TSTP Solution File: ANA019-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 19:28:46 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of clauses : 34 ( 17 unt; 1 nHn; 34 RR)
% Number of literals : 55 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_less(c_0,u,tc_nat)
| equal(c_Suc(c_minus(u,c_1,tc_nat)),u) ),
file('ANA019-2.p',unknown),
[] ).
cnf(2,axiom,
( equal(u,c_0)
| c_less(c_0,u,tc_nat) ),
file('ANA019-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| equal(c_HOL_Oabs(c_0,u),c_0) ),
file('ANA019-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(c_0,c_HOL_Oabs(v,u),u) ),
file('ANA019-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| c_lessequals(v,w,u) ),
file('ANA019-2.p',unknown),
[] ).
cnf(6,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('ANA019-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_LOrder_Ojoin__semilorder(u)
| class_Orderings_Oorder(u) ),
file('ANA019-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Ojoin__semilorder(u) ),
file('ANA019-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__semiring(u) ),
file('ANA019-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA019-2.p',unknown),
[] ).
cnf(11,axiom,
equal(v(c_0),c_0),
file('ANA019-2.p',unknown),
[] ).
cnf(12,axiom,
c_less(c_0,v_x,t_a),
file('ANA019-2.p',unknown),
[] ).
cnf(13,axiom,
c_lessequals(c_HOL_Oabs(v(c_Suc(u)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(u)),t_a),t_a),t_a),
file('ANA019-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ c_less(c_0,u,t_a)
| ~ c_lessequals(c_HOL_Oabs(v(v_xa(u)),t_a),c_times(u,c_HOL_Oabs(v_h(v_xa(u)),t_a),t_a),t_a) ),
file('ANA019-2.p',unknown),
[] ).
cnf(15,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('ANA019-2.p',unknown),
[] ).
cnf(16,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(res,[status(thm),theory(equality)],[15,8]),
[iquote('0:Res:15.0,8.0')] ).
cnf(17,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(res,[status(thm),theory(equality)],[15,9]),
[iquote('0:Res:15.0,9.0')] ).
cnf(18,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[15,10]),
[iquote('0:Res:15.0,10.0')] ).
cnf(19,plain,
~ c_lessequals(c_HOL_Oabs(v(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a),
inference(res,[status(thm),theory(equality)],[12,14]),
[iquote('0:Res:12.0,14.1')] ).
cnf(20,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_x,t_a) ),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.0,5.1')] ).
cnf(25,plain,
( ~ class_LOrder_Ojoin__semilorder(t_a)
| c_lessequals(c_0,v_x,t_a) ),
inference(sor,[status(thm)],[20,7]),
[iquote('0:SoR:20.0,7.1')] ).
cnf(26,plain,
c_lessequals(c_0,v_x,t_a),
inference(ssi,[status(thm)],[25,15,17,16,18]),
[iquote('0:SSi:25.0,15.0,17.0,16.0,18.0')] ).
cnf(31,plain,
( ~ c_less(c_0,u,tc_nat)
| c_lessequals(c_HOL_Oabs(v(u),t_a),c_times(v_x,c_HOL_Oabs(v_h(u),t_a),t_a),t_a) ),
inference(spr,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpR:1.1,13.0')] ).
cnf(36,plain,
~ c_less(c_0,v_xa(v_x),tc_nat),
inference(res,[status(thm),theory(equality)],[31,19]),
[iquote('0:Res:31.1,19.0')] ).
cnf(37,plain,
equal(v_xa(v_x),c_0),
inference(res,[status(thm),theory(equality)],[2,36]),
[iquote('0:Res:2.1,36.0')] ).
cnf(38,plain,
~ c_lessequals(c_HOL_Oabs(v(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(rew,[status(thm),theory(equality)],[37,19]),
[iquote('0:Rew:37.0,19.0')] ).
cnf(41,plain,
~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(rew,[status(thm),theory(equality)],[11,38]),
[iquote('0:Rew:11.0,38.0')] ).
cnf(51,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[3,41]),
[iquote('0:SpL:3.1,41.0')] ).
cnf(53,plain,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(ssi,[status(thm)],[51,15,17,16,18]),
[iquote('0:SSi:51.0,15.0,17.0,16.0,18.0')] ).
cnf(54,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ c_lessequals(c_0,v_x,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[6,53]),
[iquote('0:Res:6.3,53.0')] ).
cnf(57,plain,
( ~ c_lessequals(c_0,v_x,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
inference(ssi,[status(thm)],[54,15,17,16,18]),
[iquote('0:SSi:54.0,15.0,17.0,16.0,18.0')] ).
cnf(58,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a),
inference(mrr,[status(thm)],[57,26]),
[iquote('0:MRR:57.0,26.0')] ).
cnf(63,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[4,58]),
[iquote('0:Res:4.1,58.0')] ).
cnf(65,plain,
$false,
inference(ssi,[status(thm)],[63,15,17,16,18]),
[iquote('0:SSi:63.0,15.0,17.0,16.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n024.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 02:58:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 35 clauses, backtracked 0 clauses, performed 0 splits and kept 36 clauses.
% 0.19/0.41 SPASS allocated 75656 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.41 0:00:00.04 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 4, length 34 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : cls_NatBin_OSuc__pred_H_0 cls_Nat_Onot__gr0_0 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_LOrder_Ojoin__semilorder_1 clsrel_Ring__and__Field_Oordered__idom_35 clsrel_Ring__and__Field_Oordered__idom_40 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 tfree_tcs
% 0.19/0.41
%------------------------------------------------------------------------------