TSTP Solution File: ANA018-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA018-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 19:28:46 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 29 ( 12 unt; 0 nHn; 29 RR)
% Number of literals : 56 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,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('ANA018-2.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('ANA018-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_less(v,w,u)
| c_lessequals(v,w,u) ),
file('ANA018-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(c_0,x,u)
| c_lessequals(c_times(x,v,u),c_times(x,w,u),u) ),
file('ANA018-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_LOrder_Ojoin__semilorder(u)
| class_Orderings_Oorder(u) ),
file('ANA018-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Osemigroup__mult(u) ),
file('ANA018-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_LOrder_Ojoin__semilorder(u) ),
file('ANA018-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA018-2.p',unknown),
[] ).
cnf(9,axiom,
c_lessequals(c_HOL_Oabs(v(u),t_b),c_times(v_c,c_HOL_Oabs(v_g(u),t_b),t_b),t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(10,axiom,
c_less(c_0,v_ca,t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(11,axiom,
c_lessequals(c_HOL_Oabs(v_x(u),t_b),c_times(v_ca,c_HOL_Oabs(v(u),t_b),t_b),t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(12,axiom,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(13,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(14,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(res,[status(thm),theory(equality)],[13,6]),
[iquote('0:Res:13.0,6.0')] ).
cnf(15,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(res,[status(thm),theory(equality)],[13,7]),
[iquote('0:Res:13.0,7.0')] ).
cnf(16,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(res,[status(thm),theory(equality)],[13,8]),
[iquote('0:Res:13.0,8.0')] ).
cnf(17,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_ca,t_b) ),
inference(res,[status(thm),theory(equality)],[10,3]),
[iquote('0:Res:10.0,3.1')] ).
cnf(20,plain,
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v(u),t_b),t_b),v,t_b)
| c_lessequals(c_HOL_Oabs(v_x(u),t_b),v,t_b) ),
inference(res,[status(thm),theory(equality)],[11,2]),
[iquote('0:Res:11.0,2.2')] ).
cnf(28,plain,
( ~ class_LOrder_Ojoin__semilorder(t_b)
| c_lessequals(c_0,v_ca,t_b) ),
inference(sor,[status(thm)],[17,5]),
[iquote('0:SoR:17.0,5.1')] ).
cnf(29,plain,
c_lessequals(c_0,v_ca,t_b),
inference(ssi,[status(thm)],[28,13,16,15,14]),
[iquote('0:SSi:28.0,13.0,16.0,15.0,14.0')] ).
cnf(43,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b) ),
inference(spl,[status(thm),theory(equality)],[1,12]),
[iquote('0:SpL:1.1,12.0')] ).
cnf(44,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(ssi,[status(thm)],[43,13,16,15,14]),
[iquote('0:SSi:43.0,13.0,16.0,15.0,14.0')] ).
cnf(58,plain,
( ~ class_LOrder_Ojoin__semilorder(t_b)
| ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v(u),t_b),t_b),v,t_b)
| c_lessequals(c_HOL_Oabs(v_x(u),t_b),v,t_b) ),
inference(sor,[status(thm)],[20,5]),
[iquote('0:SoR:20.0,5.1')] ).
cnf(59,plain,
( ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v(u),t_b),t_b),v,t_b)
| c_lessequals(c_HOL_Oabs(v_x(u),t_b),v,t_b) ),
inference(ssi,[status(thm)],[58,13,16,15,14]),
[iquote('0:SSi:58.0,13.0,16.0,15.0,14.0')] ).
cnf(61,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v(u),t_b),v,t_b)
| ~ c_lessequals(c_0,v_ca,t_b)
| c_lessequals(c_HOL_Oabs(v_x(u),t_b),c_times(v_ca,v,t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[4,59]),
[iquote('0:Res:4.3,59.0')] ).
cnf(63,plain,
( ~ c_lessequals(c_HOL_Oabs(v(u),t_b),v,t_b)
| ~ c_lessequals(c_0,v_ca,t_b)
| c_lessequals(c_HOL_Oabs(v_x(u),t_b),c_times(v_ca,v,t_b),t_b) ),
inference(ssi,[status(thm)],[61,13,16,15,14]),
[iquote('0:SSi:61.0,13.0,16.0,15.0,14.0')] ).
cnf(64,plain,
( ~ c_lessequals(c_HOL_Oabs(v(u),t_b),v,t_b)
| c_lessequals(c_HOL_Oabs(v_x(u),t_b),c_times(v_ca,v,t_b),t_b) ),
inference(mrr,[status(thm)],[63,29]),
[iquote('0:MRR:63.1,29.0')] ).
cnf(68,plain,
~ c_lessequals(c_HOL_Oabs(v(v_xa),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(res,[status(thm),theory(equality)],[64,44]),
[iquote('0:Res:64.1,44.0')] ).
cnf(69,plain,
$false,
inference(mrr,[status(thm)],[68,9]),
[iquote('0:MRR:68.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA018-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 03:00:25 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 36 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.19/0.42 SPASS allocated 75698 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 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 29 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : cls_OrderedGroup_Omult__ac__1_0 cls_Orderings_Oorder__class_Oorder__trans_0 cls_Orderings_Oorder__less__imp__le_0 cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 clsrel_LOrder_Ojoin__semilorder_1 clsrel_Ring__and__Field_Oordered__idom_21 clsrel_Ring__and__Field_Oordered__idom_35 clsrel_Ring__and__Field_Oordered__idom_42 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 tfree_tcs
% 0.19/0.42
%------------------------------------------------------------------------------