TSTP Solution File: ANA043-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA043-2 : 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 7.06s 7.27s
% Output : Refutation 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 34 ( 0 equ; 21 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 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,c_HOL_Oabs(v,u),u) ),
file('ANA043-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| equal(c_times(v,c_times(w,x,u),u),c_times(w,c_times(v,x,u),u)) ),
file('ANA043-2.p',unknown),
[] ).
cnf(3,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('ANA043-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__semigroup__mult(u) ),
file('ANA043-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA043-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA043-2.p',unknown),
[] ).
cnf(7,axiom,
c_lessequals(c_HOL_Oabs(v(u),t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),
file('ANA043-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_lessequals(c_times(c_HOL_Oabs(v_l(v_x(u),v_xa(u)),t_b),c_HOL_Oabs(v(v_k(v_x(u),v_xa(u))),t_b),t_b),c_times(u,c_times(c_HOL_Oabs(v_l(v_x(u),v_xa(u)),t_b),c_HOL_Oabs(v_h(v_k(v_x(u),v_xa(u))),t_b),t_b),t_b),t_b),
file('ANA043-2.p',unknown),
[] ).
cnf(9,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA043-2.p',unknown),
[] ).
cnf(10,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.0,4.0')] ).
cnf(11,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.0,5.0')] ).
cnf(12,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[9,6]),
[iquote('0:Res:9.0,6.0')] ).
cnf(27,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(u)
| ~ class_Ring__and__Field_Opordered__semiring(u)
| ~ c_lessequals(v,c_times(w,x,u),u)
| ~ c_lessequals(c_0,y,u)
| c_lessequals(c_times(y,v,u),c_times(w,c_times(y,x,u),u),u) ),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.1,3.3')] ).
cnf(3838,plain,
( ~ class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(v(v_k(v_x(u),v_xa(u))),t_b),c_times(u,c_HOL_Oabs(v_h(v_k(v_x(u),v_xa(u))),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(u),v_xa(u)),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[27,8]),
[iquote('0:Res:27.4,8.0')] ).
cnf(3841,plain,
( ~ c_lessequals(c_HOL_Oabs(v(v_k(v_x(u),v_xa(u))),t_b),c_times(u,c_HOL_Oabs(v_h(v_k(v_x(u),v_xa(u))),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(u),v_xa(u)),t_b),t_b) ),
inference(ssi,[status(thm)],[3838,9,12,11,10]),
[iquote('0:SSi:3838.1,3838.0,9.0,12.0,11.0,10.0,9.0,12.0,11.0,10.0')] ).
cnf(6988,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_l(v_x(v_c),v_xa(v_c)),t_b),t_b),
inference(res,[status(thm),theory(equality)],[7,3841]),
[iquote('0:Res:7.0,3841.0')] ).
cnf(6989,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[1,6988]),
[iquote('0:Res:1.1,6988.0')] ).
cnf(6990,plain,
$false,
inference(ssi,[status(thm)],[6989,9,12,11,10]),
[iquote('0:SSi:6989.0,9.0,12.0,11.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA043-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % 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 06:36:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 7.06/7.27
% 7.06/7.27 SPASS V 3.9
% 7.06/7.27 SPASS beiseite: Proof found.
% 7.06/7.27 % SZS status Theorem
% 7.06/7.27 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.06/7.27 SPASS derived 3558 clauses, backtracked 0 clauses, performed 0 splits and kept 677 clauses.
% 7.06/7.27 SPASS allocated 81952 KBytes.
% 7.06/7.27 SPASS spent 0:00:06.25 on the problem.
% 7.06/7.27 0:00:00.04 for the input.
% 7.06/7.27 0:00:00.00 for the FLOTTER CNF translation.
% 7.06/7.27 0:00:00.07 for inferences.
% 7.06/7.27 0:00:00.00 for the backtracking.
% 7.06/7.27 0:00:06.12 for the reduction.
% 7.06/7.27
% 7.06/7.27
% 7.06/7.27 Here is a proof with depth 4, length 18 :
% 7.06/7.27 % SZS output start Refutation
% See solution above
% 7.06/7.27 Formulae used in the proof : cls_OrderedGroup_Oabs__ge__zero_0 cls_OrderedGroup_Omult__left__commute_0 cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 clsrel_Ring__and__Field_Oordered__idom_17 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 tfree_tcs
% 7.06/7.27
%------------------------------------------------------------------------------