TSTP Solution File: ANA017-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 19:28:45 EDT 2022
% Result : Unsatisfiable 0.36s 0.54s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 11 unt; 0 nHn; 22 RR)
% Number of literals : 38 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 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('ANA017-2.p',unknown),
[] ).
cnf(2,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('ANA017-2.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('ANA017-2.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('ANA017-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Osemigroup__mult(u) ),
file('ANA017-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_Ring__and__Field_Opordered__semiring(u) ),
file('ANA017-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(u)
| class_OrderedGroup_Olordered__ab__group__abs(u) ),
file('ANA017-2.p',unknown),
[] ).
cnf(8,axiom,
c_lessequals(c_HOL_Oabs(v_b(u),t_b),c_times(v_ca,c_HOL_Oabs(v(u),t_b),t_b),t_b),
file('ANA017-2.p',unknown),
[] ).
cnf(9,axiom,
~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(u)),t_b),t_b),c_times(u,c_HOL_Oabs(v(v_x(u)),t_b),t_b),t_b),
file('ANA017-2.p',unknown),
[] ).
cnf(10,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA017-2.p',unknown),
[] ).
cnf(11,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)],[10,3]),
[iquote('0:Res:10.0,3.0')] ).
cnf(12,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(res,[status(thm),theory(equality)],[10,5]),
[iquote('0:Res:10.0,5.0')] ).
cnf(13,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(res,[status(thm),theory(equality)],[10,6]),
[iquote('0:Res:10.0,6.0')] ).
cnf(14,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[10,7]),
[iquote('0:Res:10.0,7.0')] ).
cnf(29,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(u,v,t_b))),t_b),t_b),c_times(u,c_times(v,c_HOL_Oabs(v(v_x(c_times(u,v,t_b))),t_b),t_b),t_b),t_b) ),
inference(spl,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpL:2.1,9.0')] ).
cnf(30,plain,
~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(u,v,t_b))),t_b),t_b),c_times(u,c_times(v,c_HOL_Oabs(v(v_x(c_times(u,v,t_b))),t_b),t_b),t_b),t_b),
inference(ssi,[status(thm)],[29,10,14,13,12]),
[iquote('0:SSi:29.0,10.0,14.0,13.0,12.0')] ).
cnf(45,plain,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_HOL_Oabs(u,t_b),v,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(w,t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(w,u,t_b),t_b),c_times(c_HOL_Oabs(w,t_b),v,t_b),t_b) ),
inference(spr,[status(thm),theory(equality)],[11,4]),
[iquote('0:SpR:11.0,4.3')] ).
cnf(49,plain,
( ~ c_lessequals(c_HOL_Oabs(u,t_b),v,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(w,t_b),t_b)
| c_lessequals(c_HOL_Oabs(c_times(w,u,t_b),t_b),c_times(c_HOL_Oabs(w,t_b),v,t_b),t_b) ),
inference(ssi,[status(thm)],[45,10,14,13,12]),
[iquote('0:SSi:45.0,10.0,14.0,13.0,12.0')] ).
cnf(255,plain,
( ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),u,t_b))),t_b),c_times(u,c_HOL_Oabs(v(v_x(c_times(c_HOL_Oabs(v_c,t_b),u,t_b))),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b) ),
inference(res,[status(thm),theory(equality)],[49,30]),
[iquote('0:Res:49.2,30.0')] ).
cnf(655,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b),
inference(res,[status(thm),theory(equality)],[8,255]),
[iquote('0:Res:8.0,255.0')] ).
cnf(656,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(res,[status(thm),theory(equality)],[1,655]),
[iquote('0:Res:1.1,655.0')] ).
cnf(657,plain,
$false,
inference(ssi,[status(thm)],[656,10,14,13,12]),
[iquote('0:SSi:656.0,10.0,14.0,13.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 04:13:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.36/0.54
% 0.36/0.54 SPASS V 3.9
% 0.36/0.54 SPASS beiseite: Proof found.
% 0.36/0.54 % SZS status Theorem
% 0.36/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.54 SPASS derived 341 clauses, backtracked 0 clauses, performed 0 splits and kept 93 clauses.
% 0.36/0.54 SPASS allocated 76981 KBytes.
% 0.36/0.54 SPASS spent 0:00:00.18 on the problem.
% 0.36/0.54 0:00:00.04 for the input.
% 0.36/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.54 0:00:00.01 for inferences.
% 0.36/0.54 0:00:00.00 for the backtracking.
% 0.36/0.54 0:00:00.11 for the reduction.
% 0.36/0.54
% 0.36/0.54
% 0.36/0.54 Here is a proof with depth 5, length 22 :
% 0.36/0.54 % SZS output start Refutation
% See solution above
% 0.36/0.54 Formulae used in the proof : cls_OrderedGroup_Oabs__ge__zero_0 cls_OrderedGroup_Omult__ac__1_0 cls_Ring__and__Field_Oabs__mult_0 cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 clsrel_Ring__and__Field_Oordered__idom_21 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_50 cls_conjecture_0 cls_conjecture_1 tfree_tcs
% 0.36/0.54
%------------------------------------------------------------------------------