TSTP Solution File: ANA039-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 19:29:00 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 10 unt; 0 nHn; 22 RR)
% Number of literals : 40 ( 0 equ; 27 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 : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(v,c_HOL_Oabs(v,u),u) ),
file('ANA039-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| c_lessequals(c_0,c_HOL_Oabs(v,u),u) ),
file('ANA039-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ANA039-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(c_0,x,u)
| c_lessequals(c_times(v,x,u),c_times(w,x,u),u) ),
file('ANA039-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA039-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Oorder(u) ),
file('ANA039-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA039-2.p',unknown),
[] ).
cnf(8,axiom,
c_lessequals(c_HOL_Oabs(v_h(u),t_a),c_times(v_c,c_HOL_Oabs(v(u),t_a),t_a),t_a),
file('ANA039-2.p',unknown),
[] ).
cnf(9,axiom,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v(v_x),t_a),t_a),t_a),
file('ANA039-2.p',unknown),
[] ).
cnf(10,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('ANA039-2.p',unknown),
[] ).
cnf(11,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(res,[status(thm),theory(equality)],[10,5]),
[iquote('0:Res:10.0,5.0')] ).
cnf(12,plain,
class_Orderings_Oorder(t_a),
inference(res,[status(thm),theory(equality)],[10,6]),
[iquote('0:Res:10.0,6.0')] ).
cnf(13,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[10,7]),
[iquote('0:Res:10.0,7.0')] ).
cnf(17,plain,
( ~ class_Orderings_Oorder(t_a)
| ~ c_lessequals(u,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),u,t_a) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.3,9.0')] ).
cnf(20,plain,
( ~ c_lessequals(u,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),u,t_a) ),
inference(mrr,[status(thm)],[17,12]),
[iquote('0:MRR:17.0,12.0')] ).
cnf(21,plain,
~ c_lessequals(c_times(v_c,c_HOL_Oabs(v(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v(v_x),t_a),t_a),t_a),
inference(res,[status(thm),theory(equality)],[8,20]),
[iquote('0:Res:8.0,20.1')] ).
cnf(120,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v(v_x),t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[4,21]),
[iquote('0:Res:4.3,21.0')] ).
cnf(121,plain,
( ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v(v_x),t_a),t_a) ),
inference(ssi,[status(thm)],[120,10,12,11,13]),
[iquote('0:SSi:120.0,10.0,12.0,11.0,13.0')] ).
cnf(122,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[2,121]),
[iquote('0:Res:2.1,121.1')] ).
cnf(123,plain,
~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a),
inference(ssi,[status(thm)],[122,10,12,11,13]),
[iquote('0:SSi:122.0,10.0,12.0,11.0,13.0')] ).
cnf(124,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[1,123]),
[iquote('0:Res:1.1,123.0')] ).
cnf(125,plain,
$false,
inference(ssi,[status(thm)],[124,10,12,11,13]),
[iquote('0:SSi:124.0,10.0,12.0,11.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 06:01:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.41
% 0.12/0.41 SPASS V 3.9
% 0.12/0.41 SPASS beiseite: Proof found.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41 SPASS derived 66 clauses, backtracked 0 clauses, performed 0 splits and kept 57 clauses.
% 0.12/0.41 SPASS allocated 75754 KBytes.
% 0.12/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.41 0:00:00.04 for the input.
% 0.12/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.41 0:00:00.00 for inferences.
% 0.12/0.41 0:00:00.00 for the backtracking.
% 0.12/0.41 0:00:00.01 for the reduction.
% 0.12/0.41
% 0.12/0.41
% 0.12/0.41 Here is a proof with depth 5, length 22 :
% 0.12/0.41 % SZS output start Refutation
% See solution above
% 0.12/0.41 Formulae used in the proof : cls_OrderedGroup_Oabs__ge__self_0 cls_OrderedGroup_Oabs__ge__zero_0 cls_Orderings_Oorder__class_Oorder__trans_0 cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_44 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_2 tfree_tcs
% 0.12/0.41
%------------------------------------------------------------------------------