%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA014-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 19:28:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 29 ( 12 unt; 1 nHn; 29 RR)
% Number of literals : 48 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 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('ANA014-2.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('ANA014-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Orderings_Oorder(u)
| c_lessequals(v,v,u) ),
file('ANA014-2.p',unknown),
[] ).
cnf(4,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('ANA014-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_0)
| equal(c_times(c_HOL_Oinverse(v,u),v,u),c_1) ),
file('ANA014-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Omonoid__mult(u) ),
file('ANA014-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Osemigroup__mult(u) ),
file('ANA014-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Ring__and__Field_Ofield(u) ),
file('ANA014-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Ring__and__Field_Oordered__idom(u) ),
file('ANA014-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Orderings_Oorder(u) ),
file('ANA014-2.p',unknown),
[] ).
cnf(11,axiom,
~ equal(c_0,v_c),
file('ANA014-2.p',unknown),
[] ).
cnf(12,axiom,
~ c_lessequals(c_HOL_Oabs(v(v_x(u)),t_a),c_times(u,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v(v_x(u)),t_a),t_a),t_a),t_a),
file('ANA014-2.p',unknown),
[] ).
cnf(13,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('ANA014-2.p',unknown),
[] ).
cnf(14,plain,
class_Ring__and__Field_Ofield(t_a),
inference(res,[status(thm),theory(equality)],[13,8]),
[iquote('0:Res:13.0,8.0')] ).
cnf(15,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(res,[status(thm),theory(equality)],[13,9]),
[iquote('0:Res:13.0,9.0')] ).
cnf(16,plain,
class_Orderings_Oorder(t_a),
inference(res,[status(thm),theory(equality)],[13,10]),
[iquote('0:Res:13.0,10.0')] ).
cnf(17,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_times(c_HOL_Oinverse(v_c,u),v_c,u),c_1) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.1,11.0')] ).
cnf(26,plain,
( ~ class_Ring__and__Field_Ofield(u)
| ~ class_OrderedGroup_Osemigroup__mult(u)
| equal(c_times(c_HOL_Oinverse(v_c,u),c_times(v_c,v,u),u),c_times(c_1,v,u)) ),
inference(spr,[status(thm),theory(equality)],[17,2]),
[iquote('0:SpR:17.1,2.1')] ).
cnf(29,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_times(c_HOL_Oinverse(v_c,u),c_times(v_c,v,u),u),c_times(c_1,v,u)) ),
inference(ssi,[status(thm)],[26,7]),
[iquote('0:SSi:26.1,7.1')] ).
cnf(92,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ c_lessequals(c_HOL_Oabs(v(v_x(u)),t_a),c_times(u,c_HOL_Oabs(c_times(v_c,v(v_x(u)),t_a),t_a),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[4,12]),
[iquote('0:SpL:4.1,12.0')] ).
cnf(97,plain,
~ c_lessequals(c_HOL_Oabs(v(v_x(u)),t_a),c_times(u,c_HOL_Oabs(c_times(v_c,v(v_x(u)),t_a),t_a),t_a),t_a),
inference(ssi,[status(thm)],[92,13,16,15,14]),
[iquote('0:SSi:92.0,13.0,16.0,15.0,14.0')] ).
cnf(102,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ c_lessequals(c_HOL_Oabs(v(v_x(c_HOL_Oabs(u,t_a))),t_a),c_HOL_Oabs(c_times(u,c_times(v_c,v(v_x(c_HOL_Oabs(u,t_a))),t_a),t_a),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[4,97]),
[iquote('0:SpL:4.1,97.0')] ).
cnf(105,plain,
~ c_lessequals(c_HOL_Oabs(v(v_x(c_HOL_Oabs(u,t_a))),t_a),c_HOL_Oabs(c_times(u,c_times(v_c,v(v_x(c_HOL_Oabs(u,t_a))),t_a),t_a),t_a),t_a),
inference(ssi,[status(thm)],[102,13,16,15,14]),
[iquote('0:SSi:102.0,13.0,16.0,15.0,14.0')] ).
cnf(166,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(c_HOL_Oabs(v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_1,v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[29,105]),
[iquote('0:SpL:29.1,105.0')] ).
cnf(168,plain,
~ c_lessequals(c_HOL_Oabs(v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_1,v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a),
inference(ssi,[status(thm)],[166,13,16,15,14]),
[iquote('0:SSi:166.0,13.0,16.0,15.0,14.0')] ).
cnf(340,plain,
( ~ class_OrderedGroup_Omonoid__mult(t_a)
| ~ c_lessequals(c_HOL_Oabs(v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a) ),
inference(spl,[status(thm),theory(equality)],[1,168]),
[iquote('0:SpL:1.1,168.0')] ).
cnf(341,plain,
~ c_lessequals(c_HOL_Oabs(v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),
inference(ssi,[status(thm)],[340,6,13,16,15,14]),
[iquote('0:SSi:340.0,6.0,13.0,16.0,15.0,14.1')] ).
cnf(380,plain,
~ class_Orderings_Oorder(t_a),
inference(res,[status(thm),theory(equality)],[3,341]),
[iquote('0:Res:3.1,341.0')] ).
cnf(381,plain,
$false,
inference(ssi,[status(thm)],[380,13,16,15,14]),
[iquote('0:SSi:380.0,13.0,16.0,15.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA014-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.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 06:00:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 220 clauses, backtracked 13 clauses, performed 1 splits and kept 98 clauses.
% 0.19/0.45 SPASS allocated 76236 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.03 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.01 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.04 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 5, length 29 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0 cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0 cls_Orderings_Oorder__class_Oaxioms__1_0 cls_Ring__and__Field_Oabs__mult_0 cls_Ring__and__Field_Ofield__class_Oaxioms__1_0 clsrel_Ring__and__Field_Ofield_12 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_58 cls_conjecture_0 cls_conjecture_1 tfree_tcs
% 0.19/0.45
%------------------------------------------------------------------------------