TSTP Solution File: ALG407-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : ALG407-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n026.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 18:00:45 EDT 2022
% Result : Unsatisfiable 237.13s 237.29s
% Output : Refutation 237.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 48
% Syntax : Number of clauses : 103 ( 78 unt; 1 nHn; 56 RR)
% Number of literals : 148 ( 69 equ; 58 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 122 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X)
| c_HOL_Ominus__class_Ominus(Y,Y,X) = c_HOL_Ozero__class_Ozero(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_inverse__zero__imp__zero_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X)
| c_HOL_Oinverse__class_Oinverse(Y,X) != c_HOL_Ozero__class_Ozero(X)
| c_HOL_Ozero__class_Ozero(X) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(X)
| c_HOL_Ominus__class_Ominus(Y,c_HOL_Ouminus__class_Ouminus(Z,X),X) = c_HOL_Oplus__class_Oplus(Y,Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(cls_inverse__inverse__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X)
| ~ class_Ring__and__Field_Odivision__by__zero(X)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(Y,X),X) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(cls_exp__diff_0,axiom,
( ~ class_SEQ_Obanach(X)
| ~ class_RealVector_Oreal__normed__field(X)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(Y,Z,X),X) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(Y,X),c_Transcendental_Oexp(Z,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__diff_0) ).
cnf(cls_inverse__eq__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(X)
| c_HOL_Oinverse__class_Oinverse(Y,X) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X),Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(cls_less__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X)
| c_HOL_Ominus__class_Ominus(Y,Z,X) != c_HOL_Ominus__class_Ominus(U,V,X)
| c_HOL_Oord__class_Oless(U,V,X)
| ~ c_HOL_Oord__class_Oless(Y,Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_mult__frac__num_0,axiom,
( ~ class_Ring__and__Field_Ofield(X)
| ~ class_Ring__and__Field_Odivision__by__zero(X)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(Y,Z,X),U,X) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(Y,U,X),Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
cnf(cls_inverse__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(X)
| ~ class_Ring__and__Field_Odivision__by__zero(X)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(Y,Z,X),X) = c_HOL_Oinverse__class_Odivide(Z,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
cnf(cls_group__add__class_Odiff__0_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(X)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X),Y,X) = c_HOL_Ouminus__class_Ouminus(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
cnf(cls_ln__unique_0,axiom,
c_Transcendental_Oln(c_Transcendental_Oexp(X,tc_RealDef_Oreal)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__unique_0) ).
cnf(cls_exp__ln_0,axiom,
( c_Transcendental_Oexp(c_Transcendental_Oln(X),tc_RealDef_Oreal) = X
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__ln_0) ).
cnf(cls_divide__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(X)
| c_HOL_Oinverse__class_Odivide(Y,Z,X) = c_HOL_Otimes__class_Otimes(Y,c_HOL_Oinverse__class_Oinverse(Z,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
cnf(cls_exp__minus_0,axiom,
( ~ class_SEQ_Obanach(X)
| ~ class_RealVector_Oreal__normed__field(X)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(Y,X),X) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(Y,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__minus_0) ).
cnf(cls_ln__mult_0,axiom,
( c_Transcendental_Oln(c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_Transcendental_Oln(X),c_Transcendental_Oln(Y),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),Y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__mult_0) ).
cnf(cls_nonzero__inverse__mult__distrib_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(Y,Z,X),X) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(Z,X),c_HOL_Oinverse__class_Oinverse(Y,X),X)
| Z = c_HOL_Ozero__class_Ozero(X)
| c_HOL_Ozero__class_Ozero(X) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X)
| c_HOL_Oplus__class_Oplus(Y,Z,X) != c_HOL_Ozero__class_Ozero(X)
| Y = c_HOL_Ouminus__class_Ouminus(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
cnf(cls_exp__add_0,axiom,
( ~ class_SEQ_Obanach(X)
| ~ class_RealVector_Oreal__normed__field(X)
| c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(Y,Z,X),X) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(Y,X),c_Transcendental_Oexp(Z,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__add_0) ).
cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X)
| c_Power_Opower__class_Opower(Y,c_Suc(Z),X) = c_HOL_Otimes__class_Otimes(Y,c_Power_Opower__class_Opower(Y,Z,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
cnf(cls_exp__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__gt__zero_0) ).
cnf(cls_ln__inj__iff_0,axiom,
( c_Transcendental_Oln(X) != c_Transcendental_Oln(Y)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),Y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X,tc_RealDef_Oreal)
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__inj__iff_0) ).
cnf(cls_exp__eq__one__iff_1,axiom,
c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__eq__one__iff_1) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X) = c_HOL_Oplus__class_Oplus(X,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_real__mult__assoc_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal),Z,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X,c_HOL_Otimes__class_Otimes(Y,Z,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X)
| c_HOL_Oplus__class_Oplus(Y,Z,X) = c_HOL_Oplus__class_Oplus(Z,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_zero__less__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X),c_Power_Opower__class_Opower(Y,Z,X),X)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X),Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(X,X,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
cnf(cls_norm__power_0,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(X)
| c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(Y,Z,X),X) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(Y,X),Z,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__power_0) ).
cnf(cls_real__mult__order_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),Y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
cnf(cls_real__mult__1_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X,tc_RealDef_Oreal) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
cnf(cls_real__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(Y,X,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
cnf(cls_t_I1_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_t_I1_J_0) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(Y,Z,X),c_HOL_Otimes__class_Otimes(Y,U,X),X)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X),Y,X)
| ~ c_HOL_Oord__class_Oless(Z,U,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
cnf(cls_m_I1_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_m_I1_J_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(896,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[cls_conjecture_1,cls_Suc__eq__plus1_0,theory(equality)]) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(898,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[cls_conjecture_2,cls_real__mult__assoc_0,cls_Suc__eq__plus1_0,theory(equality)]) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
cnf(1115,plain,
c_HOL_Otimes__class_Otimes(X,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X,
inference('PARAMODULATE',[status(thm)],[cls_real__mult__1_0,cls_real__mult__commute_0,theory(equality)]) ).
cnf(1116,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[898,1115,theory(equality)]) ).
cnf(1119,plain,
c_HOL_Ominus__class_Ominus(X,X,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_eq__iff__diff__eq__0_0,clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add]) ).
cnf(1289,plain,
c_HOL_Oplus__class_Oplus(X,Y,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(Y,X,tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_class__semiring_Osemiring__rules_I24_J_0,clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(1304,plain,
c_HOL_Oinverse__class_Oinverse(X,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X,tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_inverse__eq__divide_0,clsarity_RealDef__Oreal__Ring__and__Field_Ofield]) ).
cnf(1312,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X,tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_group__add__class_Odiff__0_0,clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]) ).
cnf(1388,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X,tc_RealDef_Oreal),tc_RealDef_Oreal) = X,
inference('HYPERRESOLVE',[status(thm)],[cls_inverse__inverse__eq_0,clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero]) ).
cnf(1403,plain,
c_Transcendental_Oexp(c_Transcendental_Oln(v_t____),tc_RealDef_Oreal) = v_t____,
inference('HYPERRESOLVE',[status(thm)],[cls_exp__ln_0,cls_t_I1_J_0]) ).
cnf(1404,plain,
c_Transcendental_Oexp(c_Transcendental_Oln(v_m____),tc_RealDef_Oreal) = v_m____,
inference('HYPERRESOLVE',[status(thm)],[cls_exp__ln_0,cls_m_I1_J_0]) ).
cnf(1457,plain,
c_HOL_Ominus__class_Ominus(X,c_HOL_Ouminus__class_Ouminus(Y,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X,Y,tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_diff__minus__eq__add_0,clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]) ).
cnf(1462,plain,
( c_Transcendental_Oln(c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_Transcendental_Oln(X),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oln(Y),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),Y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X,tc_RealDef_Oreal) ),
inference('REWRITE',[status(thm)],[cls_ln__mult_0,1457,theory(equality)]) ).
cnf(1473,plain,
c_HOL_Ominus__class_Ominus(X,c_HOL_Ouminus__class_Ouminus(Y,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(Y,c_HOL_Ouminus__class_Ouminus(X,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1289,1457,theory(equality)]) ).
cnf(1550,plain,
c_HOL_Oinverse__class_Odivide(X,Y,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X,c_HOL_Oinverse__class_Oinverse(Y,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_divide__inverse_0,clsarity_RealDef__Oreal__Ring__and__Field_Ofield]) ).
cnf(1621,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal),Z,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(Y,c_HOL_Otimes__class_Otimes(X,Z,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('PARAMODULATE',[status(thm)],[cls_real__mult__assoc_0,cls_real__mult__commute_0,theory(equality)]) ).
cnf(1622,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal),Z,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X,c_HOL_Otimes__class_Otimes(Z,Y,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('PARAMODULATE',[status(thm)],[cls_real__mult__assoc_0,cls_real__mult__commute_0,theory(equality)]) ).
cnf(1623,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1116,1622,theory(equality)]) ).
cnf(1624,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_t____,v_m____,tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[896,1622,theory(equality)]) ).
cnf(1629,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X,c_HOL_Otimes__class_Otimes(Y,Z,tc_RealDef_Oreal),tc_RealDef_Oreal),U,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X,Y,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(Z,U,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('PARAMODULATE',[status(thm)],[cls_real__mult__assoc_0,cls_real__mult__assoc_0,theory(equality)]) ).
cnf(1832,plain,
c_Power_Opower__class_Opower(X,c_Suc(Y),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X,c_Power_Opower__class_Opower(X,Y,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_class__semiring_Osemiring__rules_I35_J_0,clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(1839,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1623,1629,1832,theory(equality)]) ).
cnf(1840,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1624,1621,1629,1832,theory(equality)]) ).
cnf(1842,plain,
c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(X,Y,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(X,tc_Complex_Ocomplex),Y,tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_norm__power_0,clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
cnf(1845,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1839,1842,theory(equality)]) ).
cnf(1846,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1840,1842,theory(equality)]) ).
cnf(1851,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X,Y,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(Y,X,tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_inverse__divide_0,clsarity_RealDef__Oreal__Ring__and__Field_Ofield,clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero]) ).
cnf(1890,plain,
c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_exp__minus_0,clsarity_RealDef__Oreal__SEQ_Obanach,clsarity_RealDef__Oreal__RealVector_Oreal__normed__field]) ).
cnf(1913,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,X,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_zero__less__power_0,clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,cls_t_I1_J_0]) ).
cnf(2257,plain,
c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X,Y,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X,tc_RealDef_Oreal),c_Transcendental_Oexp(Y,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_exp__diff_0,clsarity_RealDef__Oreal__SEQ_Obanach,clsarity_RealDef__Oreal__RealVector_Oreal__normed__field]) ).
cnf(2263,plain,
c_HOL_Ouminus__class_Ouminus(v_t____,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[cls_less__eqI_0,clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,cls_real__less__def_1,cls_t_I1_J_0]),1119,1312,theory(equality)]) ).
cnf(2264,plain,
c_HOL_Ouminus__class_Ouminus(v_m____,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[cls_less__eqI_0,clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,cls_real__less__def_1,cls_m_I1_J_0]),1119,1312,theory(equality)]) ).
cnf(2295,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X,Y,tc_RealDef_Oreal),Z,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X,Z,tc_RealDef_Oreal),Y,tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_mult__frac__num_0,clsarity_RealDef__Oreal__Ring__and__Field_Ofield,clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero]) ).
cnf(2305,plain,
c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(Y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X,tc_RealDef_Oreal),c_Transcendental_Oexp(Y,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[cls_exp__add_0,clsarity_RealDef__Oreal__SEQ_Obanach,clsarity_RealDef__Oreal__RealVector_Oreal__normed__field]),1890,2257,1457,theory(equality)]) ).
cnf(2386,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_real__mult__order_0,cls_t_I1_J_0,cls_m_I1_J_0]) ).
cnf(2387,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[cls_real__mult__order_0,cls_m_I1_J_0,cls_t_I1_J_0]) ).
cnf(3428,plain,
c_Transcendental_Oln(c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_Transcendental_Oln(v_t____),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oln(v_m____),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[1462,cls_t_I1_J_0,cls_m_I1_J_0]),1473,theory(equality)]) ).
cnf(3429,plain,
c_Transcendental_Oln(c_HOL_Otimes__class_Otimes(v_t____,v_m____,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_Transcendental_Oln(v_t____),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oln(v_m____),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('HYPERRESOLVE',[status(thm)],[1462,cls_m_I1_J_0,cls_t_I1_J_0]) ).
cnf(3435,plain,
c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(Y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(X,c_HOL_Ouminus__class_Ouminus(Y,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[1462,cls_exp__gt__zero_0,cls_exp__gt__zero_0]),cls_ln__unique_0,2305,theory(equality)]) ).
cnf(3441,plain,
c_Transcendental_Oln(c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal)) = c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference('REWRITE',[status(thm)],[3428,1404,1403,3435,theory(equality)]) ).
cnf(3442,plain,
c_Transcendental_Oln(c_HOL_Otimes__class_Otimes(v_t____,v_m____,tc_RealDef_Oreal)) = c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference('REWRITE',[status(thm)],[3429,1404,1403,3435,theory(equality)]) ).
cnf(3885,plain,
c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(Y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(X,Y,tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1457,3435,theory(equality)]) ).
cnf(9079,plain,
v_t____ != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[cls_eq__neg__iff__add__eq__0_1,2263,clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]),cls_ln__unique_0,1388,1304,cls_exp__eq__one__iff_1,3885,theory(equality)]) ).
cnf(9363,plain,
c_HOL_Oinverse__class_Oinverse(v_t____,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference('UR-RESOLVE',[status(thm)],[cls_inverse__zero__imp__zero_0,9079,clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring]) ).
cnf(9603,plain,
v_m____ != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[cls_eq__neg__iff__add__eq__0_1,2264,clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]),cls_ln__unique_0,1388,1304,cls_exp__eq__one__iff_1,3885,theory(equality)]) ).
cnf(9935,plain,
c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference('UR-RESOLVE',[status(thm)],[cls_inverse__zero__imp__zero_0,9603,clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring]) ).
cnf(43463,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,X,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,X,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[cls_mult__strict__left__mono_0,1913,clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,1846]),1115,theory(equality)]) ).
cnf(45306,plain,
c_Transcendental_Oexp(c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(v_m____,v_t____,tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[cls_ln__inj__iff_0,2386,cls_ln__unique_0,cls_exp__gt__zero_0]),3441,theory(equality)]) ).
cnf(45307,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[1845,45306,theory(equality)]) ).
cnf(46100,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,X,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,X,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[43463,45306,theory(equality)]) ).
cnf(46343,plain,
c_Transcendental_Oexp(c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(v_t____,v_m____,tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[cls_ln__inj__iff_0,2387,cls_ln__unique_0,cls_exp__gt__zero_0]),3442,theory(equality)]) ).
cnf(68985,plain,
c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(c_Transcendental_Oln(c_HOL_Oinverse__class_Odivide(v_t____,c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[cls_nonzero__inverse__mult__distrib_0,9935,clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,9363]),46343,1388,1851,1550,theory(equality)]) ).
cnf(68987,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[45307,2295,68985,theory(equality)]) ).
cnf(69616,plain,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,X,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,X,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference('REWRITE',[status(thm)],[46100,2295,68985,theory(equality)]) ).
cnf(71261,plain,
$false,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[68987,cls_real__mult__assoc_0,theory(equality)]),69616,2295,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG407-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n026.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 : Wed Jun 8 21:30:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-08T21:30:02
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-06-08T21:30:02
% 0.47/0.70
% 0.47/0.70 ; Recognized possible right inverse assertion (|c_HOL_Oord__class_Oless| ?X (|c_Suc| ?X) |tc_nat|).
% 0.54/0.73 WARNING:
% 0.54/0.73 |class_OrderedGroup_Oab__semigroup__idem__mult| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 0.54/0.73 WARNING:
% 0.54/0.73 |class_Lattices_Oboolean__algebra| is a 1-ary relation that occurs only negatively; disabling rows that contain it.
% 237.13/237.29 ; Recognized possible right inverse assertion (|c_HOL_Oord__class_Oless| ?X (|c_Suc| ?X) |tc_nat|).
% 237.13/237.29
% 237.13/237.29 #||
% 237.13/237.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 237.13/237.29 % SZS output start Refutation
% See solution above
% 237.23/237.38 ||#
% 237.23/237.38
% 237.23/237.38 ; Summary of computation:
% 237.23/237.38 ; 685997 formulas have been input or derived (from 1294 formulas).
% 237.23/237.38 ; 71261 (10%) were retained. Of these,
% 237.23/237.38 ; 10172 (14%) were simplified or subsumed later,
% 237.23/237.38 ; 61089 (86%) are still being kept.
% 237.23/237.38 ;
% 237.23/237.38 ; Run time in seconds excluding printing time:
% 237.23/237.38 ; 0.217 0% Read assertion file (1 call)
% 237.23/237.38 ; 0.029 0% Assert (1,232 calls)
% 237.23/237.38 ; 15.135 6% Process new row (629,442 calls)
% 237.23/237.38 ; 68.461 29% Resolution (2,586 calls)
% 237.23/237.38 ; 0.130 0% Paramodulation (1,293 calls)
% 237.23/237.38 ; 0.000 0% Factoring (22 calls)
% 237.23/237.38 ; 1.628 1% Condensing (175,573 calls)
% 237.23/237.38 ; 64.682 27% Forward subsumption (175,573 calls)
% 237.23/237.38 ; 9.936 4% Backward subsumption (23,049 calls)
% 237.23/237.38 ; 6.668 3% Clause clause subsumption (1,271,418 calls)
% 237.23/237.38 ; 46.355 20% Forward simplification (600,809 calls)
% 237.23/237.38 ; 4.670 2% Backward simplification (71,251 calls)
% 237.23/237.38 ; 16.687 7% Ordering (2,057,189 calls)
% 237.23/237.38 ; 0.000 0% Sortal reasoning (32 calls)
% 237.23/237.39 ; 0.003 0% Purity testing (1 call)
% 237.23/237.39 ; 2.231 1% Other
% 237.23/237.39 ; 236.832 Total
% 237.23/237.39 ; 236.918 Real time
% 237.23/237.39 ;
% 237.23/237.40 ; Term-hash-array has 147,706 terms in all.
% 237.23/237.40 ; Feature-vector-row-index has 20,148 entries (20,148 at peak, 23,049 added, 2,901 deleted).
% 237.23/237.40 ; Feature-vector-row-index has 88,587 nodes (88,587 at peak, 111,732 added, 23,145 deleted).
% 237.23/237.40 ; Retrieved 6,453,077 possibly forward subsuming rows in 175,573 calls.
% 237.23/237.40 ; Retrieved 355,660 possibly backward subsumed rows in 23,049 calls.
% 237.23/237.40 ; Path-index has 128,744 entries (128,744 at peak, 151,610 added, 22,866 deleted).
% 237.23/237.40 ; Path-index has 73,367 nodes (73,510 at peak, 82,395 added, 9,028 deleted).
% 237.23/237.40 ; Trie-index has 128,744 entries (128,744 at peak, 151,610 added, 22,866 deleted).
% 237.23/237.40 ; Trie-index has 1,147,351 nodes (1,147,351 at peak, 1,384,615 added, 237,264 deleted).
% 237.23/237.40 ; Retrieved 4,105,470 generalization terms in 6,464,209 calls.
% 237.23/237.40 ; Retrieved 67,381 instance terms in 48,758 calls.
% 237.23/237.40 ; Retrieved 87,907,164 unifiable terms in 282,655 calls.
% 237.23/237.40 ;
% 237.23/237.40 ; The agenda of rows to process has 153 entries:
% 237.23/237.40 ; 1 with value 38 13 with value 47 5 with value 53
% 237.23/237.40 ; 1 with value 39 21 with value 48 1 with value 59
% 237.23/237.40 ; 2 with value 42 19 with value 49 1 with value 60
% 237.23/237.40 ; 4 with value 43 18 with value 50 1 with value 63
% 237.23/237.40 ; 1 with value 44 20 with value 51 2 with value 75
% 237.23/237.40 ; 9 with value 45 16 with value 52 4 with value 77
% 237.23/237.40 ; 14 with value 46
% 237.23/237.40 ; The agenda of rows to give has 59819 entries:
% 237.23/237.40 ; 35 with value (4 11) 1693 with value (4 47) 8 with value (4 83)
% 237.23/237.40 ; 259 with value (4 12) 1378 with value (4 48) 12 with value (4 84)
% 237.23/237.40 ; 336 with value (4 13) 1016 with value (4 49) 1 with value (4 85)
% 237.23/237.40 ; 558 with value (4 14) 437 with value (4 50) 5 with value (4 86)
% 237.23/237.40 ; 845 with value (4 15) 390 with value (4 51) 5 with value (4 87)
% 237.23/237.40 ; 1316 with value (4 16) 431 with value (4 52) 10 with value (4 88)
% 237.23/237.40 ; 1290 with value (4 17) 398 with value (4 53) 11 with value (4 89)
% 237.23/237.40 ; 1379 with value (4 18) 495 with value (4 54) 6 with value (4 90)
% 237.23/237.40 ; 1794 with value (4 19) 405 with value (4 55) 12 with value (4 91)
% 237.23/237.40 ; 1188 with value (4 20) 451 with value (4 56) 12 with value (4 92)
% 237.23/237.40 ; 1830 with value (4 21) 465 with value (4 57) 20 with value (4 93)
% 237.23/237.40 ; 1826 with value (4 22) 492 with value (4 58) 9 with value (4 94)
% 237.23/237.40 ; 2258 with value (4 23) 525 with value (4 59) 11 with value (4 95)
% 237.23/237.40 ; 2022 with value (4 24) 415 with value (4 60) 6 with value (4 96)
% 237.23/237.40 ; 1852 with value (4 25) 441 with value (4 61) 5 with value (4 97)
% 237.23/237.40 ; 1551 with value (4 26) 240 with value (4 62) 17 with value (4 98)
% 237.23/237.40 ; 1515 with value (4 27) 202 with value (4 63) 18 with value (4 99)
% 237.23/237.40 ; 1614 with value (4 28) 224 with value (4 64) 5 with value (4 100)
% 237.23/237.40 ; 1418 with value (4 29) 287 with value (4 65) 8 with value (4 101)
% 237.23/237.40 ; 1387 with value (4 30) 239 with value (4 66) 14 with value (4 102)
% 237.23/237.40 ; 1264 with value (4 31) 205 with value (4 67) 15 with value (4 103)
% 237.23/237.40 ; 1077 with value (4 32) 200 with value (4 68) 1 with value (4 104)
% 237.23/237.40 ; 1119 with value (4 33) 212 with value (4 69) 4 with value (4 106)
% 237.23/237.40 ; 928 with value (4 34) 177 with value (4 70) 7 with value (4 107)
% 237.23/237.40 ; 1382 with value (4 35) 255 with value (4 71) 11 with value (4 108)
% 237.23/237.40 ; 795 with value (4 36) 179 with value (4 72) 9 with value (4 109)
% 237.23/237.40 ; 1109 with value (4 37) 237 with value (4 73) 8 with value (4 110)
% 237.23/237.40 ; 945 with value (4 38) 107 with value (4 74) 8 with value (4 111)
% 237.23/237.40 ; 1263 with value (4 39) 102 with value (4 75) 6 with value (4 112)
% 237.23/237.40 ; 1061 with value (4 40) 99 with value (4 76) 1 with value (4 116)
% 237.23/237.40 ; 1347 with value (4 41) 60 with value (4 77) 1 with value (4 117)
% 237.23/237.40 ; 1692 with value (4 42) 40 with value (4 78) 1 with value (4 120)
% 237.23/237.40 ; 1653 with value (4 43) 65 with value (4 79) 1 with value (4 125)
% 237.23/237.40 ; 1689 with value (4 44) 17 with value (4 80) 1 with value (4 126)
% 237.23/237.40 ; 1634 with value (4 45) 39 with value (4 81) 4 with value (4 131)
% 237.23/237.40 ; 1681 with value (4 46) 16 with value (4 82)
% 237.23/237.40 Evaluation took:
% 237.23/237.40 236.934 seconds of real time
% 237.23/237.40 226.29375 seconds of user run time
% 237.23/237.40 10.651639 seconds of system run time
% 237.23/237.40 [Run times include 61.452 seconds GC run time.]
% 237.23/237.40 0 calls to %EVAL
% 237.23/237.40 0 page faults and
% 237.23/237.40 13,353,672,376 bytes consed.
% 237.23/237.40 :PROOF-FOUND
% 237.23/237.40 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-08T21:33:59
% 237.23/237.40 :PROOF-FOUND
% 237.23/237.40 *
%------------------------------------------------------------------------------