TSTP Solution File: ANA010-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 19:28:40 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 11 unt; 0 nHn; 20 RR)
% Number of literals : 33 ( 0 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 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('ANA010-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,x,u)
| c_lessequals(v,x,u) ),
file('ANA010-2.p',unknown),
[] ).
cnf(3,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('ANA010-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| class_Orderings_Oorder(u) ),
file('ANA010-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA010-2.p',unknown),
[] ).
cnf(6,axiom,
c_lessequals(c_0,v(u),t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(7,axiom,
c_lessequals(v(u),c_times(v_c,v_g(u),t_b),t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_lessequals(v(v_x(u)),c_times(u,c_HOL_Oabs(v_g(v_x(u)),t_b),t_b),t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(9,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(10,plain,
equal(c_times(c_HOL_Oabs(u,t_b),c_HOL_Oabs(v,t_b),t_b),c_HOL_Oabs(c_times(u,v,t_b),t_b)),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.0,3.0')] ).
cnf(11,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.0,5.0')] ).
cnf(16,plain,
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(u,v(v),t_b)
| c_lessequals(u,c_times(v_c,v_g(v),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[7,2]),
[iquote('0:Res:7.0,2.1')] ).
cnf(18,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,c_times(v_c,v_g(u),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[6,16]),
[iquote('0:Res:6.0,16.1')] ).
cnf(21,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_times(v_c,v_g(u),t_b),t_b) ),
inference(sor,[status(thm)],[18,4]),
[iquote('0:SoR:18.0,4.1')] ).
cnf(22,plain,
c_lessequals(c_0,c_times(v_c,v_g(u),t_b),t_b),
inference(ssi,[status(thm)],[21,9,11]),
[iquote('0:SSi:21.0,9.0,11.0')] ).
cnf(26,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| equal(c_HOL_Oabs(c_times(v_c,v_g(u),t_b),t_b),c_times(v_c,v_g(u),t_b)) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.0,1.1')] ).
cnf(28,plain,
equal(c_HOL_Oabs(c_times(v_c,v_g(u),t_b),t_b),c_times(v_c,v_g(u),t_b)),
inference(ssi,[status(thm)],[26,9,11]),
[iquote('0:SSi:26.0,9.0,11.0')] ).
cnf(41,plain,
~ c_lessequals(v(v_x(c_HOL_Oabs(u,t_b))),c_HOL_Oabs(c_times(u,v_g(v_x(c_HOL_Oabs(u,t_b))),t_b),t_b),t_b),
inference(spl,[status(thm),theory(equality)],[10,8]),
[iquote('0:SpL:10.0,8.0')] ).
cnf(94,plain,
~ c_lessequals(v(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),
inference(spl,[status(thm),theory(equality)],[28,41]),
[iquote('0:SpL:28.0,41.0')] ).
cnf(98,plain,
$false,
inference(mrr,[status(thm)],[94,7]),
[iquote('0:MRR:94.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.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 03:47:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 76 clauses, backtracked 0 clauses, performed 0 splits and kept 49 clauses.
% 0.20/0.42 SPASS allocated 75746 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.01 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 5, length 20 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : cls_OrderedGroup_Oabs__of__nonneg_0 cls_Orderings_Oorder__class_Oorder__trans_0 cls_Ring__and__Field_Oabs__mult_0 clsrel_OrderedGroup_Olordered__ab__group__abs_17 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 tfree_tcs
% 0.20/0.42
%------------------------------------------------------------------------------