TSTP Solution File: ANA009-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 19:28:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 7 unt; 0 nHn; 13 RR)
% Number of literals : 23 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u)
| ~ c_lessequals(v,w,u)
| c_lessequals(c_plus(v,x,u),c_plus(w,x,u),u) ),
file('ANA009-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_plus(v,c_uminus(v,u),u),c_0) ),
file('ANA009-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u) ),
file('ANA009-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__group__add(u) ),
file('ANA009-2.p',unknown),
[] ).
cnf(5,axiom,
c_lessequals(v_lb(u),v(u),t_b),
file('ANA009-2.p',unknown),
[] ).
cnf(6,axiom,
~ c_lessequals(c_0,c_plus(v(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('ANA009-2.p',unknown),
[] ).
cnf(7,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA009-2.p',unknown),
[] ).
cnf(8,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(res,[status(thm),theory(equality)],[7,3]),
[iquote('0:Res:7.0,3.0')] ).
cnf(9,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(res,[status(thm),theory(equality)],[7,4]),
[iquote('0:Res:7.0,4.0')] ).
cnf(13,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u)
| ~ c_lessequals(v,w,u)
| c_lessequals(c_0,c_plus(w,c_uminus(v,u),u),u) ),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.1,1.2')] ).
cnf(15,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(v_lb(v_x),v(v_x),t_b) ),
inference(res,[status(thm),theory(equality)],[13,6]),
[iquote('0:Res:13.3,6.0')] ).
cnf(16,plain,
~ c_lessequals(v_lb(v_x),v(v_x),t_b),
inference(ssi,[status(thm)],[15,7,9,8]),
[iquote('0:SSi:15.1,15.0,7.0,9.0,8.0,7.0,9.0,8.0')] ).
cnf(17,plain,
$false,
inference(mrr,[status(thm)],[16,5]),
[iquote('0:MRR:16.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 04:19:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 7 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.20/0.42 SPASS allocated 75603 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.00 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 2, length 13 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : cls_OrderedGroup_Oadd__le__cancel__right_1 cls_OrderedGroup_Oright__minus_0 clsrel_Ring__and__Field_Oordered__idom_37 clsrel_Ring__and__Field_Oordered__idom_4 cls_conjecture_0 cls_conjecture_2 tfree_tcs
% 0.20/0.42
%------------------------------------------------------------------------------