TSTP Solution File: SWV674-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV674-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 21:44:46 EDT 2022
% Result : Unsatisfiable 2.28s 2.52s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of clauses : 49 ( 26 unt; 1 nHn; 49 RR)
% Number of literals : 73 ( 0 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(347,axiom,
( ~ class_Power_Opower(u)
| equal(c_Power_Opower__class_Opower(v,c_HOL_Ozero__class_Ozero(tc_nat),u),c_HOL_Oone__class_Oone(u)) ),
file('SWV674-1.p',unknown),
[] ).
cnf(366,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('SWV674-1.p',unknown),
[] ).
cnf(536,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('SWV674-1.p',unknown),
[] ).
cnf(571,axiom,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ equal(c_HOL_Ozero__class_Ozero(t_a),v_a) ),
file('SWV674-1.p',unknown),
[] ).
cnf(580,axiom,
equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),u),
file('SWV674-1.p',unknown),
[] ).
cnf(613,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Oring__1__no__zero__divisors(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(614,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Oring__no__zero__divisors(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(615,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Ono__zero__divisors(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(616,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Ocomm__semiring__1(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(617,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Oab__semigroup__mult(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(618,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Ocomm__monoid__mult(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(619,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Odivision__ring(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(620,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Ozero__neq__one(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(621,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Osemiring__0(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(622,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Oab__group__add(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(623,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Omult__zero(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(624,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Omonoid__mult(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(625,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_OrderedGroup_Ogroup__add(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(626,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Oring(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(627,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Ring__and__Field_Oidom(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(628,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| class_Power_Opower(u) ),
file('SWV674-1.p',unknown),
[] ).
cnf(683,axiom,
class_Ring__and__Field_Ofield(t_a),
file('SWV674-1.p',unknown),
[] ).
cnf(685,axiom,
~ equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a)),
file('SWV674-1.p',unknown),
[] ).
cnf(686,plain,
~ equal(c_HOL_Ozero__class_Ozero(t_a),v_a),
inference(mrr,[status(thm)],[571,683]),
[iquote('0:MRR:571.0,683.0')] ).
cnf(696,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),v_x,t_a)),
inference(rew,[status(thm),theory(equality)],[580,685]),
[iquote('0:Rew:580.0,685.0')] ).
cnf(740,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)],[683,366]),
[iquote('0:Res:683.0,366.0')] ).
cnf(743,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors(t_a),
inference(res,[status(thm),theory(equality)],[683,613]),
[iquote('0:Res:683.0,613.0')] ).
cnf(744,plain,
class_Ring__and__Field_Oring__no__zero__divisors(t_a),
inference(res,[status(thm),theory(equality)],[683,614]),
[iquote('0:Res:683.0,614.0')] ).
cnf(745,plain,
class_Ring__and__Field_Ono__zero__divisors(t_a),
inference(res,[status(thm),theory(equality)],[683,615]),
[iquote('0:Res:683.0,615.0')] ).
cnf(746,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_a),
inference(res,[status(thm),theory(equality)],[683,616]),
[iquote('0:Res:683.0,616.0')] ).
cnf(747,plain,
class_OrderedGroup_Oab__semigroup__mult(t_a),
inference(res,[status(thm),theory(equality)],[683,617]),
[iquote('0:Res:683.0,617.0')] ).
cnf(748,plain,
class_OrderedGroup_Ocomm__monoid__mult(t_a),
inference(res,[status(thm),theory(equality)],[683,618]),
[iquote('0:Res:683.0,618.0')] ).
cnf(749,plain,
class_Ring__and__Field_Odivision__ring(t_a),
inference(res,[status(thm),theory(equality)],[683,619]),
[iquote('0:Res:683.0,619.0')] ).
cnf(750,plain,
class_Ring__and__Field_Ozero__neq__one(t_a),
inference(res,[status(thm),theory(equality)],[683,620]),
[iquote('0:Res:683.0,620.0')] ).
cnf(751,plain,
class_Ring__and__Field_Osemiring__0(t_a),
inference(res,[status(thm),theory(equality)],[683,621]),
[iquote('0:Res:683.0,621.0')] ).
cnf(752,plain,
class_OrderedGroup_Oab__group__add(t_a),
inference(res,[status(thm),theory(equality)],[683,622]),
[iquote('0:Res:683.0,622.0')] ).
cnf(753,plain,
class_Ring__and__Field_Omult__zero(t_a),
inference(res,[status(thm),theory(equality)],[683,623]),
[iquote('0:Res:683.0,623.0')] ).
cnf(754,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(res,[status(thm),theory(equality)],[683,624]),
[iquote('0:Res:683.0,624.0')] ).
cnf(755,plain,
class_OrderedGroup_Ogroup__add(t_a),
inference(res,[status(thm),theory(equality)],[683,625]),
[iquote('0:Res:683.0,625.0')] ).
cnf(756,plain,
class_Ring__and__Field_Oring(t_a),
inference(res,[status(thm),theory(equality)],[683,626]),
[iquote('0:Res:683.0,626.0')] ).
cnf(757,plain,
class_Ring__and__Field_Oidom(t_a),
inference(res,[status(thm),theory(equality)],[683,627]),
[iquote('0:Res:683.0,627.0')] ).
cnf(758,plain,
class_Power_Opower(t_a),
inference(res,[status(thm),theory(equality)],[683,628]),
[iquote('0:Res:683.0,628.0')] ).
cnf(819,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)],[536,686]),
[iquote('0:Res:536.2,686.0')] ).
cnf(884,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)],[819,749]),
[iquote('0:MRR:819.0,749.0')] ).
cnf(885,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)),
inference(rew,[status(thm),theory(equality)],[884,696]),
[iquote('0:Rew:884.0,696.0')] ).
cnf(16684,plain,
( ~ class_Power_Opower(t_a)
| ~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)) ),
inference(spl,[status(thm),theory(equality)],[347,885]),
[iquote('0:SpL:347.1,885.0')] ).
cnf(16691,plain,
( ~ class_Power_Opower(t_a)
| ~ equal(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a),c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(v_a,v_x,t_a),t_a)) ),
inference(rew,[status(thm),theory(equality)],[740,16684]),
[iquote('0:Rew:740.0,16684.1')] ).
cnf(16692,plain,
~ class_Power_Opower(t_a),
inference(obv,[status(thm),theory(equality)],[16691]),
[iquote('0:Obv:16691.1')] ).
cnf(16693,plain,
$false,
inference(ssi,[status(thm)],[16692,683,743,757,756,752,747,755,751,748,744,750,745,753,758,754,749,746]),
[iquote('0:SSi:16692.0,683.0,743.0,757.0,756.0,752.0,747.0,755.0,751.0,748.0,744.0,750.0,745.0,753.0,758.0,754.0,749.0,746.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV674-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 16 00:27:34 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.28/2.52
% 2.28/2.52 SPASS V 3.9
% 2.28/2.52 SPASS beiseite: Proof found.
% 2.28/2.52 % SZS status Theorem
% 2.28/2.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.28/2.52 SPASS derived 13636 clauses, backtracked 5 clauses, performed 2 splits and kept 2327 clauses.
% 2.28/2.52 SPASS allocated 85620 KBytes.
% 2.28/2.52 SPASS spent 0:00:02.02 on the problem.
% 2.28/2.52 0:00:00.06 for the input.
% 2.28/2.52 0:00:00.00 for the FLOTTER CNF translation.
% 2.28/2.52 0:00:00.14 for inferences.
% 2.28/2.52 0:00:00.03 for the backtracking.
% 2.28/2.52 0:00:01.68 for the reduction.
% 2.28/2.52
% 2.28/2.52
% 2.28/2.52 Here is a proof with depth 1, length 49 :
% 2.28/2.52 % SZS output start Refutation
% See solution above
% 2.28/2.52 Formulae used in the proof : cls_power__0_0 cls_inverse__eq__divide_0 cls_nonzero__power__inverse_0 cls_nz_0 cls_minus__nat_Odiff__0_0 clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__no__zero__divisors 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__mult clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocomm__monoid__mult clsrel_Ring__and__Field_Ofield_Ring__and__Field_Odivision__ring clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ozero__neq__one 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_Ogroup__add clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oidom clsrel_Ring__and__Field_Ofield_Power_Opower tfree_tcs cls_conjecture_1
% 2.28/2.52
%------------------------------------------------------------------------------