TSTP Solution File: ANA016-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA016-2 : 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 19:28:44 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 7 unt; 3 nHn; 18 RR)
% Number of literals : 34 ( 0 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Omonoid__mult(u)
| equal(c_times(c_1,v,u),v) ),
file('ANA016-2.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('ANA016-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_0)
| equal(c_times(v,c_HOL_Oinverse(v,u),u),c_1) ),
file('ANA016-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Omonoid__mult(u) ),
file('ANA016-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Osemigroup__mult(u) ),
file('ANA016-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Ring__and__Field_Ofield(u) ),
file('ANA016-2.p',unknown),
[] ).
cnf(7,axiom,
~ equal(c_0,v_c),
file('ANA016-2.p',unknown),
[] ).
cnf(8,axiom,
~ equal(c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),v_g(v_x)),
file('ANA016-2.p',unknown),
[] ).
cnf(9,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('ANA016-2.p',unknown),
[] ).
cnf(10,plain,
class_Ring__and__Field_Ofield(t_a),
inference(res,[status(thm),theory(equality)],[9,6]),
[iquote('0:Res:9.0,6.0')] ).
cnf(69,plain,
( ~ class_Ring__and__Field_Ofield(u)
| ~ class_OrderedGroup_Osemigroup__mult(u)
| equal(v,c_0)
| equal(c_times(v,c_times(c_HOL_Oinverse(v,u),w,u),u),c_times(c_1,w,u)) ),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.2,2.1')] ).
cnf(75,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_0)
| equal(c_times(v,c_times(c_HOL_Oinverse(v,u),w,u),u),c_times(c_1,w,u)) ),
inference(ssi,[status(thm)],[69,5]),
[iquote('0:SSi:69.1,5.1')] ).
cnf(84,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ equal(c_times(c_1,v_g(v_x),t_a),v_g(v_x))
| equal(c_0,v_c) ),
inference(spl,[status(thm),theory(equality)],[75,8]),
[iquote('0:SpL:75.2,8.0')] ).
cnf(85,plain,
( ~ equal(c_times(c_1,v_g(v_x),t_a),v_g(v_x))
| equal(c_0,v_c) ),
inference(ssi,[status(thm)],[84,9,10]),
[iquote('0:SSi:84.0,9.0,10.0')] ).
cnf(86,plain,
~ equal(c_times(c_1,v_g(v_x),t_a),v_g(v_x)),
inference(mrr,[status(thm)],[85,7]),
[iquote('0:MRR:85.1,7.0')] ).
cnf(93,plain,
( ~ class_OrderedGroup_Omonoid__mult(t_a)
| ~ equal(v_g(v_x),v_g(v_x)) ),
inference(spl,[status(thm),theory(equality)],[1,86]),
[iquote('0:SpL:1.1,86.0')] ).
cnf(94,plain,
~ class_OrderedGroup_Omonoid__mult(t_a),
inference(obv,[status(thm),theory(equality)],[93]),
[iquote('0:Obv:93.1')] ).
cnf(95,plain,
$false,
inference(ssi,[status(thm)],[94,4,9,10]),
[iquote('0:SSi:94.0,4.0,9.0,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA016-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 02:41:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 57 clauses, backtracked 6 clauses, performed 2 splits and kept 40 clauses.
% 0.19/0.42 SPASS allocated 75709 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.00 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 18 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0 cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0 cls_Ring__and__Field_Oright__inverse_0 clsrel_Ring__and__Field_Ofield_12 clsrel_Ring__and__Field_Ofield_21 clsrel_Ring__and__Field_Oordered__field_0 cls_conjecture_0 cls_conjecture_2 tfree_tcs
% 0.19/0.42
%------------------------------------------------------------------------------