TSTP Solution File: SWW259+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW259+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 : 300s
% DateTime : Tue Aug 22 11:06:56 EDT 2023
% Result : Theorem 223.27s 185.33s
% Output : CNFRefutation 223.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 160
% Syntax : Number of formulae : 195 ( 25 unt; 148 typ; 0 def)
% Number of atoms : 107 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 51 ~; 46 |; 2 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 184 ( 119 >; 65 *; 0 +; 0 <<)
% Number of predicates : 75 ( 73 usr; 2 prp; 0-3 aty)
% Number of functors : 75 ( 75 usr; 28 con; 0-4 aty)
% Number of variables : 42 (; 41 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Rings_Odvd__class_Odvd > c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant > c_Polynomial_Opos__poly > hBOOL > class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct > class_Rings_Ozero__neq__one > class_Rings_Osemiring__0 > class_Rings_Osemiring > class_Rings_Oring__no__zero__divisors > class_Rings_Oring__1__no__zero__divisors > class_Rings_Oring__1 > class_Rings_Oring > class_Rings_Oordered__semiring > class_Rings_Oordered__ring > class_Rings_Oordered__comm__semiring > class_Rings_Oordered__cancel__semiring > class_Rings_Ono__zero__divisors > class_Rings_Omult__zero > class_Rings_Olinordered__semiring__strict > class_Rings_Olinordered__semiring__1__strict > class_Rings_Olinordered__semiring__1 > class_Rings_Olinordered__semiring > class_Rings_Olinordered__semidom > class_Rings_Olinordered__ring__strict > class_Rings_Olinordered__ring > class_Rings_Olinordered__idom > class_Rings_Olinordered__comm__semiring__strict > class_Rings_Oidom > class_Rings_Odvd > class_Rings_Odivision__ring__inverse__zero > class_Rings_Odivision__ring > class_Rings_Ocomm__semiring__1 > class_Rings_Ocomm__semiring__0 > class_Rings_Ocomm__semiring > class_Rings_Ocomm__ring__1 > class_Rings_Ocomm__ring > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Oord > class_Orderings_Olinorder > class_Int_Oring__char__0 > class_Groups_Ozero > class_Groups_Oordered__comm__monoid__add > class_Groups_Oordered__cancel__ab__semigroup__add > class_Groups_Oordered__ab__semigroup__add__imp__le > class_Groups_Oordered__ab__semigroup__add > class_Groups_Oordered__ab__group__add > class_Groups_Oone > class_Groups_Omonoid__mult > class_Groups_Omonoid__add > class_Groups_Olinordered__ab__group__add > class_Groups_Ogroup__add > class_Groups_Ocomm__monoid__mult > class_Groups_Ocomm__monoid__add > class_Groups_Ocancel__semigroup__add > class_Groups_Ocancel__comm__monoid__add > class_Groups_Ocancel__ab__semigroup__add > class_Groups_Oab__semigroup__mult > class_Groups_Oab__semigroup__add > class_Groups_Oab__group__add > class_Fields_Olinordered__field__inverse__zero > class_Fields_Olinordered__field > class_Fields_Ofield__inverse__zero > class_Fields_Ofield > class_Divides_Osemiring__div > c_Power_Opower_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Polynomial_Oorder > c_Polynomial_Omonom > c_Groups_Oplus__class_Oplus > c_Groups_Ominus__class_Ominus > c_Divides_Odiv__class_Odiv > tc_fun > hAPP > c_Rings_Oinverse__class_Oinverse > c_RealVector_Onorm__class_Onorm > c_Polynomial_Opoly > c_Nat__Transfer_Otsub > c_Groups_Ouminus__class_Ouminus > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > tc_Polynomial_Opoly > c_Power_Opower__class_Opower > c_Nat_OSuc > c_Groups_Ozero__class_Ozero > c_Groups_Otimes__class_Otimes > c_Groups_Oone__class_Oone > c_Complex_Oexpi > v_w____ > v_thesis____ > v_s____ > v_q____ > v_pa____ > v_p > v_m____ > v_k____ > v_c____ > v_a____ > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > c_Complex_Oii > #skF_17 > #skF_2 > #skF_18 > #skF_35 > #skF_6 > #skF_15 > #skF_25 > #skF_19 > #skF_29 > #skF_34 > #skF_26 > #skF_12 > #skF_30 > #skF_14 > #skF_33 > #skF_13 > #skF_5 > #skF_10 > #skF_3 > #skF_8 > #skF_21 > #skF_32 > #skF_31 > #skF_23 > #skF_28 > #skF_11 > #skF_22 > #skF_24 > #skF_27 > #skF_7 > #skF_1 > #skF_9 > #skF_4 > #skF_20 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
tff(class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
tff(class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
tff(c_Nat__Transfer_Otsub,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(class_Groups_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
tff(tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
tff(class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
tff(class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff('#skF_35',type,
'#skF_35': $i > $i ).
tff(class_Groups_Ocancel__comm__monoid__add,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Rings_Ocomm__ring,type,
class_Rings_Ocomm__ring: $i > $o ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(class_Rings_Odvd,type,
class_Rings_Odvd: $i > $o ).
tff(c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Polynomial_Osynthetic__div,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff(v_thesis____,type,
v_thesis____: $o ).
tff(c_Polynomial_Omonom,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(c_Power_Opower_Opower,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_Rings_Ocomm__semiring__0,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff(class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(c_Complex_Oii,type,
c_Complex_Oii: $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i ) > $i ).
tff(class_Rings_Odivision__ring,type,
class_Rings_Odivision__ring: $i > $o ).
tff(c_Complex_Oexpi,type,
c_Complex_Oexpi: $i > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i ) > $i ).
tff(class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff('#skF_33',type,
'#skF_33': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Osmult,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(class_Rings_Odivision__ring__inverse__zero,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(class_Rings_Oring__1,type,
class_Rings_Oring__1: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(c_Rings_Odvd__class_Odvd,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(v_m____,type,
v_m____: $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_Polynomial_Opos__poly,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
tff(class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
tff(c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(v_k____,type,
v_k____: $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(class_Fields_Olinordered__field,type,
class_Fields_Olinordered__field: $i > $o ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Rings_Oidom,type,
class_Rings_Oidom: $i > $o ).
tff(class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i * $i ) > $i ).
tff(class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
tff(c_Groups_Ouminus__class_Ouminus,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff(c_Polynomial_OpCons,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_Nat_OSuc,type,
c_Nat_OSuc: $i > $i ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_c____,type,
v_c____: $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i * $i ) > $i ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff(c_Polynomial_Opcompose,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(v_w____,type,
v_w____: $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(v_p,type,
v_p: $i ).
tff(class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(v_a____,type,
v_a____: $i ).
tff(c_Rings_Oinverse__class_Oinverse,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(class_Fields_Olinordered__field__inverse__zero,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(v_q____,type,
v_q____: $i ).
tff(class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(c_Polynomial_Oorder,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(v_s____,type,
v_s____: $i ).
tff(v_pa____,type,
v_pa____: $i ).
tff(f_5712,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
tff(f_1466,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
tff(f_5742,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
tff(f_5734,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
tff(f_175,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( ( V_x != V_y )
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
tff(f_179,axiom,
! [V_w,V_z] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
tff(f_3130,axiom,
! [V_n] : ( c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
tff(f_6032,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f_6030,hypothesis,
! [B_t] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
=> v_thesis____ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_4740,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
tff(f_43,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv0) ).
tff(f_41,axiom,
! [V_d2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)
=> ? [B_e] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,V_d2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096) ).
tff(c_3031,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5712]) ).
tff(c_682,plain,
! [T_a_716,V_aa_2_715] :
( c_Orderings_Oord__class_Oless(T_a_716,c_Groups_Ouminus__class_Ouminus(T_a_716,V_aa_2_715),V_aa_2_715)
| ~ c_Orderings_Oord__class_Oless(T_a_716,c_Groups_Ozero__class_Ozero(T_a_716),V_aa_2_715)
| ~ class_Groups_Olinordered__ab__group__add(T_a_716) ),
inference(cnfTransformation,[status(thm)],[f_1466]) ).
tff(c_3091,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5742]) ).
tff(c_3075,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5734]) ).
tff(c_51042,plain,
! [T_a_3831,V_y_3832,V_x_3833] :
( c_Orderings_Oord__class_Oless(T_a_3831,V_y_3832,V_x_3833)
| c_Orderings_Oord__class_Oless(T_a_3831,V_x_3833,V_y_3832)
| ( V_y_3832 = V_x_3833 )
| ~ class_Rings_Olinordered__idom(T_a_3831) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_68,plain,
! [V_z_58,V_w_57] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_58),V_w_57) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w_57),V_z_58) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_1727,plain,
! [V_n_1557] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_1557,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(V_n_1557) ),
inference(cnfTransformation,[status(thm)],[f_3130]) ).
tff(c_3323,plain,
~ v_thesis____,
inference(cnfTransformation,[status(thm)],[f_6032]) ).
tff(c_3321,plain,
! [B_t_2799] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
inference(cnfTransformation,[status(thm)],[f_6030]) ).
tff(c_3324,plain,
! [B_t_2799] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
inference(negUnitSimplification,[status(thm)],[c_3323,c_3321]) ).
tff(c_3343,plain,
! [B_t_2799] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
inference(demodulation,[status(thm),theory(equality)],[c_1727,c_3324]) ).
tff(c_3470,plain,
! [B_t_2799] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_3343]) ).
tff(c_51261,plain,
! [V_y_3832] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_3832,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_3832)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))),V_y_3832)
| ( c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))) = V_y_3832 )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_51042,c_3470]) ).
tff(c_51579,plain,
! [V_y_3832] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_3832,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_3832)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))),V_y_3832)
| ( c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))) = V_y_3832 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3075,c_51261]) ).
tff(c_92565,plain,
! [T_a_113848,V_x_113849,V_z_113850,V_y_113851] :
( c_Orderings_Oord__class_Oless(T_a_113848,V_x_113849,V_z_113850)
| ~ c_Orderings_Oord__class_Oless(T_a_113848,V_y_113851,V_z_113850)
| ~ c_Orderings_Oord__class_Oless(T_a_113848,V_x_113849,V_y_113851)
| ~ class_Orderings_Opreorder(T_a_113848) ),
inference(cnfTransformation,[status(thm)],[f_4740]) ).
tff(c_92605,plain,
! [V_x_113849,V_y_3832] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_113849,V_y_3832)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_113849,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_3832,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_3832)
| ( c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))) = V_y_3832 ) ),
inference(resolution,[status(thm)],[c_51579,c_92565]) ).
tff(c_93323,plain,
! [V_x_114265,V_y_114266] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_114265,V_y_114266)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_114265,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_114266,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_114266)
| ( c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))) = V_y_114266 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_3091,c_92605]) ).
tff(c_93326,plain,
! [V_y_114266] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),V_y_114266)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_114266,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_114266)
| ( c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))) = V_y_114266 )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))))
| ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_682,c_93323]) ).
tff(c_93358,plain,
! [V_y_114266] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),V_y_114266)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_114266,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_114266)
| ( c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))) = V_y_114266 )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_3031,c_93326]) ).
tff(c_96144,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),
inference(splitLeft,[status(thm)],[c_93358]) ).
tff(c_12,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_3473,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_1727,c_12]) ).
tff(c_399404,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_96144,c_3473]) ).
tff(c_399406,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),
inference(splitRight,[status(thm)],[c_93358]) ).
tff(c_6,plain,
! [V_d2_4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(V_d2_4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_8,plain,
! [V_d2_4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),'#skF_2'(V_d2_4))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_4,plain,
! [V_d2_4] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(V_d2_4),V_d2_4)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2_4) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_399633,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),
inference(resolution,[status(thm)],[c_399406,c_4]) ).
tff(c_406788,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),'#skF_2'(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))))) ),
inference(resolution,[status(thm)],[c_399633,c_3470]) ).
tff(c_407130,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),'#skF_2'(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))))),
inference(splitLeft,[status(thm)],[c_406788]) ).
tff(c_407559,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),
inference(resolution,[status(thm)],[c_8,c_407130]) ).
tff(c_407566,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_399406,c_407559]) ).
tff(c_407567,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(splitRight,[status(thm)],[c_406788]) ).
tff(c_408004,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),
inference(resolution,[status(thm)],[c_6,c_407567]) ).
tff(c_408026,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_399406,c_408004]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW259+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n004.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
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 19:18:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 223.27/185.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 223.27/185.34
% 223.27/185.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 223.36/185.37
% 223.36/185.37 Inference rules
% 223.36/185.37 ----------------------
% 223.36/185.37 #Ref : 152
% 223.36/185.37 #Sup : 83657
% 223.36/185.37 #Fact : 16
% 223.36/185.37 #Define : 0
% 223.36/185.37 #Split : 111
% 223.36/185.37 #Chain : 0
% 223.36/185.37 #Close : 0
% 223.36/185.37
% 223.36/185.37 Ordering : KBO
% 223.36/185.37
% 223.36/185.37 Simplification rules
% 223.36/185.37 ----------------------
% 223.36/185.37 #Subsume : 30605
% 223.36/185.37 #Demod : 50063
% 223.36/185.37 #Tautology : 13782
% 223.36/185.37 #SimpNegUnit : 3403
% 223.36/185.37 #BackRed : 17
% 223.36/185.37
% 223.36/185.37 #Partial instantiations: 158436
% 223.36/185.37 #Strategies tried : 1
% 223.36/185.37
% 223.36/185.37 Timing (in seconds)
% 223.36/185.37 ----------------------
% 223.36/185.38 Preprocessing : 2.42
% 223.36/185.38 Parsing : 1.33
% 223.36/185.38 CNF conversion : 0.19
% 223.36/185.38 Main loop : 181.85
% 223.36/185.38 Inferencing : 17.16
% 223.36/185.38 Reduction : 104.12
% 223.36/185.38 Demodulation : 81.30
% 223.36/185.38 BG Simplification : 0.66
% 223.36/185.38 Subsumption : 48.90
% 223.36/185.38 Abstraction : 0.92
% 223.36/185.38 MUC search : 0.00
% 223.36/185.38 Cooper : 0.00
% 223.36/185.38 Total : 184.34
% 223.36/185.38 Index Insertion : 0.00
% 223.36/185.38 Index Deletion : 0.00
% 223.36/185.38 Index Matching : 0.00
% 223.36/185.38 BG Taut test : 0.00
%------------------------------------------------------------------------------