%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA023-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 19:28:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 27 ( 13 unt; 0 nHn; 27 RR)
% Number of literals : 46 ( 0 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(u)
| equal(c_plus(c_0,v,u),v) ),
file('ANA023-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(v,c_minus(w,x,u),u)
| c_lessequals(c_plus(v,x,u),w,u) ),
file('ANA023-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(c_plus(v,w,u),x,u)
| c_lessequals(v,c_minus(x,w,u),u) ),
file('ANA023-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ANA023-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Orderings_Olinorder(u)
| class_Orderings_Oorder(u) ),
file('ANA023-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Ocomm__monoid__add(u) ),
file('ANA023-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Olinorder(u) ),
file('ANA023-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Opordered__ab__group__add(u) ),
file('ANA023-2.p',unknown),
[] ).
cnf(9,axiom,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('ANA023-2.p',unknown),
[] ).
cnf(10,axiom,
c_lessequals(v_k(v_x),v(v_x),t_b),
file('ANA023-2.p',unknown),
[] ).
cnf(11,axiom,
~ c_lessequals(c_0,c_minus(v(v_x),v_g(v_x),t_b),t_b),
file('ANA023-2.p',unknown),
[] ).
cnf(12,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA023-2.p',unknown),
[] ).
cnf(13,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.0,6.0')] ).
cnf(14,plain,
class_Orderings_Olinorder(t_b),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(15,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.0,8.0')] ).
cnf(19,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) ),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.0,2.1')] ).
cnf(21,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v(v_x),t_b) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.2,11.0')] ).
cnf(23,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),
inference(mrr,[status(thm)],[19,15]),
[iquote('0:MRR:19.0,15.0')] ).
cnf(24,plain,
~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v(v_x),t_b),
inference(mrr,[status(thm)],[21,15]),
[iquote('0:MRR:21.0,15.0')] ).
cnf(27,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
inference(spr,[status(thm),theory(equality)],[1,23]),
[iquote('0:SpR:1.1,23.0')] ).
cnf(29,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(ssi,[status(thm)],[27,12,14,13,15]),
[iquote('0:SSi:27.0,12.0,14.0,13.0,15.0')] ).
cnf(33,plain,
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_k(v_x),u,t_b)
| c_lessequals(v_g(v_x),u,t_b) ),
inference(res,[status(thm),theory(equality)],[29,4]),
[iquote('0:Res:29.0,4.1')] ).
cnf(34,plain,
( ~ c_lessequals(v_k(v_x),u,t_b)
| c_lessequals(v_g(v_x),u,t_b) ),
inference(ssi,[status(thm)],[33,5,12,14,13,15]),
[iquote('0:SSi:33.0,5.0,12.0,14.0,13.0,15.1')] ).
cnf(36,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ c_lessequals(v_g(v_x),v(v_x),t_b) ),
inference(spl,[status(thm),theory(equality)],[1,24]),
[iquote('0:SpL:1.1,24.0')] ).
cnf(37,plain,
~ c_lessequals(v_g(v_x),v(v_x),t_b),
inference(ssi,[status(thm)],[36,12,14,13,15]),
[iquote('0:SSi:36.0,12.0,14.0,13.0,15.0')] ).
cnf(38,plain,
~ c_lessequals(v_k(v_x),v(v_x),t_b),
inference(res,[status(thm),theory(equality)],[34,37]),
[iquote('0:Res:34.1,37.0')] ).
cnf(40,plain,
$false,
inference(mrr,[status(thm)],[38,10]),
[iquote('0:MRR:38.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA023-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n010.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 05:06:31 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 21 clauses, backtracked 0 clauses, performed 0 splits and kept 29 clauses.
% 0.19/0.42 SPASS allocated 75633 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.06 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 4, length 27 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 cls_OrderedGroup_Ocompare__rls__9_0 cls_OrderedGroup_Ocompare__rls__9_1 cls_Orderings_Oorder__class_Oorder__trans_0 clsrel_Orderings_Olinorder_4 clsrel_Ring__and__Field_Oordered__idom_23 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_54 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 tfree_tcs
% 0.19/0.42
%------------------------------------------------------------------------------