TSTP Solution File: ANA030-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 19:28:54 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 33 ( 11 unt; 0 nHn; 33 RR)
% Number of literals : 61 ( 0 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 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('ANA030-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_plus(v,c_uminus(w,u),u),c_minus(v,w,u)) ),
file('ANA030-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(u)
| ~ c_lessequals(c_minus(v,w,u),x,u)
| c_lessequals(v,c_plus(x,w,u),u) ),
file('ANA030-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_minus(v,c_uminus(w,u),u),c_plus(v,w,u)) ),
file('ANA030-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_plus(c_uminus(v,u),c_uminus(w,u),u),c_uminus(c_plus(v,w,u),u)) ),
file('ANA030-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_uminus(c_minus(v,w,u),u),c_minus(w,v,u)) ),
file('ANA030-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_uminus(c_uminus(v,u),u),v) ),
file('ANA030-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Orderings_Olinorder(u)
| c_lessequals(v,c_Orderings_Omax(w,v,u),u) ),
file('ANA030-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Orderings_Olinorder(u)
| ~ c_lessequals(c_Orderings_Omax(v,w,u),x,u)
| c_lessequals(v,x,u) ),
file('ANA030-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| class_OrderedGroup_Opordered__ab__group__add(u) ),
file('ANA030-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Orderings_Olinorder(u) ),
file('ANA030-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Oab__group__add(u) ),
file('ANA030-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA030-2.p',unknown),
[] ).
cnf(14,axiom,
c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v(u),v_g(u),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),
file('ANA030-2.p',unknown),
[] ).
cnf(15,axiom,
~ c_lessequals(v(v_x(u)),c_plus(v_g(v_x(u)),c_times(u,c_HOL_Oabs(v_h(v_x(u)),t_b),t_b),t_b),t_b),
file('ANA030-2.p',unknown),
[] ).
cnf(16,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA030-2.p',unknown),
[] ).
cnf(17,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_minus(c_uminus(v,u),w,u),c_uminus(c_plus(v,w,u),u)) ),
inference(rew,[status(thm),theory(equality)],[2,5]),
[iquote('0:Rew:2.1,5.1')] ).
cnf(18,plain,
class_Orderings_Olinorder(t_b),
inference(res,[status(thm),theory(equality)],[16,11]),
[iquote('0:Res:16.0,11.0')] ).
cnf(19,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(res,[status(thm),theory(equality)],[16,12]),
[iquote('0:Res:16.0,12.0')] ).
cnf(20,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[16,13]),
[iquote('0:Res:16.0,13.0')] ).
cnf(26,plain,
( ~ class_Orderings_Olinorder(u)
| ~ class_OrderedGroup_Olordered__ab__group__abs(u)
| equal(c_HOL_Oabs(c_Orderings_Omax(v,c_0,u),u),c_Orderings_Omax(v,c_0,u)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.1,1.1')] ).
cnf(49,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_uminus(c_uminus(c_plus(v,w,u),u),u),c_minus(w,c_uminus(v,u),u)) ),
inference(spr,[status(thm),theory(equality)],[17,6]),
[iquote('0:SpR:17.1,6.1')] ).
cnf(54,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_uminus(c_uminus(c_plus(v,w,u),u),u),c_minus(w,c_uminus(v,u),u)) ),
inference(obv,[status(thm),theory(equality)],[49]),
[iquote('0:Obv:49.0')] ).
cnf(55,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_plus(v,w,u),c_plus(w,v,u)) ),
inference(rew,[status(thm),theory(equality)],[7,54,4]),
[iquote('0:Rew:7.1,54.1,4.1,54.1')] ).
cnf(426,plain,
( ~ class_Orderings_Olinorder(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_Orderings_Omax(c_minus(v(u),v_g(u),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b) ),
inference(spr,[status(thm),theory(equality)],[26,14]),
[iquote('0:SpR:26.2,14.0')] ).
cnf(427,plain,
c_lessequals(c_Orderings_Omax(c_minus(v(u),v_g(u),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),
inference(ssi,[status(thm)],[426,16,20,18,19]),
[iquote('0:SSi:426.1,426.0,16.0,20.0,18.0,19.0,16.0,20.0,18.0,19.0')] ).
cnf(428,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v(u),v_g(u),t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[427,9]),
[iquote('0:Res:427.0,9.1')] ).
cnf(429,plain,
c_lessequals(c_minus(v(u),v_g(u),t_b),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),
inference(ssi,[status(thm)],[428,16,20,18,19]),
[iquote('0:SSi:428.0,16.0,20.0,18.0,19.0')] ).
cnf(430,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(v(u),c_plus(c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),v_g(u),t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[429,3]),
[iquote('0:Res:429.0,3.1')] ).
cnf(431,plain,
c_lessequals(v(u),c_plus(c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),v_g(u),t_b),t_b),
inference(ssi,[status(thm)],[430,10,16,20,18,19]),
[iquote('0:SSi:430.0,10.0,16.0,20.0,18.0,19.1')] ).
cnf(432,plain,
( ~ class_OrderedGroup_Oab__group__add(t_b)
| c_lessequals(v(u),c_plus(v_g(u),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),t_b) ),
inference(spr,[status(thm),theory(equality)],[55,431]),
[iquote('0:SpR:55.1,431.0')] ).
cnf(434,plain,
c_lessequals(v(u),c_plus(v_g(u),c_times(v_c,c_HOL_Oabs(v_h(u),t_b),t_b),t_b),t_b),
inference(ssi,[status(thm)],[432,16,20,18,19]),
[iquote('0:SSi:432.0,16.0,20.0,18.0,19.0')] ).
cnf(435,plain,
$false,
inference(unc,[status(thm)],[434,15]),
[iquote('0:UnC:434.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 05:53:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 201 clauses, backtracked 0 clauses, performed 0 splits and kept 67 clauses.
% 0.20/0.44 SPASS allocated 76060 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.01 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.02 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 5, length 33 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : cls_OrderedGroup_Oabs__of__nonneg_0 cls_OrderedGroup_Ocompare__rls__1_0 cls_OrderedGroup_Ocompare__rls__8_0 cls_OrderedGroup_Odiff__minus__eq__add_0 cls_OrderedGroup_Ominus__add__distrib_0 cls_OrderedGroup_Ominus__diff__eq_0 cls_OrderedGroup_Ominus__minus_0 cls_Orderings_Ole__maxI2_0 cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0 clsrel_OrderedGroup_Olordered__ab__group__abs_1 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_4 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_1 cls_conjecture_2 tfree_tcs
% 0.20/0.44
%------------------------------------------------------------------------------