TSTP Solution File: ANA044-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA044-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 19:29:03 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 13 ( 5 unt; 0 nHn; 13 RR)
% Number of literals : 32 ( 0 equ; 23 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 5 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_Olordered__ab__group__abs(u)
| ~ c_lessequals(c_0,v,u)
| equal(c_HOL_Oabs(v,u),v) ),
file('ANA044-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(u)
| ~ c_lessequals(c_0,v,u)
| ~ c_lessequals(c_0,w,u)
| c_lessequals(c_0,c_times(v,w,u),u) ),
file('ANA044-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__cancel__semiring(u) ),
file('ANA044-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA044-2.p',unknown),
[] ).
cnf(5,axiom,
c_lessequals(c_0,v_l(u,v),t_b),
file('ANA044-2.p',unknown),
[] ).
cnf(6,axiom,
c_lessequals(c_0,v_h(u),t_b),
file('ANA044-2.p',unknown),
[] ).
cnf(7,axiom,
~ equal(c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b)),
file('ANA044-2.p',unknown),
[] ).
cnf(8,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA044-2.p',unknown),
[] ).
cnf(15,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(u)
| ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| ~ c_lessequals(c_0,v,u)
| ~ c_lessequals(c_0,w,u)
| equal(c_HOL_Oabs(c_times(v,w,u),u),c_times(v,w,u)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.3,1.1')] ).
cnf(17,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ equal(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b)) ),
inference(spl,[status(thm),theory(equality)],[15,7]),
[iquote('0:SpL:15.4,7.0')] ).
cnf(18,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b) ),
inference(obv,[status(thm),theory(equality)],[17]),
[iquote('0:Obv:17.4')] ).
cnf(19,plain,
( ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b) ),
inference(ssi,[status(thm)],[18,4,8,3]),
[iquote('0:SSi:18.1,18.0,4.0,8.1,3.0,8.1')] ).
cnf(20,plain,
$false,
inference(mrr,[status(thm)],[19,5,6]),
[iquote('0:MRR:19.0,19.1,5.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA044-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n007.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 05:32:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 7 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.19/0.41 SPASS allocated 75611 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 2, length 13 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : cls_OrderedGroup_Oabs__of__nonneg_0 cls_Ring__and__Field_Omult__nonneg__nonneg_0 clsrel_Ring__and__Field_Oordered__idom_40 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 cls_conjecture_3 tfree_tcs
% 0.19/0.41
%------------------------------------------------------------------------------