TSTP Solution File: ANA020-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA020-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 19:28:47 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 25 ( 14 unt; 0 nHn; 25 RR)
% Number of literals : 40 ( 0 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 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_Olordered__ab__group__abs(u)
| equal(c_HOL_Oabs(c_0,u),c_0) ),
file('ANA020-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(c_0,c_HOL_Oabs(v,u),u) ),
file('ANA020-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| c_lessequals(v,w,u) ),
file('ANA020-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(u)
| ~ c_lessequals(c_0,v,u)
| ~ c_lessequals(c_0,w,u)
| c_lessequals(c_0,c_times(v,w,u),u) ),
file('ANA020-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__semiring(u) ),
file('ANA020-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Oorder(u) ),
file('ANA020-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA020-2.p',unknown),
[] ).
cnf(8,axiom,
equal(v(c_0),c_0),
file('ANA020-2.p',unknown),
[] ).
cnf(9,axiom,
c_less(c_0,v_c,t_a),
file('ANA020-2.p',unknown),
[] ).
cnf(10,axiom,
equal(v_x,c_0),
file('ANA020-2.p',unknown),
[] ).
cnf(11,axiom,
~ c_lessequals(c_HOL_Oabs(v(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('ANA020-2.p',unknown),
[] ).
cnf(12,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('ANA020-2.p',unknown),
[] ).
cnf(13,plain,
~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_c,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(rew,[status(thm),theory(equality)],[8,11,10]),
[iquote('0:Rew:8.0,11.0,10.0,11.0')] ).
cnf(14,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.0,5.0')] ).
cnf(15,plain,
class_Orderings_Oorder(t_a),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.0,6.0')] ).
cnf(16,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(17,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a) ),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.0,3.1')] ).
cnf(19,plain,
c_lessequals(c_0,v_c,t_a),
inference(mrr,[status(thm)],[17,15]),
[iquote('0:MRR:17.0,15.0')] ).
cnf(26,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpL:1.1,13.0')] ).
cnf(28,plain,
~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(ssi,[status(thm)],[26,12,15,14,16]),
[iquote('0:SSi:26.0,12.0,15.0,14.0,16.0')] ).
cnf(32,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ c_lessequals(c_0,v_c,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[4,28]),
[iquote('0:Res:4.3,28.0')] ).
cnf(33,plain,
( ~ c_lessequals(c_0,v_c,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
inference(ssi,[status(thm)],[32,12,15,14,16]),
[iquote('0:SSi:32.0,12.0,15.0,14.0,16.0')] ).
cnf(34,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a),
inference(mrr,[status(thm)],[33,19]),
[iquote('0:MRR:33.0,19.0')] ).
cnf(35,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[2,34]),
[iquote('0:Res:2.1,34.0')] ).
cnf(37,plain,
$false,
inference(ssi,[status(thm)],[35,12,15,14,16]),
[iquote('0:SSi:35.0,12.0,15.0,14.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA020-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 06:11:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 16 clauses, backtracked 0 clauses, performed 0 splits and kept 23 clauses.
% 0.19/0.40 SPASS allocated 75619 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.03 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 3, length 25 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : cls_OrderedGroup_Oabs__eq__0_1 cls_OrderedGroup_Oabs__ge__zero_0 cls_Orderings_Oorder__less__imp__le_0 cls_Ring__and__Field_Omult__nonneg__nonneg_0 clsrel_Ring__and__Field_Oordered__idom_40 clsrel_Ring__and__Field_Oordered__idom_44 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 cls_conjecture_3 cls_conjecture_4 tfree_tcs
% 0.19/0.40
%------------------------------------------------------------------------------