TSTP Solution File: SWV679-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV679-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : Wed Jul 20 21:44:47 EDT 2022
% Result : Unsatisfiable 107.50s 107.66s
% Output : Refutation 111.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 58
% Syntax : Number of clauses : 102 ( 58 unt; 10 nHn; 102 RR)
% Number of literals : 163 ( 0 equ; 59 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 35 ( 34 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(62,axiom,
( ~ c_lessequals(c_Suc(u),v,tc_nat)
| c_HOL_Oord__class_Oless(u,v,tc_nat) ),
file('SWV679-1.p',unknown),
[] ).
cnf(180,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_HOL_Oord__class_Oless(v,w,u)
| ~ c_lessequals(x,v,u)
| c_HOL_Oord__class_Oless(x,w,u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(313,axiom,
( ~ c_HOL_Oord__class_Oless(u,c_Suc(v),tc_nat)
| c_lessequals(u,v,tc_nat) ),
file('SWV679-1.p',unknown),
[] ).
cnf(381,axiom,
~ c_lessequals(c_Suc(u),u,tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(385,axiom,
( ~ c_HOL_Oord__class_Oless(u,v,tc_nat)
| c_lessequals(u,v,tc_nat) ),
file('SWV679-1.p',unknown),
[] ).
cnf(406,axiom,
( c_lessequals(u,v,tc_nat)
| c_lessequals(c_Suc(v),u,tc_nat) ),
file('SWV679-1.p',unknown),
[] ).
cnf(448,axiom,
( ~ class_Ring__and__Field_Odivision__ring(u)
| equal(v,c_HOL_Ozero__class_Ozero(u))
| equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v,u),w,u),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v,w,u),u)) ),
file('SWV679-1.p',unknown),
[] ).
cnf(556,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(u),v,u),c_HOL_Oinverse__class_Oinverse(v,u)) ),
file('SWV679-1.p',unknown),
[] ).
cnf(564,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_HOL_Ozero__class_Ozero(u))
| equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(w,x,u),c_Power_Opower__class_Opower(v,x,u),u),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(w,v,u),x,u)) ),
file('SWV679-1.p',unknown),
[] ).
cnf(568,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| ~ c_lessequals(v,w,tc_nat)
| equal(x,c_HOL_Ozero__class_Ozero(u))
| equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(x,v,u),c_Power_Opower__class_Opower(x,w,u),u),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(x,u),c_HOL_Ominus__class_Ominus(w,v,tc_nat),u)) ),
file('SWV679-1.p',unknown),
[] ).
cnf(614,axiom,
( ~ class_OrderedGroup_Omonoid__mult(u)
| equal(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(u),v,u),c_HOL_Oone__class_Oone(u)) ),
file('SWV679-1.p',unknown),
[] ).
cnf(639,axiom,
~ c_lessequals(v_n,v_m,tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(640,axiom,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ equal(c_HOL_Ozero__class_Ozero(t_a),v_a) ),
file('SWV679-1.p',unknown),
[] ).
cnf(641,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Oring__1__no__zero__divisors(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(642,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Ocancel__ab__semigroup__add(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(643,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Ocancel__semigroup__add(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(644,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Ono__zero__divisors(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(645,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Ocomm__semiring__1(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(646,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Oab__semigroup__add(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(647,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Odivision__ring(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(648,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Ocomm__monoid__add(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(649,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Ozero__neq__one(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(650,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Ocomm__ring__1(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(651,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Osemiring__1(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(652,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Osemiring__0(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(653,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Oab__group__add(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(654,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Omult__zero(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(655,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Omonoid__mult(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(656,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Omonoid__add(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(657,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Ogroup__add(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(658,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Oring__1(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(659,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Oidom(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(660,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Power_Opower(u) ),
file('SWV679-1.p',unknown),
[] ).
cnf(661,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(662,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(663,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(664,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(665,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(666,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(667,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(668,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(669,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(670,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(671,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(672,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(673,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(674,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(675,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(676,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(677,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(678,axiom,
class_Divides_Osemiring__div(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(679,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(680,axiom,
class_Orderings_Opreorder(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(681,axiom,
class_Orderings_Olinorder(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(682,axiom,
class_Orderings_Oorder(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(683,axiom,
class_Power_Opower(tc_nat),
file('SWV679-1.p',unknown),
[] ).
cnf(684,axiom,
class_Ring__and__Field_Ofield(t_a),
file('SWV679-1.p',unknown),
[] ).
cnf(685,axiom,
( ~ equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a))
| c_lessequals(v_n,v_m,tc_nat) ),
file('SWV679-1.p',unknown),
[] ).
cnf(688,plain,
~ equal(c_HOL_Ozero__class_Ozero(t_a),v_a),
inference(mrr,[status(thm)],[640,684]),
[iquote('0:MRR:640.0,684.0')] ).
cnf(711,plain,
~ equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a)),
inference(mrr,[status(thm)],[685,639]),
[iquote('0:MRR:685.1,639.0')] ).
cnf(725,plain,
equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),u,t_a),c_HOL_Oinverse__class_Oinverse(u,t_a)),
inference(res,[status(thm),theory(equality)],[684,556]),
[iquote('0:Res:684.0,556.0')] ).
cnf(728,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(t_a),
inference(res,[status(thm),theory(equality)],[684,641]),
[iquote('0:Res:684.0,641.0')] ).
cnf(729,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[684,642]),
[iquote('0:Res:684.0,642.0')] ).
cnf(730,plain,
class_OrderedGroup_Ocancel__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[684,643]),
[iquote('0:Res:684.0,643.0')] ).
cnf(731,plain,
class_Ring__and__Field_Ono__zero__divisors(t_a),
inference(res,[status(thm),theory(equality)],[684,644]),
[iquote('0:Res:684.0,644.0')] ).
cnf(732,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_a),
inference(res,[status(thm),theory(equality)],[684,645]),
[iquote('0:Res:684.0,645.0')] ).
cnf(733,plain,
class_OrderedGroup_Oab__semigroup__add(t_a),
inference(res,[status(thm),theory(equality)],[684,646]),
[iquote('0:Res:684.0,646.0')] ).
cnf(734,plain,
class_Ring__and__Field_Odivision__ring(t_a),
inference(res,[status(thm),theory(equality)],[684,647]),
[iquote('0:Res:684.0,647.0')] ).
cnf(735,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(res,[status(thm),theory(equality)],[684,648]),
[iquote('0:Res:684.0,648.0')] ).
cnf(736,plain,
class_Ring__and__Field_Ozero__neq__one(t_a),
inference(res,[status(thm),theory(equality)],[684,649]),
[iquote('0:Res:684.0,649.0')] ).
cnf(737,plain,
class_Ring__and__Field_Ocomm__ring__1(t_a),
inference(res,[status(thm),theory(equality)],[684,650]),
[iquote('0:Res:684.0,650.0')] ).
cnf(738,plain,
class_Ring__and__Field_Osemiring__1(t_a),
inference(res,[status(thm),theory(equality)],[684,651]),
[iquote('0:Res:684.0,651.0')] ).
cnf(739,plain,
class_Ring__and__Field_Osemiring__0(t_a),
inference(res,[status(thm),theory(equality)],[684,652]),
[iquote('0:Res:684.0,652.0')] ).
cnf(740,plain,
class_OrderedGroup_Oab__group__add(t_a),
inference(res,[status(thm),theory(equality)],[684,653]),
[iquote('0:Res:684.0,653.0')] ).
cnf(741,plain,
class_Ring__and__Field_Omult__zero(t_a),
inference(res,[status(thm),theory(equality)],[684,654]),
[iquote('0:Res:684.0,654.0')] ).
cnf(742,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(res,[status(thm),theory(equality)],[684,655]),
[iquote('0:Res:684.0,655.0')] ).
cnf(743,plain,
class_OrderedGroup_Omonoid__add(t_a),
inference(res,[status(thm),theory(equality)],[684,656]),
[iquote('0:Res:684.0,656.0')] ).
cnf(744,plain,
class_OrderedGroup_Ogroup__add(t_a),
inference(res,[status(thm),theory(equality)],[684,657]),
[iquote('0:Res:684.0,657.0')] ).
cnf(745,plain,
class_Ring__and__Field_Oring__1(t_a),
inference(res,[status(thm),theory(equality)],[684,658]),
[iquote('0:Res:684.0,658.0')] ).
cnf(746,plain,
class_Ring__and__Field_Oidom(t_a),
inference(res,[status(thm),theory(equality)],[684,659]),
[iquote('0:Res:684.0,659.0')] ).
cnf(747,plain,
class_Power_Opower(t_a),
inference(res,[status(thm),theory(equality)],[684,660]),
[iquote('0:Res:684.0,660.0')] ).
cnf(786,plain,
( ~ class_Ring__and__Field_Odivision__ring(t_a)
| equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),u,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,u,t_a),t_a)) ),
inference(res,[status(thm),theory(equality)],[448,688]),
[iquote('0:Res:448.2,688.0')] ).
cnf(888,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a)),
inference(rew,[status(thm),theory(equality)],[725,711]),
[iquote('0:Rew:725.0,711.0')] ).
cnf(896,plain,
equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),u,t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,u,t_a),t_a)),
inference(mrr,[status(thm)],[786,734]),
[iquote('0:MRR:786.0,734.0')] ).
cnf(899,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),t_a)),
inference(rew,[status(thm),theory(equality)],[896,888]),
[iquote('0:Rew:896.0,888.0')] ).
cnf(1042,plain,
~ c_HOL_Oord__class_Oless(c_Suc(u),u,tc_nat),
inference(res,[status(thm),theory(equality)],[385,381]),
[iquote('0:Res:385.1,381.0')] ).
cnf(1175,plain,
( c_lessequals(u,v,tc_nat)
| c_HOL_Oord__class_Oless(v,u,tc_nat) ),
inference(res,[status(thm),theory(equality)],[406,62]),
[iquote('0:Res:406.1,62.0')] ).
cnf(1200,plain,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
inference(res,[status(thm),theory(equality)],[1175,639]),
[iquote('0:Res:1175.0,639.0')] ).
cnf(63466,plain,
( ~ class_Orderings_Oorder(tc_nat)
| ~ c_lessequals(u,v_m,tc_nat)
| c_HOL_Oord__class_Oless(u,v_n,tc_nat) ),
inference(res,[status(thm),theory(equality)],[1200,180]),
[iquote('0:Res:1200.0,180.1')] ).
cnf(63473,plain,
( ~ c_lessequals(u,v_m,tc_nat)
| c_HOL_Oord__class_Oless(u,v_n,tc_nat) ),
inference(ssi,[status(thm)],[63466,679,676,670,665,663,677,675,674,667,666,673,672,661,683,680,671,662,681,664,678,682,669,668]),
[iquote('0:SSi:63466.0,679.0,676.0,670.0,665.0,663.0,677.0,675.0,674.0,667.0,666.0,673.0,672.0,661.0,683.0,680.0,671.0,662.0,681.0,664.0,678.0,682.0,669.0,668.0')] ).
cnf(69483,plain,
( c_HOL_Oord__class_Oless(v_m,u,tc_nat)
| c_HOL_Oord__class_Oless(u,v_n,tc_nat) ),
inference(res,[status(thm),theory(equality)],[1175,63473]),
[iquote('0:Res:1175.0,63473.0')] ).
cnf(69674,plain,
c_HOL_Oord__class_Oless(v_m,c_Suc(v_n),tc_nat),
inference(res,[status(thm),theory(equality)],[69483,1042]),
[iquote('0:Res:69483.1,1042.0')] ).
cnf(69714,plain,
c_lessequals(v_m,v_n,tc_nat),
inference(res,[status(thm),theory(equality)],[69674,313]),
[iquote('0:Res:69674.0,313.0')] ).
cnf(150344,plain,
( ~ class_OrderedGroup_Omonoid__mult(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_HOL_Ozero__class_Ozero(u))
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(u),c_Power_Opower__class_Opower(v,w,u),u),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(u),v,u),w,u)) ),
inference(spr,[status(thm),theory(equality)],[614,564]),
[iquote('0:SpR:614.1,564.2')] ).
cnf(150376,plain,
( ~ class_OrderedGroup_Omonoid__mult(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_HOL_Ozero__class_Ozero(u))
| equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v,u),w,u),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v,w,u),u)) ),
inference(rew,[status(thm),theory(equality)],[556,150344]),
[iquote('0:Rew:556.1,150344.3,556.1,150344.3')] ).
cnf(150377,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_HOL_Ozero__class_Ozero(u))
| equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v,u),w,u),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v,w,u),u)) ),
inference(ssi,[status(thm)],[150376,655]),
[iquote('0:SSi:150376.0,655.1')] ).
cnf(150378,plain,
( ~ class_Ring__and__Field_Ofield(u)
| ~ c_lessequals(v,w,tc_nat)
| equal(x,c_HOL_Ozero__class_Ozero(u))
| equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(x,v,u),c_Power_Opower__class_Opower(x,w,u),u),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(x,c_HOL_Ominus__class_Ominus(w,v,tc_nat),u),u)) ),
inference(rew,[status(thm),theory(equality)],[150377,568]),
[iquote('0:Rew:150377.2,568.3')] ).
cnf(158384,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_m,v_n,tc_nat)
| ~ equal(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a),t_a))
| equal(c_HOL_Ozero__class_Ozero(t_a),v_a) ),
inference(spl,[status(thm),theory(equality)],[150378,899]),
[iquote('0:SpL:150378.3,899.0')] ).
cnf(159415,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_m,v_n,tc_nat)
| equal(c_HOL_Ozero__class_Ozero(t_a),v_a) ),
inference(obv,[status(thm),theory(equality)],[158384]),
[iquote('0:Obv:158384.2')] ).
cnf(159416,plain,
( ~ c_lessequals(v_m,v_n,tc_nat)
| equal(c_HOL_Ozero__class_Ozero(t_a),v_a) ),
inference(ssi,[status(thm)],[159415,684,745,737,728,742,733,729,743,741,739,731,730,738,736,746,744,740,747,734,735,732]),
[iquote('0:SSi:159415.0,684.0,745.0,737.0,728.0,742.0,733.0,729.0,743.0,741.0,739.0,731.0,730.0,738.0,736.0,746.0,744.0,740.0,747.0,734.0,735.0,732.0')] ).
cnf(159417,plain,
equal(c_HOL_Ozero__class_Ozero(t_a),v_a),
inference(mrr,[status(thm)],[159416,69714]),
[iquote('0:MRR:159416.0,69714.0')] ).
cnf(159418,plain,
$false,
inference(mrr,[status(thm)],[159417,688]),
[iquote('0:MRR:159417.0,688.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWV679-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.11 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Wed Jun 15 21:50:56 EDT 2022
% 0.12/0.32 % CPUTime :
% 107.50/107.66
% 107.50/107.66 SPASS V 3.9
% 107.50/107.66 SPASS beiseite: Proof found.
% 107.50/107.66 % SZS status Theorem
% 107.50/107.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 107.50/107.66 SPASS derived 127652 clauses, backtracked 7802 clauses, performed 9 splits and kept 25876 clauses.
% 107.50/107.66 SPASS allocated 161355 KBytes.
% 107.50/107.66 SPASS spent 0:1:47.14 on the problem.
% 107.50/107.66 0:00:00.06 for the input.
% 107.50/107.66 0:00:00.00 for the FLOTTER CNF translation.
% 107.50/107.66 0:00:01.36 for inferences.
% 107.50/107.66 0:00:05.03 for the backtracking.
% 107.50/107.66 0:1:39.48 for the reduction.
% 107.50/107.66
% 107.50/107.66
% 107.50/107.66 Here is a proof with depth 6, length 102 :
% 107.50/107.66 % SZS output start Refutation
% See solution above
% 111.85/112.03 Formulae used in the proof : cls_Suc__le__eq_0 cls_xt1_I7_J_0 cls_less__Suc__eq__le_0 cls_Suc__n__not__le__n_0 cls_nat__less__le_0 cls_not__less__eq__eq_0 cls_nonzero__power__inverse_0 cls_inverse__eq__divide_0 cls_nonzero__power__divide_0 cls_power__diff__inverse_0 cls_power__one_0 cls_CHAINED_0 cls_CHAINED_0_01 clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocancel__ab__semigroup__add clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocancel__semigroup__add clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ono__zero__divisors clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1 clsrel_Ring__and__Field_Ofield_OrderedGroup_Oab__semigroup__add clsrel_Ring__and__Field_Ofield_Ring__and__Field_Odivision__ring clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocomm__monoid__add clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ozero__neq__one clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__ring__1 clsrel_Ring__and__Field_Ofield_Ring__and__Field_Osemiring__1 clsrel_Ring__and__Field_Ofield_Ring__and__Field_Osemiring__0 clsrel_Ring__and__Field_Ofield_OrderedGroup_Oab__group__add clsrel_Ring__and__Field_Ofield_Ring__and__Field_Omult__zero clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__add clsrel_Ring__and__Field_Ofield_OrderedGroup_Ogroup__add clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1 clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oidom clsrel_Ring__and__Field_Ofield_Power_Opower clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add clsarity_nat__OrderedGroup_Opordered__comm__monoid__add clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add clsarity_nat__OrderedGroup_Ocancel__semigroup__add clsarity_nat__Ring__and__Field_Ono__zero__divisors clsarity_nat__Ring__and__Field_Oordered__semidom clsarity_nat__Ring__and__Field_Ocomm__semiring__1 clsarity_nat__OrderedGroup_Oab__semigroup__add clsarity_nat__OrderedGroup_Ocomm__monoid__add clsarity_nat__Ring__and__Field_Ozero__neq__one clsarity_nat__Ring__and__Field_Osemiring__1 clsarity_nat__Ring__and__Field_Osemiring__0 clsarity_nat__Ring__and__Field_Omult__zero clsarity_nat__OrderedGroup_Omonoid__mult clsarity_nat__OrderedGroup_Omonoid__add clsarity_nat__Divides_Osemiring__div clsarity_nat__Nat_Osemiring__char__0 clsarity_nat__Orderings_Opreorder clsarity_nat__Orderings_Olinorder clsarity_nat__Orderings_Oorder clsarity_nat__Power_Opower tfree_tcs cls_conjecture_0
% 111.85/112.03
%------------------------------------------------------------------------------