TSTP Solution File: ANA015-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA015-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 19:28:44 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 24 ( 11 unt; 0 nHn; 24 RR)
% Number of literals : 44 ( 0 equ; 27 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 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(c_0,c_HOL_Oabs(v,u),u) ),
file('ANA015-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(u)
| equal(c_times(c_times(v,w,u),x,u),c_times(v,c_times(w,x,u),u)) ),
file('ANA015-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| equal(c_times(c_HOL_Oabs(v,u),c_HOL_Oabs(w,u),u),c_HOL_Oabs(c_times(v,w,u),u)) ),
file('ANA015-2.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(x,v,u),c_times(x,w,u),u) ),
file('ANA015-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Osemigroup__mult(u) ),
file('ANA015-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Ring__and__Field_Ofield(u) ),
file('ANA015-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Ring__and__Field_Oordered__idom(u) ),
file('ANA015-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA015-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA015-2.p',unknown),
[] ).
cnf(10,axiom,
c_lessequals(c_HOL_Oabs(v_g(u),t_a),c_times(v_d,c_HOL_Oabs(v(u),t_a),t_a),t_a),
file('ANA015-2.p',unknown),
[] ).
cnf(11,axiom,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(u)),t_a),t_a),c_times(u,c_HOL_Oabs(v(v_x(u)),t_a),t_a),t_a),
file('ANA015-2.p',unknown),
[] ).
cnf(12,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('ANA015-2.p',unknown),
[] ).
cnf(13,plain,
class_Ring__and__Field_Ofield(t_a),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.0,6.0')] ).
cnf(14,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(15,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.0,8.0')] ).
cnf(16,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[12,9]),
[iquote('0:Res:12.0,9.0')] ).
cnf(25,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(u,v,t_a))),t_a),t_a),c_times(u,c_times(v,c_HOL_Oabs(v(v_x(c_times(u,v,t_a))),t_a),t_a),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[2,11]),
[iquote('0:SpL:2.1,11.0')] ).
cnf(27,plain,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(u,v,t_a))),t_a),t_a),c_times(u,c_times(v,c_HOL_Oabs(v(v_x(c_times(u,v,t_a))),t_a),t_a),t_a),t_a),
inference(ssi,[status(thm)],[25,5,12,16,15,14,13]),
[iquote('0:SSi:25.0,5.0,12.0,16.0,15.0,14.0,13.1')] ).
cnf(30,plain,
( ~ class_Ring__and__Field_Oordered__idom(u)
| ~ class_Ring__and__Field_Opordered__semiring(u)
| ~ c_lessequals(c_HOL_Oabs(v,u),w,u)
| ~ c_lessequals(c_0,c_HOL_Oabs(x,u),u)
| c_lessequals(c_HOL_Oabs(c_times(x,v,u),u),c_times(c_HOL_Oabs(x,u),w,u),u) ),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.1,4.3')] ).
cnf(74,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),u,t_a))),t_a),c_times(u,c_HOL_Oabs(v(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),u,t_a))),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
inference(res,[status(thm),theory(equality)],[30,27]),
[iquote('0:Res:30.4,27.0')] ).
cnf(77,plain,
( ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),u,t_a))),t_a),c_times(u,c_HOL_Oabs(v(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),u,t_a))),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
inference(ssi,[status(thm)],[74,12,16,15,14,13]),
[iquote('0:SSi:74.1,74.0,12.0,16.0,15.0,14.0,13.0,12.0,16.0,15.0,14.0,13.0')] ).
cnf(169,plain,
~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a),
inference(res,[status(thm),theory(equality)],[10,77]),
[iquote('0:Res:10.0,77.0')] ).
cnf(170,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[1,169]),
[iquote('0:Res:1.1,169.0')] ).
cnf(171,plain,
$false,
inference(ssi,[status(thm)],[170,12,16,15,14,13]),
[iquote('0:SSi:170.0,12.0,16.0,15.0,14.0,13.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ANA015-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 06:17:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 86 clauses, backtracked 0 clauses, performed 0 splits and kept 55 clauses.
% 0.18/0.43 SPASS allocated 76127 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.01 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.02 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 4, length 24 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : cls_OrderedGroup_Oabs__ge__zero_0 cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0 cls_Ring__and__Field_Oabs__mult_0 cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 clsrel_Ring__and__Field_Ofield_21 clsrel_Ring__and__Field_Oordered__field_0 clsrel_Ring__and__Field_Oordered__field_34 clsrel_Ring__and__Field_Oordered__field_46 clsrel_Ring__and__Field_Oordered__field_47 cls_conjecture_1 cls_conjecture_2 tfree_tcs
% 0.18/0.43
%------------------------------------------------------------------------------