TSTP Solution File: ALG400-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG400-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 18:03:34 EDT 2022
% Result : Unsatisfiable 1.75s 1.93s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of clauses : 35 ( 27 unt; 2 nHn; 35 RR)
% Number of literals : 43 ( 0 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 24 ( 23 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(219,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_Polynomial_Opoly(w,x,u),u),c_Polynomial_Opoly(c_Polynomial_Osmult(v,w,u),x,u)) ),
file('ALG400-1.p',unknown),
[] ).
cnf(220,axiom,
equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Oinverse__class_Oinverse(v,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(u,v,tc_Complex_Ocomplex)),
file('ALG400-1.p',unknown),
[] ).
cnf(308,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(v,w,u),c_HOL_Otimes__class_Otimes(w,v,u)) ),
file('ALG400-1.p',unknown),
[] ).
cnf(469,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(470,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(557,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(558,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(559,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(560,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(561,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(562,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(563,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(564,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(565,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(566,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(567,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(568,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(569,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(570,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(571,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(572,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(573,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(574,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(575,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('ALG400-1.p',unknown),
[] ).
cnf(603,axiom,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('ALG400-1.p',unknown),
[] ).
cnf(604,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('ALG400-1.p',unknown),
[] ).
cnf(880,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(v,u,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[308,220]),
[iquote('0:SpR:308.1,220.0')] ).
cnf(913,plain,
equal(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(v,u,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[880,568,559,564,558,574,573,569,566,565,560,571,570,557,470,469,575,563,567,562,572,561]),
[iquote('0:SSi:880.0,568.0,559.0,564.0,558.0,574.0,573.0,569.0,566.0,565.0,560.0,571.0,570.0,557.0,470.0,469.0,575.0,563.0,567.0,562.0,572.0,561.0')] ).
cnf(9446,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| equal(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),w,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v,w,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[219,913]),
[iquote('0:SpR:219.1,913.0')] ).
cnf(9487,plain,
equal(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),w,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v,w,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[9446,568,559,564,558,574,573,569,566,565,560,571,570,557,470,469,575,563,567,562,572,561]),
[iquote('0:SSi:9446.0,568.0,559.0,564.0,558.0,574.0,573.0,569.0,566.0,565.0,560.0,571.0,570.0,557.0,470.0,469.0,575.0,563.0,567.0,562.0,572.0,561.0')] ).
cnf(9489,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[9487,603]),
[iquote('0:Rew:9487.0,603.1')] ).
cnf(9490,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[9487,604]),
[iquote('0:Rew:9487.0,604.1')] ).
cnf(9536,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(obv,[status(thm),theory(equality)],[9490]),
[iquote('0:Obv:9490.0')] ).
cnf(9537,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(obv,[status(thm),theory(equality)],[9489]),
[iquote('0:Obv:9489.0')] ).
cnf(9538,plain,
$false,
inference(mrr,[status(thm)],[9537,9536]),
[iquote('0:MRR:9537.0,9536.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG400-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n023.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 : Thu Jun 9 02:37:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.75/1.93
% 1.75/1.93 SPASS V 3.9
% 1.75/1.93 SPASS beiseite: Proof found.
% 1.75/1.93 % SZS status Theorem
% 1.75/1.93 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.75/1.93 SPASS derived 6379 clauses, backtracked 0 clauses, performed 0 splits and kept 1667 clauses.
% 1.75/1.93 SPASS allocated 82173 KBytes.
% 1.75/1.93 SPASS spent 0:00:01.58 on the problem.
% 1.75/1.93 0:00:00.06 for the input.
% 1.75/1.93 0:00:00.00 for the FLOTTER CNF translation.
% 1.75/1.93 0:00:00.08 for inferences.
% 1.75/1.93 0:00:00.00 for the backtracking.
% 1.75/1.93 0:00:01.37 for the reduction.
% 1.75/1.93
% 1.75/1.93
% 1.75/1.93 Here is a proof with depth 2, length 35 :
% 1.75/1.93 % SZS output start Refutation
% See solution above
% 1.75/1.93 Formulae used in the proof : cls_poly__smult_0 cls_complex__divide__def_0 cls_class__semiring_Omul__c_0 clsarity_Complex__Ocomplex__Ring__and__Field_Oidom clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1 clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult clsarity_Complex__Ocomplex__Ring__and__Field_Ofield clsarity_Complex__Ocomplex__Int_Oring__char__0 clsarity_Complex__Ocomplex__Int_Onumber__ring clsarity_Complex__Ocomplex__Int_Onumber cls_conjecture_0 cls_conjecture_1
% 1.81/2.00
%------------------------------------------------------------------------------