%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA045-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 19:29:04 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 10 RR)
% Number of literals : 13 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 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('ANA045-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| equal(c_times(c_1,v,u),v) ),
file('ANA045-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA045-2.p',unknown),
[] ).
cnf(4,axiom,
~ c_lessequals(c_0,c_times(u,c_HOL_Oabs(v_g(v_x(u)),t_b),t_b),t_b),
file('ANA045-2.p',unknown),
[] ).
cnf(5,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA045-2.p',unknown),
[] ).
cnf(6,plain,
equal(c_times(c_1,u,t_b),u),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.0,2.0')] ).
cnf(7,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.0,3.0')] ).
cnf(11,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),
inference(spl,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpL:6.0,4.0')] ).
cnf(13,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.1,11.0')] ).
cnf(14,plain,
$false,
inference(ssi,[status(thm)],[13,5,7]),
[iquote('0:SSi:13.0,5.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ANA045-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n011.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 05:31:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.40
% 0.13/0.40 SPASS V 3.9
% 0.13/0.40 SPASS beiseite: Proof found.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40 SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.13/0.40 SPASS allocated 75592 KBytes.
% 0.13/0.40 SPASS spent 0:00:00.05 on the problem.
% 0.13/0.40 0:00:00.03 for the input.
% 0.13/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.40 0:00:00.00 for inferences.
% 0.13/0.40 0:00:00.00 for the backtracking.
% 0.13/0.40 0:00:00.00 for the reduction.
% 0.13/0.40
% 0.13/0.40
% 0.13/0.40 Here is a proof with depth 3, length 10 :
% 0.13/0.40 % SZS output start Refutation
% See solution above
% 0.13/0.40 Formulae used in the proof : cls_OrderedGroup_Oabs__ge__zero_0 cls_Ring__and__Field_Omult__cancel__right1_2 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 tfree_tcs
% 0.13/0.40
%------------------------------------------------------------------------------