%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA012-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 19:28:42 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 9 unt; 1 nHn; 20 RR)
% Number of literals : 34 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| ~ equal(c_HOL_Oabs(v,u),c_0)
| equal(v,c_0) ),
file('ANA012-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Orderings_Oorder(u)
| c_lessequals(v,v,u) ),
file('ANA012-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_0)
| equal(c_times(c_HOL_Oinverse(v,u),v,u),c_1) ),
file('ANA012-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Ring__and__Field_Ofield(u) ),
file('ANA012-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA012-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__field(u)
| class_Orderings_Oorder(u) ),
file('ANA012-2.p',unknown),
[] ).
cnf(7,axiom,
~ equal(c_0,v_c),
file('ANA012-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_lessequals(c_1,c_times(u,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('ANA012-2.p',unknown),
[] ).
cnf(9,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('ANA012-2.p',unknown),
[] ).
cnf(10,plain,
class_Ring__and__Field_Ofield(t_a),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.0,4.0')] ).
cnf(11,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.0,5.0')] ).
cnf(12,plain,
class_Orderings_Oorder(t_a),
inference(res,[status(thm),theory(equality)],[9,6]),
[iquote('0:Res:9.0,6.0')] ).
cnf(14,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| ~ equal(c_HOL_Oabs(v_c,u),c_0) ),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.2,7.0')] ).
cnf(18,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(c_1,c_1,t_a)
| equal(c_HOL_Oabs(v_c,t_a),c_0) ),
inference(spl,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpL:3.2,8.0')] ).
cnf(19,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| equal(c_HOL_Oabs(v_c,t_a),c_0) ),
inference(ssi,[status(thm)],[18,9,12,11,10]),
[iquote('0:SSi:18.0,9.0,12.0,11.0,10.0')] ).
cnf(20,plain,
( ~ class_Orderings_Oorder(t_a)
| equal(c_HOL_Oabs(v_c,t_a),c_0) ),
inference(res,[status(thm),theory(equality)],[2,19]),
[iquote('0:Res:2.1,19.0')] ).
cnf(21,plain,
equal(c_HOL_Oabs(v_c,t_a),c_0),
inference(ssi,[status(thm)],[20,9,12,11,10]),
[iquote('0:SSi:20.0,9.0,12.0,11.0,10.0')] ).
cnf(24,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ equal(c_0,c_0) ),
inference(spl,[status(thm),theory(equality)],[21,14]),
[iquote('0:SpL:21.0,14.1')] ).
cnf(26,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(obv,[status(thm),theory(equality)],[24]),
[iquote('0:Obv:24.1')] ).
cnf(27,plain,
$false,
inference(ssi,[status(thm)],[26,9,12,11,10]),
[iquote('0:SSi:26.0,9.0,12.0,11.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA012-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 04:02:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 14 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.20/0.41 SPASS allocated 75607 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.04 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 3, length 20 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : cls_OrderedGroup_Oabs__eq__0_0 cls_Orderings_Oorder__class_Oaxioms__1_0 cls_Ring__and__Field_Ofield__class_Oaxioms__1_0 clsrel_Ring__and__Field_Oordered__field_0 clsrel_Ring__and__Field_Oordered__field_47 clsrel_Ring__and__Field_Oordered__field_58 cls_conjecture_0 cls_conjecture_1 tfree_tcs
% 0.20/0.41
%------------------------------------------------------------------------------