt; 1 nHn; 25 RR)
% Number of literals : 54 ( 0 equ; 34 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(c_0,c_HOL_Oabs(v,u),u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Orderings_Olinorder(u)
| c_lessequals(v,w,u)
| c_less(w,v,u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Orderings_Olinorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(x,w,u)
| c_lessequals(c_Orderings_Omax(v,x,u),w,u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| c_lessequals(v,w,u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_LOrder_Ojoin__semilorder(u)
| class_Orderings_Oorder(u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| class_LOrder_Ojoin__semilorder(u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Olinorder(u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA025-2.p',unknown),
[] ).
cnf(10,axiom,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('ANA025-2.p',unknown),
[] ).
cnf(11,axiom,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v(v_x),v_g(v_x),t_b),t_b),t_b),
file('ANA025-2.p',unknown),
[] ).
cnf(12,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA025-2.p',unknown),
[] ).
cnf(13,plain,
class_Orderings_Olinorder(t_b),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.0,8.0')] ).
cnf(14,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[12,9]),
[iquote('0:Res:12.0,9.0')] ).
cnf(15,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.2,10.0')] ).
cnf(21,plain,
( ~ class_Orderings_Olinorder(t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.3,11.0')] ).
cnf(22,plain,
c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(mrr,[status(thm)],[15,13]),
[iquote('0:MRR:15.0,13.0')] ).
cnf(24,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(mrr,[status(thm)],[21,13]),
[iquote('0:MRR:21.0,13.0')] ).
cnf(37,plain,
( ~ class_Orderings_Oorder(u)
| ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.2,4.1')] ).
cnf(40,plain,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
inference(obv,[status(thm),theory(equality)],[37]),
[iquote('0:Obv:37.0')] ).
cnf(47,plain,
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_0,u,t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),u,t_b) ),
inference(res,[status(thm),theory(equality)],[22,40]),
[iquote('0:Res:22.0,40.1')] ).
cnf(49,plain,
( ~ c_lessequals(c_0,u,t_b)
| c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),u,t_b) ),
inference(ssi,[status(thm)],[47,7,6,12,14,13]),
[iquote('0:SSi:47.0,7.0,6.0,12.0,14.1,13.1')] ).
cnf(50,plain,
~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v(v_x),v_g(v_x),t_b),t_b),t_b),
inference(mrr,[status(thm)],[24,49]),
[iquote('0:MRR:24.1,49.1')] ).
cnf(54,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[1,50]),
[iquote('0:Res:1.1,50.0')] ).
cnf(57,plain,
$false,
inference(ssi,[status(thm)],[54,12,14,13]),
[iquote('0:SSi:54.0,12.0,14.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA025-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 06:39:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 33 clauses.
% 0.18/0.40 SPASS allocated 75661 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 2, length 25 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.40 Formulae used in the proof : cls_OrderedGroup_Oabs__ge__zero_0 cls_Orderings_Olinorder__not__le_0 cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2 cls_Orderings_Oorder__class_Oorder__trans_0 cls_Orderings_Oorder__less__imp__le_0 clsrel_LOrder_Ojoin__semilorder_1 clsrel_OrderedGroup_Olordered__ab__group__abs_15 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_2 cls_conjecture_3 tfree_tcs
% 0.18/0.40
%------------------------------------------------------------------------------