%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:40 AM UTC 2026
% Result : Theorem 42.64s 17.14s
% Output : Refutation 47.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1106
% Syntax : Number of formulae : 2214 ( 667 unt; 0 typ; 0 def)
% Number of atoms : 5937 (1606 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 35583 ( 317 ~; 136 |; 525 &;31543 @)
% ( 257 <=>;2805 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 100 usr; 8 con; 0-5 aty)
% Number of variables : 5085 ( 0 ^;5018 !; 67 ?;5085 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i ).
thf(v_f_____decl,type,
v_f____: $i ).
thf(v_ga_____decl,type,
v_ga____: $i ).
thf(class_Groups_Olinordered__ab__group__add_decl,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_decl,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Groups_Oordered__ab__group__add_decl,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(tc_Int_Oint_decl,type,
tc_Int_Oint: $i ).
thf(class_Rings_Oring_decl,type,
class_Rings_Oring: $i > $o ).
thf(c_Groups_Otimes__class_Otimes_decl,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(class_Rings_Oring__1_decl,type,
class_Rings_Oring__1: $i > $o ).
thf(c_Int_Oring__1__class_Oof__int_decl,type,
c_Int_Oring__1__class_Oof__int: $i > $i > $i ).
thf(class_Rings_Oordered__ring_decl,type,
class_Rings_Oordered__ring: $i > $o ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(class_Rings_Olinordered__semiring__1__strict_decl,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Rings_Olinordered__semiring__1_decl,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_decl,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(c_Groups_Ominus__class_Ominus_decl,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Power_Opower__class_Opower_decl,type,
c_Power_Opower__class_Opower: $i > $i ).
thf(c_Groups_Oone__class_Oone_decl,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(class_Rings_Ocomm__ring__1_decl,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(c_Int_Onat_decl,type,
c_Int_Onat: $i ).
thf(class_Rings_Oidom_decl,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_decl,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Oordered__semiring_decl,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_RealDef_Oreal_decl,type,
c_RealDef_Oreal: $i > $i ).
thf(class_Power_Opower_decl,type,
class_Power_Opower: $i > $o ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i > $i ).
thf(class_Rings_Ocomm__semiring__1_decl,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_decl,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Rings_Omult__zero_decl,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Groups_Ominus_decl,type,
class_Groups_Ominus: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(class_Rings_Ocomm__semiring_decl,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(c_SMT_Oz3div_decl,type,
c_SMT_Oz3div: $i > $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_decl,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Rings_Olinordered__idom_decl,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_RComplete_Onatceiling_decl,type,
c_RComplete_Onatceiling: $i > $i ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_decl,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Ono__zero__divisors_decl,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_decl,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_decl,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_decl,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(c_Transcendental_Oln_decl,type,
c_Transcendental_Oln: $i > $i ).
thf(class_Groups_Ozero_decl,type,
class_Groups_Ozero: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_decl,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Rings_Olinordered__semidom_decl,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_decl,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Groups_Oab__semigroup__add_decl,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Rings_Osemiring__1_decl,type,
class_Rings_Osemiring__1: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_decl,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Fun_Oswap_decl,type,
c_Fun_Oswap: $i > $i > $i > $i > $i > $i ).
thf(c_RComplete_Onatfloor_decl,type,
c_RComplete_Onatfloor: $i > $i ).
thf(class_Rings_Olinordered__ring_decl,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(c_Nat__Transfer_Otsub_decl,type,
c_Nat__Transfer_Otsub: $i > $i > $i ).
thf(class_Groups_Oone_decl,type,
class_Groups_Oone: $i > $o ).
thf(class_Rings_Ozero__neq__one_decl,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Groups_Omonoid__mult_decl,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_decl,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Rings_Olinordered__comm__semiring__strict_decl,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_decl,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(c_Orderings_Oorder__class_Ostrict__mono_decl,type,
c_Orderings_Oorder__class_Ostrict__mono: $i > $i > $i > $o ).
thf(class_Groups_Omonoid__add_decl,type,
class_Groups_Omonoid__add: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_decl,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Osemiring_decl,type,
class_Rings_Osemiring: $i > $o ).
thf(c_Nat_Ofunpow_decl,type,
c_Nat_Ofunpow: $i > $i ).
thf(c_Nat_Ocompow_decl,type,
c_Nat_Ocompow: $i > $i > $i ).
thf(class_Rings_Osemiring__0_decl,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_RealVector_Ometric__space_decl,type,
class_RealVector_Ometric__space: $i > $o ).
thf(c_SEQ_Oconvergent_decl,type,
c_SEQ_Oconvergent: $i > $i > $o ).
thf(c_SEQ_OCauchy_decl,type,
c_SEQ_OCauchy: $i > $i > $o ).
thf(class_SEQ_Ocomplete__space_decl,type,
class_SEQ_Ocomplete__space: $i > $o ).
thf(class_Rings_Olinordered__semiring_decl,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_decl,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(c_Nat__Transfer_Otransfer__morphism_decl,type,
c_Nat__Transfer_Otransfer__morphism: $i > $i > $i > $i > $o ).
thf(v_r_decl,type,
v_r: $i ).
thf(c_Record_Oiso__tuple__update__accessor__cong__assist_decl,type,
c_Record_Oiso__tuple__update__accessor__cong__assist: $i > $i > $i > $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_decl,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_SEQ_Osubseq_decl,type,
c_SEQ_Osubseq: $i > $o ).
thf(class_Lattices_Oab__semigroup__idem__mult_decl,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(c_SEQ_Odecseq_decl,type,
c_SEQ_Odecseq: $i > $i > $o ).
thf(c_SEQ_Oincseq_decl,type,
c_SEQ_Oincseq: $i > $i > $o ).
thf(c_Int_Onat__aux_decl,type,
c_Int_Onat__aux: $i > $i > $i ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(1168,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(895,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
thf(4262,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(513,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
thf(2876,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
thf(2463,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(3969,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(823,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Olinorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__mono__eq) ).
thf(4015,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Olinorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) )
& ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1057,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).
thf(4877,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(1554,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(783,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(3873,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
thf(4188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( D @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__mult) ).
thf(2094,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(799,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__zero) ).
thf(3944,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(463,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(2744,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3div__def) ).
thf(1369,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_SMT_Oz3div ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(1823,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(362,axiom,
tc_RealDef_Oreal @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(2336,plain,
tc_RealDef_Oreal @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
thf(2131,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1064,axiom,
tc_Nat_Onat @ class_Rings_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(4909,plain,
tc_Nat_Onat @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(824,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(4022,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(728,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(3666,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1014,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(4729,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
thf(3434,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(592,axiom,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
thf(3167,plain,
! [A: $i,B: $i] :
( ( B @ class_Power_Opower )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(732,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(3698,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(808,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(3979,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(2595,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(70,axiom,
tc_RealDef_Oreal @ class_Rings_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(1315,plain,
tc_RealDef_Oreal @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(779,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(3863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(5028,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1013,axiom,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(4728,plain,
tc_Nat_Onat @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(1686,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(2250,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1068,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(4931,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(562,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).
thf(3072,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(1882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(2622,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B = A )
=> ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(128,axiom,
tc_Int_Oint @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1522,plain,
tc_Int_Oint @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__eq) ).
thf(2062,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(2776,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
thf(1401,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(794,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) )
<=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
thf(3910,plain,
! [A: $i,B: $i] :
( ( ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) )
=> ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) )
=> ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat) ).
thf(1205,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(499,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
thf(2837,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
thf(4215,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
thf(4623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(25,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(1173,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(1211,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
thf(3990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1010,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4714,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B = A )
| ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(1158,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(297,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__neg) ).
thf(2117,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(291,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zminus__int) ).
thf(2104,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(3040,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(4391,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(587,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0) ).
thf(3153,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
thf(1422,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1007,axiom,
v_f____ @ c_SEQ_Osubseq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f_I1_J) ).
thf(4697,plain,
v_f____ @ c_SEQ_Osubseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(2248,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc) ).
thf(1793,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power) ).
thf(3402,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
thf(1533,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(651,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
thf(3382,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(4479,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
thf(1655,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(10,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(1137,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(2740,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).
thf(1999,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
thf(1327,plain,
! [A: $i,B: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(890,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).
thf(4247,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(635,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
thf(3313,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).
thf(2042,plain,
! [A: $i] :
( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(4980,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
thf(3848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
thf(2195,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).
thf(4234,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
thf(1671,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(4575,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(68,axiom,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(1310,plain,
tc_Int_Oint @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1046,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0) ).
thf(4839,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(996,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(4647,plain,
tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(851,axiom,
tc_Nat_Onat @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(4110,plain,
tc_Nat_Onat @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(230,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
thf(1867,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(4220,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(2184,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(4856,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
thf(4440,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__le) ).
thf(2168,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0) ).
thf(1260,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(3414,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(4294,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(678,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(3481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(788,axiom,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(3895,plain,
tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(3717,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(4941,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).
thf(1196,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2723,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(270,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
thf(2046,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(813,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
thf(3994,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(841,axiom,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(4079,plain,
tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(3777,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
thf(1359,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1366,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2516,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(864,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
thf(4156,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(1072,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(4948,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatceiling )
= ( B @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
thf(1623,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatceiling )
= ( B @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(930,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
thf(4386,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ c_Nat_OSuc )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_Onat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).
thf(1746,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ c_Nat_OSuc )
= ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_Onat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
thf(3103,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
thf(3236,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A
!= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int__split) ).
thf(3629,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(1243,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(1127,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(2763,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(964,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
thf(4496,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oring )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(1576,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3730,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(1101,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(5056,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__0__iff) ).
thf(1601,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(3281,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
thf(4198,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(790,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(3898,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(2082,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(861,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__mult) ).
thf(4137,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(1475,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(2400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1025,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(4760,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4963,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(494,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
thf(2825,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(785,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean6a) ).
thf(3878,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(2136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(970,axiom,
tc_Nat_Onat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
thf(4524,plain,
tc_Nat_Onat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
thf(3938,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(723,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
thf(3644,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(267,axiom,
! [A: $i] :
~ ( A @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).
thf(2039,plain,
! [A: $i] :
~ ( A @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(730,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
thf(3689,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(3342,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__real__def) ).
thf(1871,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1026,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__add) ).
thf(4761,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1104,axiom,
! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
thf(5064,plain,
! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(2217,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(725,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).
thf(3653,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(1511,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(445,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
thf(2682,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
thf(1832,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1028,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
thf(4766,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
thf(2745,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(451,axiom,
tc_RealDef_Oreal @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(2703,plain,
tc_RealDef_Oreal @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(4637,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(1628,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(4539,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(669,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
thf(3442,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(3263,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(1287,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(979,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SEQ_Oincseq ) )
<=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incseq__def) ).
thf(4563,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ c_SEQ_Oincseq ) ) )
& ( ( A @ ( B @ c_SEQ_Oincseq ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(943,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(4422,plain,
tc_Nat_Onat @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(582,axiom,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
thf(3131,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(163,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
thf(1660,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(838,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(4070,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
thf(2667,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1455,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(625,axiom,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(3280,plain,
tc_Int_Oint @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(1992,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(4568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__comm__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(404,axiom,
tc_Int_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(2466,plain,
tc_Int_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
thf(1545,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(1922,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_RComplete_Onatfloor @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
thf(3998,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_RComplete_Onatfloor @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_RComplete_Onatfloor @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(772,axiom,
tc_Int_Oint @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(3840,plain,
tc_Int_Oint @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(505,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__self) ).
thf(2857,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
<=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).
thf(1890,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) )
=> ( ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
& ( ( ( B @ c_Nat_OSuc @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ c_Nat__Transfer_Otsub ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
thf(2767,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ c_Nat__Transfer_Otsub ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(4270,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(3835,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_SEQ_Ocomplete__space )
=> ( ( B @ ( C @ c_SEQ_Oconvergent ) )
=> ( ( A @ c_SEQ_Osubseq )
=> ( A @ ( B @ ( tc_Nat_Onat @ ( C @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_SEQ_Oconvergent ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convergent__subseq__convergent) ).
thf(4265,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_SEQ_Ocomplete__space )
=> ( ( B @ ( C @ c_SEQ_Oconvergent ) )
=> ( ( A @ c_SEQ_Osubseq )
=> ( A @ ( B @ ( tc_Nat_Onat @ ( C @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_SEQ_Oconvergent ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(3231,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( B @ class_SEQ_Ocomplete__space )
=> ( ( A @ ( B @ c_SEQ_OCauchy ) )
=> ( A @ ( B @ c_SEQ_Oconvergent ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cauchy__convergent) ).
thf(3099,plain,
! [A: $i,B: $i] :
( ( B @ class_SEQ_Ocomplete__space )
=> ( ( A @ ( B @ c_SEQ_OCauchy ) )
=> ( A @ ( B @ c_SEQ_Oconvergent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(1800,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(877,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(4194,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).
thf(1247,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(921,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(4358,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(115,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
thf(1479,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(151,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1609,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).
thf(2635,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(4675,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(4368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(3014,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_RComplete_Onatfloor @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor) ).
thf(2730,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_RComplete_Onatfloor @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(802,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(3951,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(2158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(4383,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(210,axiom,
tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(1815,plain,
tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(4460,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(120,axiom,
tc_RealDef_Oreal @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(1494,plain,
tc_RealDef_Oreal @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(3602,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(703,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(3557,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__diff) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(623,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(3268,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(619,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(3258,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(938,axiom,
tc_Nat_Onat @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(4411,plain,
tc_Nat_Onat @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).
thf(2616,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(480,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(2794,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(806,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(3966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(871,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(4173,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
thf(4297,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(2650,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(1418,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(734,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
thf(3702,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(515,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__add__one__self__le__self) ).
thf(2880,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1096,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(5032,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(632,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(3300,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(1581,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(3851,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(563,axiom,
tc_Int_Oint @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(3075,plain,
tc_Int_Oint @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(1811,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(654,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(3393,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1089,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(5013,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(950,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
thf(4454,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
thf(4600,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ? [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B
= ( C @ c_Nat_OSuc ) ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat) ).
thf(1858,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(667,axiom,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
thf(3438,plain,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(228,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(1864,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(93,axiom,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1383,plain,
tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(4134,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(4783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(586,axiom,
tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(3152,plain,
tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(59,axiom,
tc_RealDef_Oreal @ class_Rings_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(1283,plain,
tc_RealDef_Oreal @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
thf(2073,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
thf(2058,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(4504,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(846,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(4087,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(3327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(1697,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(597,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(3184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(2508,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2964,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(835,axiom,
! [A: $i] :
( ? [B: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
<=> ? [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
thf(4055,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
& ( ? [B: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ? [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(1377,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(827,axiom,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
thf(4033,plain,
! [A: $i,B: $i] :
( ( ( B @ class_Rings_Osemiring__0 )
& ( B @ class_Power_Opower ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(498,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(2833,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(343,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
thf(2281,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( v_ga____ @ hAPP ) @ ( A @ ( v_ga____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
thf(4842,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( v_ga____ @ hAPP ) @ ( A @ ( v_ga____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(1215,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(761,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(3808,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(2002,plain,
! [A: $i,B: $i] :
( ( B
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
thf(3756,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(614,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(3243,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(486,axiom,
tc_Int_Oint @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2809,plain,
tc_Int_Oint @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(80,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(1345,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(345,axiom,
( ( tc_Nat_Onat @ c_RealDef_Oreal )
= ( tc_RealDef_Oreal @ c_Nat_Osemiring__1__class_Oof__nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__eq__of__nat) ).
thf(2286,plain,
( ( tc_Nat_Onat @ c_RealDef_Oreal )
= ( tc_RealDef_Oreal @ c_Nat_Osemiring__1__class_Oof__nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(829,axiom,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(4038,plain,
! [A: $i] :
( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(608,axiom,
! [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
thf(3226,plain,
! [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(1943,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(2154,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(793,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(3906,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(4588,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(844,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
thf(4082,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(4483,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
thf(3510,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).
thf(1564,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
thf(2922,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(570,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__1) ).
thf(3097,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(705,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
thf(3567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Omonoid__mult )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
thf(3720,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(3984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(5017,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(18,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
thf(1153,plain,
tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(111,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1470,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( B @ ( C @ ( D @ c_Fun_Oswap ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__self) ).
thf(1783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( B @ ( C @ ( D @ c_Fun_Oswap ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).
thf(1311,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
thf(4910,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
=> ~ ( ? [D: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
& ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
| ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(410,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
thf(2496,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(701,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
thf(3550,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(3418,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(180,axiom,
tc_Int_Oint @ class_Rings_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1730,plain,
tc_Int_Oint @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
thf(4853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
thf(3582,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(672,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A )
<=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff) ).
thf(3450,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B
= ( A @ ( c_Int_Onat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(3503,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
thf(4323,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ! [D: $i] :
( ( B
= ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
thf(2910,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(937,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(4407,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ozero )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ c_Groups_Ozero__class_Ozero )
= A ) )
& ( ( ( B @ c_Groups_Ozero__class_Ozero )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(697,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(3531,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
thf(1199,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(1768,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(378,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
thf(2382,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).
thf(5049,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(1900,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__power) ).
thf(1255,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(891,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ c_RComplete_Onatfloor )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
thf(4252,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ c_RComplete_Onatfloor )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(4344,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).
thf(3239,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( A @ ( B @ c_SEQ_Odecseq ) )
<=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decseq__def) ).
thf(4499,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( ( ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ c_SEQ_Odecseq ) ) )
& ( ( A @ ( B @ c_SEQ_Odecseq ) )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(3814,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(727,axiom,
! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
thf(3664,plain,
! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(691,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(3514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
thf(3339,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(4044,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(3827,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
thf(2428,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
thf(1519,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(933,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ class_Orderings_Oorder )
& ( C @ class_Orderings_Oorder ) )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( E @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( C @ ( B @ c_Orderings_Oorder__class_Ostrict__mono ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__monoI) ).
thf(4397,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ class_Orderings_Oorder )
& ( C @ class_Orderings_Oorder ) )
=> ( ! [D: $i,E: $i] :
( ( E @ ( D @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( E @ ( A @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( C @ ( B @ c_Orderings_Oorder__class_Ostrict__mono ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(1087,axiom,
! [A: $i] :
( ( A @ c_SEQ_Osubseq )
<=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subseq__def) ).
thf(5002,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ c_SEQ_Osubseq ) )
& ( ( A @ c_SEQ_Osubseq )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(1174,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Nat_OSuc @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
thf(2133,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Nat_OSuc @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(3233,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
thf(4204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(388,axiom,
tc_Int_Oint @ class_Rings_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(2414,plain,
tc_Int_Oint @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__iff) ).
thf(3250,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(801,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__geq) ).
thf(3948,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(399,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(2445,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(862,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
thf(4140,plain,
! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(440,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_Transcendental_Oln )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__one) ).
thf(2670,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_Transcendental_Oln )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1920,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1011,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(4725,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).
thf(1178,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(318,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1) ).
thf(2179,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1080,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(4979,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(358,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(2327,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(32,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
thf(1195,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
thf(3727,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(836,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int) ).
thf(4063,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
thf(4280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_RComplete_Onatceiling @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__mono) ).
thf(2758,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_RComplete_Onatceiling @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).
thf(4585,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
thf(2433,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(491,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(2820,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1__strict )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(686,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3499,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(560,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(3065,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).
thf(3750,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Nat_Osemiring__char__0 )
=> ( ( ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).
thf(4776,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Nat_Osemiring__char__0 )
=> ( ( ( B = A )
=> ( ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(1457,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
thf(3144,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1021,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
thf(4746,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(1836,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(2181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(941,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).
thf(4417,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(3050,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).
thf(1392,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1015,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(4732,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(724,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
thf(3647,plain,
! [A: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(295,axiom,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(2112,plain,
tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(842,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(4080,plain,
tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(795,axiom,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(3931,plain,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(3033,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(3408,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Osemiring )
=> ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__int) ).
thf(1740,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(715,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).
thf(3595,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1105,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
thf(5066,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(826,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
thf(4027,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(4316,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
thf(1983,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( E @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).
thf(4974,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( E @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( C @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ ( F @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(4486,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(1970,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(993,axiom,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(4636,plain,
tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(887,axiom,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(4233,plain,
tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(693,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(3518,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(849,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
thf(4095,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(4883,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(822,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(4012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(2638,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(856,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(4123,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
thf(1350,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
thf(3699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(349,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
thf(2300,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2498,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__int__eq) ).
thf(3782,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(311,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(2157,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(500,axiom,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
thf(2840,plain,
! [A: $i] :
~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1100,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(5053,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
thf(3254,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(289,axiom,
! [A: $i] : ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
thf(2100,plain,
! [A: $i] : ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(1851,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__nilpotent) ).
thf(1772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(53,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(1259,plain,
tc_RealDef_Oreal @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(530,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__one) ).
thf(2946,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
thf(2990,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(4668,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(483,axiom,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2801,plain,
tc_Int_Oint @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(967,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(4512,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
thf(2685,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
thf(3218,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(4429,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(971,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ ( F @ ( G @ ( H @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ ( G @ ( H @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( A @ ( E @ hAPP ) @ ( F @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).
thf(4525,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ ( F @ ( G @ ( H @ ( I @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( B @ ( C @ ( G @ ( H @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ( ( A @ ( E @ hAPP ) @ ( F @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(1425,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).
thf(1878,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(3386,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) )
& ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(11,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(1138,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1067,axiom,
tc_Nat_Onat @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(4930,plain,
tc_Nat_Onat @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
thf(1755,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(798,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
thf(3941,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(3440,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
thf(3205,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(544,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Ometric__space )
=> ( ( A @ ( B @ c_SEQ_Oconvergent ) )
=> ( A @ ( B @ c_SEQ_OCauchy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convergent__Cauchy) ).
thf(3018,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Ometric__space )
=> ( ( A @ ( B @ c_SEQ_Oconvergent ) )
=> ( A @ ( B @ c_SEQ_OCauchy ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1061,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
thf(4898,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
thf(4049,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(1964,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
thf(3846,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(4772,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
thf(1182,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
thf(3714,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(2868,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1023,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mono__iff) ).
thf(4750,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
thf(2053,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(2613,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(2085,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(741,axiom,
! [A: $i,B: $i] :
( ( B @ class_SEQ_Ocomplete__space )
=> ( ( A @ ( B @ c_SEQ_OCauchy ) )
<=> ( A @ ( B @ c_SEQ_Oconvergent ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cauchy__convergent__iff) ).
thf(3723,plain,
! [A: $i,B: $i] :
( ( B @ class_SEQ_Ocomplete__space )
=> ( ( ( A @ ( B @ c_SEQ_Oconvergent ) )
=> ( A @ ( B @ c_SEQ_OCauchy ) ) )
& ( ( A @ ( B @ c_SEQ_OCauchy ) )
=> ( A @ ( B @ c_SEQ_Oconvergent ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(4530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(4320,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1683,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(3775,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
thf(3141,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(569,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(3094,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Oone__class_Oone )
!= ( A @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(869,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
thf(4167,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Nat_OSuc )
!= A )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(876,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(4191,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(1584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(4861,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(997,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
thf(4648,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(238,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1889,plain,
tc_Int_Oint @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(3555,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(951,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(4457,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
thf(3294,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(1155,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( B @ c_SEQ_Osubseq )
=> ( A @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_seq__suble) ).
thf(4736,plain,
! [A: $i,B: $i] :
( ( B @ c_SEQ_Osubseq )
=> ( A @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1038,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(4804,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(699,axiom,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless__0) ).
thf(3541,plain,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
thf(1451,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(607,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(3222,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(249,axiom,
tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(1947,plain,
tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(507,axiom,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(2862,plain,
tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1074,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( B @ c_Nat_OSuc ) )
=> ~ ! [C: $i] :
( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( C @ c_Nat_OSuc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessE) ).
thf(4953,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A
!= ( B @ c_Nat_OSuc ) )
=> ~ ! [C: $i] :
( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( C @ c_Nat_OSuc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(305,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__one) ).
thf(2140,plain,
( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).
thf(2370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
thf(1825,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
thf(1324,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).
thf(2968,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1103,axiom,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(5063,plain,
tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(1263,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(718,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(3611,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(680,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(3486,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(1588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(409,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
thf(2487,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(558,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).
thf(3059,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__mono) ).
thf(3354,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(42,axiom,
tc_Int_Oint @ class_Rings_Oring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(1231,plain,
tc_Int_Oint @ class_Rings_Oring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(309,axiom,
tc_RealDef_Oreal @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
thf(2153,plain,
tc_RealDef_Oreal @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).
thf(2900,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(369,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
thf(2355,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__mult) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( v_f____ @ hAPP ) @ ( A @ ( v_f____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
thf(4231,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( v_f____ @ hAPP ) @ ( A @ ( v_f____ @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
thf(2813,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(720,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Nat__Transfer_Otransfer__morphism ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__morphism__nat__int) ).
thf(3628,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ ( c_Int_Onat @ ( tc_Nat_Onat @ ( tc_Int_Oint @ c_Nat__Transfer_Otransfer__morphism ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).
thf(1874,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__int) ).
thf(3692,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(1063,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__conj) ).
thf(4902,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(47,axiom,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(1246,plain,
tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(477,axiom,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
thf(2788,plain,
tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(995,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(4644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(901,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(4288,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(843,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(4081,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(712,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
thf(3587,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(595,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(3173,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(465,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(2748,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(62,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
thf(1286,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(383,axiom,
! [A: $i] : ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
thf(2402,plain,
! [A: $i] : ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(949,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).
thf(4448,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(4036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__comm__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__gt__zero__iff) ).
thf(2189,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(3841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(392,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
thf(2423,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(4995,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(676,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__div__distrib) ).
thf(3476,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(1333,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(863,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
thf(4148,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(873,axiom,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(4184,plain,
tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(1202,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(920,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__int) ).
thf(4352,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(386,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor @ ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
thf(2408,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor @ ( A @ c_RComplete_Onatfloor @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(284,axiom,
tc_Int_Oint @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(2089,plain,
tc_Int_Oint @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
thf(4004,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(1996,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(909,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
thf(4308,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(977,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(4550,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(760,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(3807,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(726,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(3660,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(2677,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(520,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2904,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(1959,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
thf(3042,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).
thf(1273,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(576,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(3111,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(923,axiom,
tc_Nat_Onat @ class_Rings_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(4365,plain,
tc_Nat_Onat @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(589,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(3158,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(1251,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(581,axiom,
tc_RealDef_Oreal @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
thf(3130,plain,
tc_RealDef_Oreal @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(955,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(4470,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(928,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(4380,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
thf(2275,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
= ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(2149,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1__no__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( I @ ( J @ hAPP ) @ ( K @ hAPP ) )
= ( F @ ( G @ hAPP ) @ ( H @ hAPP ) ) )
=> ( ( I @ ( J @ ( K @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( F @ ( G @ ( H @ ( A @ ( D @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).
thf(4613,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ( I @ ( J @ hAPP ) @ ( K @ hAPP ) )
= ( F @ ( G @ hAPP ) @ ( H @ hAPP ) ) )
=> ( ( I @ ( J @ ( K @ ( C @ ( D @ ( E @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( F @ ( G @ ( H @ ( A @ ( D @ ( B @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
thf(3871,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( c_Int_Onat @ hAPP ) )
= ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).
thf(2717,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( c_Int_Onat @ hAPP ) )
= ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(39,axiom,
tc_Int_Oint @ class_Rings_Oordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(1219,plain,
tc_Int_Oint @ class_Rings_Oordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(683,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
thf(3491,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(1483,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
thf(3079,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(939,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
thf(4412,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(528,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
thf(2941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(1301,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(4340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(1595,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(655,axiom,
! [A: $i,B: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
thf(3396,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(2376,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(19,axiom,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1154,plain,
tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(830,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__distrib) ).
thf(4041,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(999,axiom,
tc_Nat_Onat @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(4662,plain,
tc_Nat_Onat @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ c_Nat_OSuc ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__if) ).
thf(3319,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ c_Nat_OSuc ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__int) ).
thf(2859,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(963,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ! [B: $i] :
? [C: $i] : ( A @ ( C @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean3) ).
thf(4494,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ! [B: $i] :
? [C: $i] : ( A @ ( C @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(762,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(3811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocancel__ab__semigroup__add )
=> ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult2) ).
thf(2789,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
thf(1620,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(1652,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1037,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(4801,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(954,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).
thf(4465,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( ( A
= ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(2806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(713,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(3590,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(2817,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(5022,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(495,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2827,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1085,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_Onat__aux ) )
= ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__aux__def) ).
thf(4998,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Int_Onat__aux ) )
= ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ! [E: $i] : ( E @ c_Nat_OSuc @ ( C @ hAPP ) @ ( E @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less) ).
thf(4159,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ! [E: $i] : ( E @ c_Nat_OSuc @ ( C @ hAPP ) @ ( E @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(503,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
thf(2849,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(567,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ( ( A @ c_Nat_OSuc @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= B )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth2) ).
thf(3086,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ( ( A @ c_Nat_OSuc @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= B )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__eq) ).
thf(1752,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(622,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(3266,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatfloor )
= ( B @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
thf(2674,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_RComplete_Onatfloor )
= ( B @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).
thf(1124,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
thf(4946,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
thf(1428,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
thf(1503,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(961,axiom,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(4485,plain,
tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(751,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(3773,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(3964,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
thf(1707,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
thf(1733,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A )
=> ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(714,axiom,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(3594,plain,
tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(1027,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
thf(4764,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(681,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(3487,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__ring )
=> ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(661,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
thf(3416,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(52,axiom,
tc_Int_Oint @ class_Rings_Oidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(1258,plain,
tc_Int_Oint @ class_Rings_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(568,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
thf(3091,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(633,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
thf(3302,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(158,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
thf(1638,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(593,axiom,
tc_Int_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(3170,plain,
tc_Int_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(168,axiom,
! [A: $i] :
( ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__iff) ).
thf(1675,plain,
! [A: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(1669,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(323,axiom,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__zle__int) ).
thf(2193,plain,
! [A: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
thf(1786,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1035,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
thf(4796,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(352,axiom,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
thf(2308,plain,
! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1045,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(4837,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(3208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
!= ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(889,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(4236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(229,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(1865,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(768,axiom,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
thf(3832,plain,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(1765,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(3579,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(738,axiom,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(3719,plain,
tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
thf(2358,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(1356,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Ominus )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int__left) ).
thf(2079,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(572,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(3101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
thf(2679,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).
thf(3155,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(389,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
thf(2415,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(990,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
thf(4620,plain,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(754,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
thf(3779,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(3384,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(814,axiom,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3996,plain,
tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(224,axiom,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1853,plain,
tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Power_Opower )
=> ( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(3038,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(908,axiom,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__1) ).
thf(4305,plain,
! [A: $i] :
( ( A @ class_Rings_Osemiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le) ).
thf(2774,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(1043,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(4828,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__disj) ).
thf(3270,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(119,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless) ).
thf(1492,plain,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(348,axiom,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(2299,plain,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
thf(3106,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(675,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ? [C: $i] :
( A
= ( C @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).
thf(3468,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( A
= ( C @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(179,axiom,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__eq) ).
thf(1722,plain,
! [A: $i] :
( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(4805,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(193,axiom,
tc_Int_Oint @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
thf(1771,plain,
tc_Int_Oint @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
thf(2943,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(882,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
thf(4213,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(989,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ! [E: $i] : ( E @ c_Nat_OSuc @ ( C @ hAPP ) @ ( E @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less__iff) ).
thf(4616,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ! [E: $i] : ( E @ c_Nat_OSuc @ ( C @ hAPP ) @ ( E @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(839,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(4073,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
thf(2802,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(687,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__0) ).
thf(3500,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
thf(1690,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(711,axiom,
tc_RealDef_Oreal @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Nat_Osemiring__char__0) ).
thf(3586,plain,
tc_RealDef_Oreal @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(561,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(3066,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__cancel__iff) ).
thf(2896,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(958,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(4477,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__1) ).
thf(1307,plain,
! [A: $i] :
( ( A @ class_Rings_Oring__1 )
=> ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
thf(2065,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(4388,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(493,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2824,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(934,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).
thf(4401,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(1471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(488,axiom,
tc_RealDef_Oreal @ class_RealVector_Ometric__space,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Ometric__space) ).
thf(2812,plain,
tc_RealDef_Oreal @ class_RealVector_Ometric__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
thf(2742,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(820,axiom,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(4009,plain,
tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
thf(1731,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
thf(3932,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).
thf(4181,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( D @ hAPP ) ) )
=> ( ( B @ ( C @ ( A @ ( G @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_update__accessor__noop__compE) ).
thf(4850,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
=> ( ( ( B @ ( D @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( D @ hAPP ) ) )
=> ( ( B @ ( C @ ( A @ ( G @ ( G @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( E @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(1149,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(905,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(4296,plain,
tc_Nat_Onat @ class_Groups_Omonoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(679,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3483,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(2278,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(525,axiom,
! [A: $i] :
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
thf(2928,plain,
! [A: $i] :
~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1005,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
thf(4684,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).
thf(1820,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(547,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
thf(3027,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(4420,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(2343,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(729,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_Onat @ hAPP ) )
= A )
<=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
thf(3668,plain,
! [A: $i,B: $i] :
( ( ( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) )
=> ( ( B @ ( c_Int_Onat @ hAPP ) )
= A ) )
& ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= A )
=> ( ( ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(4462,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(294,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
thf(2111,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(1630,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1042,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(4818,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) )
& ( ( C
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).
thf(2446,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) )
& ( ( C
= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(467,axiom,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(2757,plain,
tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
thf(2410,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ? [D: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
& ( D @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).
thf(3614,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ? [D: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
& ( D @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ? [D: $i] :
( ( D @ ( C @ hAPP ) @ hBOOL )
& ( D @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
& ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(1460,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__no__zero__divisors )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
| ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(431,axiom,
tc_RealDef_Oreal @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
thf(2647,plain,
tc_RealDef_Oreal @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1012,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(4726,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2252,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(438,axiom,
! [A: $i,B: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).
thf(2664,plain,
! [A: $i,B: $i] :
~ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(537,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self1) ).
thf(2974,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1083,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ! [C: $i] :
( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( C @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessE) ).
thf(4990,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ! [C: $i] :
( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
!= ( C @ c_Nat_OSuc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(1112,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
thf(1171,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
thf(1926,plain,
! [A: $i,B: $i] :
( ( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
| ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A )
<=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
thf(1699,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A ) )
& ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= A )
=> ( B
= ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(2171,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(575,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(3110,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(922,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__implies__Suc) ).
thf(4362,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(638,axiom,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle) ).
thf(3325,plain,
! [A: $i,B: $i] : ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(907,axiom,
v_ga____ @ c_SEQ_Osubseq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_g_I1_J) ).
thf(4304,plain,
v_ga____ @ c_SEQ_Osubseq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(49,axiom,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(1250,plain,
tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(878,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
thf(4196,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(992,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
thf(4626,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
thf(3348,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__le__cancel__iff) ).
thf(2770,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
thf(4844,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
thf(2051,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(2481,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(526,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
thf(2931,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(2288,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).
thf(3953,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__int) ).
thf(2797,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(1775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Olinorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__mono__less__eq) ).
thf(2244,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Olinorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(2207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(4890,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).
thf(1694,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(2693,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1973,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(865,axiom,
tc_Nat_Onat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
thf(4158,plain,
tc_Nat_Onat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
thf(1805,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(413,axiom,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
thf(2506,plain,
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(4473,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(845,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__funpow) ).
thf(4084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( C @ c_Fun_Ocomp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B
= ( E @ ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) ) )
& ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__ge__zero) ).
thf(1626,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(4405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(532,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(2952,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
thf(1662,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(476,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean4) ).
thf(2784,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(2652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
thf(3161,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(972,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(4529,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__minus) ).
thf(1134,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Oring__1 )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Oorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__monoD) ).
thf(4292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Oorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
thf(2629,plain,
! [A: $i] :
( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__semiring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1) ).
thf(2597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(629,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(3292,plain,
! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(28,axiom,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(1181,plain,
tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
thf(1551,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__semigroup__add )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(4426,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
thf(1948,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(670,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
thf(3444,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1018,axiom,
tc_Nat_Onat @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(4741,plain,
tc_Nat_Onat @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(1304,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__ring__1 )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(600,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
thf(2107,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
thf(1758,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1062,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(4901,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(707,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__add) ).
thf(3576,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(1055,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(4868,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(894,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
thf(4260,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( E @ c_Fun_Oswap ) ) ) ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( C @ ( F @ ( E @ c_Fun_Oswap ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__swap) ).
thf(5025,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( G @ ( E @ c_Fun_Oswap ) ) ) ) @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( B @ ( C @ ( F @ ( E @ c_Fun_Oswap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(3981,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(2878,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(412,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(2503,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(1277,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(834,axiom,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__neg) ).
thf(4052,plain,
! [A: $i] :
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(913,axiom,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(4319,plain,
tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__add) ).
thf(1145,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(2256,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
thf(1547,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
thf(1798,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
thf(3376,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(508,axiom,
tc_Int_Oint @ class_Rings_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2863,plain,
tc_Int_Oint @ class_Rings_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int) ).
thf(1961,plain,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ! [I: $i] :
( ( I @ ( D @ hAPP ) @ ( E @ hAPP ) )
= ( I @ ( A @ hAPP ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).
thf(4864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( E @ ( F @ ( G @ ( H @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= ( A @ ( B @ ( F @ ( G @ ( C @ c_Fun_Ocomp ) ) ) @ hAPP ) ) )
=> ! [I: $i] :
( ( I @ ( D @ hAPP ) @ ( E @ hAPP ) )
= ( I @ ( A @ hAPP ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(577,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(3112,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(437,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negD) ).
thf(2661,plain,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ? [B: $i] :
( A
= ( B @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(538,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(2977,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(566,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
thf(3082,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(769,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
thf(3833,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
<=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).
thf(2518,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ? [E: $i] :
( ( B
= ( E @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
& ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( E @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( D @ ( C @ hAPP ) @ hBOOL ) ) )
& ( ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(456,axiom,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(2720,plain,
! [A: $i] :
( ( A @ class_Rings_Ozero__neq__one )
=> ( ( A @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(986,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(4593,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).
thf(2882,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( ( ~ ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) )
& ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) )
=> ( ( C
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( D @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
thf(1845,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
thf(4255,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
thf(1743,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).
thf(4366,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(1566,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(792,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
thf(3904,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
thf(1605,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(620,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(3260,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(3754,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1073,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(4950,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(2732,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(3462,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1107,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
thf(5074,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(89,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(1368,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(3228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(2821,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(4754,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(557,axiom,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3058,plain,
tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(4894,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(1076,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
thf(4961,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(41,axiom,
tc_RealDef_Oreal @ class_Rings_Ocomm__ring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(1230,plain,
tc_RealDef_Oreal @ class_Rings_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).
thf(2850,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( c_Int_Onat @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(2160,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(2831,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(2689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(435,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(2656,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(2092,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(1186,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(740,axiom,
v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp) ).
thf(3722,plain,
v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(976,axiom,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(4549,plain,
tc_Nat_Onat @ class_Rings_Olinordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Oordered__ring )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(44,axiom,
tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
thf(1235,plain,
tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2337,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Transcendental_Oln )
= ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__mult) ).
thf(3127,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Transcendental_Oln )
= ( A @ c_Transcendental_Oln @ ( B @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(61,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(1285,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ class_Power_Opower )
=> ( ( A @ c_Power_Opower__class_Opower )
= ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
thf(1336,plain,
! [A: $i] :
( ( A @ class_Power_Opower )
=> ( ( A @ c_Power_Opower__class_Opower )
= ( A @ c_Groups_Otimes__class_Otimes @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Power_Opower_Opower ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(1220,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oidom )
=> ( ( ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) )
=> ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( ( B
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(3642,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(978,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(4561,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(918,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(4346,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(201,axiom,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
thf(1790,plain,
! [A: $i] :
( ( A
!= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(2224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(3305,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(787,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
thf(3885,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B
= ( A @ c_Nat_OSuc ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(1813,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
thf(3114,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(3063,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(2920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(1095,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(5030,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(301,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(2128,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(4132,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(355,axiom,
tc_Int_Oint @ class_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
thf(2322,plain,
tc_Int_Oint @ class_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1086,axiom,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(5001,plain,
tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(519,axiom,
tc_RealDef_Oreal @ class_Rings_Omult__zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(2903,plain,
tc_RealDef_Oreal @ class_Rings_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1082,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
thf(4982,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) ) ) )
& ( ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(704,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(3564,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
thf(3329,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(269,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(2044,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(1130,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
=> ( ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_update__accessor__noopE) ).
thf(4117,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
=> ( ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(531,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(2948,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(1543,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(4959,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(2379,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
<=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) )
& ! [C: $i] :
( ( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( C @ ( B @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__nat) ).
thf(3356,plain,
! [A: $i,B: $i] :
( ( ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) )
& ! [C: $i] :
( ( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( C @ ( B @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL ) )
& ! [C: $i] :
( ( A
= ( C @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) )
=> ( C @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(60,axiom,
tc_Int_Oint @ class_Rings_Oring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(1284,plain,
tc_Int_Oint @ class_Rings_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(12,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1140,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(3024,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(848,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(4093,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(2939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(3961,plain,
! [A: $i,B: $i] :
( ( B @ class_RealVector_Oreal__normed__algebra )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
thf(3256,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
thf(3520,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__mult) ).
thf(4257,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(627,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).
thf(3288,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
thf(4217,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__0__iff) ).
thf(1404,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Oring__1__class_Oof__int ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(296,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__zero__iff) ).
thf(2113,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(3829,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(1141,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(579,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
thf(3124,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(393,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
thf(2426,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self2) ).
thf(1802,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Divides_Osemiring__div )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).
thf(3493,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oordered__ring )
=> ( ( ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(1353,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(4748,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(370,axiom,
tc_Int_Oint @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(2357,plain,
tc_Int_Oint @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).
thf(2843,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(2711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_RealVector_Oreal__normed__algebra )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(1506,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
thf(1749,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
thf(4046,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(897,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).
thf(4267,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1717,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
thf(4111,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(4414,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
thf(1966,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
thf(2347,plain,
! [A: $i,B: $i] :
( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
& ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(1017,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(4738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(840,axiom,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(4078,plain,
tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(2643,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(436,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__int__eq) ).
thf(2658,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Int_Oring__1__class_Oof__int ) )
= ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( v_ga____ @ ( v_f____ @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) @ ( A @ ( v_ga____ @ ( v_f____ @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( v_ga____ @ ( v_f____ @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) @ ( A @ ( v_ga____ @ ( v_f____ @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1108,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( v_ga____ @ ( v_f____ @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) @ ( A @ ( v_ga____ @ ( v_f____ @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(758,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ c_Transcendental_Oln )
= ( A @ c_Transcendental_Oln ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__inj__iff) ).
thf(3797,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ c_Transcendental_Oln )
= ( A @ c_Transcendental_Oln ) ) )
& ( ( ( B @ c_Transcendental_Oln )
= ( A @ c_Transcendental_Oln ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
thf(2760,plain,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(800,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
thf(3946,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(902,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(4289,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(1839,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
thf(3139,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(1918,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
thf(1316,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(4698,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
=> ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
| ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1) ).
thf(2352,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(449,axiom,
! [A: $i] :
( ( A @ c_Nat_Ofunpow )
= ( A @ ( A @ c_Nat_Ocompow ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__code__def) ).
thf(2696,plain,
! [A: $i] :
( ( A @ c_Nat_Ofunpow )
= ( A @ ( A @ c_Nat_Ocompow ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(137,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(1553,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
thf(2870,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
thf(4165,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2828,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(3171,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(533,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(2960,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
thf(4944,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
thf(1321,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
thf(1834,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nat__Transfer_Otsub ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
thf(4656,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(698,axiom,
! [A: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__le__0__conv) ).
thf(3533,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__commute) ).
thf(3447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( E @ c_Fun_Oswap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(2310,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ class_Rings_Ozero__neq__one )
& ( C @ class_Rings_Ono__zero__divisors )
& ( C @ class_Rings_Omult__zero )
& ( C @ class_Power_Opower ) )
=> ( ( ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(220,axiom,
tc_RealDef_Oreal @ class_Groups_Oone,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(1844,plain,
tc_RealDef_Oreal @ class_Groups_Oone,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(422,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(2611,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(357,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(2325,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(874,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
thf(4185,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
thf(1781,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
thf(2209,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(4102,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
thf(4006,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(293,axiom,
tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(2110,plain,
tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__diff) ).
thf(2305,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
thf(4170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ocomp ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
thf(2907,plain,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
thf(4310,plain,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).
thf(2792,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
thf(1646,plain,
! [A: $i,B: $i] :
( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(855,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
thf(4121,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(417,axiom,
tc_Int_Oint @ class_Groups_Ozero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(2594,plain,
tc_Int_Oint @ class_Groups_Ozero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(79,axiom,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1341,plain,
! [A: $i] :
( A
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(167,axiom,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(1674,plain,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(3825,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Olinorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__mono__less) ).
thf(4089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ class_Orderings_Olinorder )
& ( E @ class_Orderings_Oorder ) )
=> ( ( C @ ( E @ ( D @ c_Orderings_Oorder__class_Ostrict__mono ) ) )
=> ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__add) ).
thf(4126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ ( D @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ ( D @ c_Fun_Ocomp ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(3748,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Olinordered__semiring__strict )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(2971,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(1854,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__idom )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
thf(2608,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__ring__1 )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(1088,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(5010,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
thf(3331,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(308,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(2152,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(674,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
thf(3465,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oab__semigroup__add )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(2174,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__add )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).
thf(2283,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(2389,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(4666,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(385,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
thf(2406,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1004,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(4681,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(1508,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(4010,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(692,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(3516,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(1523,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1020,axiom,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(4745,plain,
tc_Nat_Onat @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(1861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(171,axiom,
tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(1689,plain,
tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(596,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
thf(3181,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(381,axiom,
tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
thf(2399,plain,
tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(685,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(3497,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(359,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0) ).
thf(2330,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_Onat @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(2362,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(3793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( E
!= ( F @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B != A )
& ( D = C ) )
=> ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
!= ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(935,axiom,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(4404,plain,
tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(298,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
thf(2120,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(948,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
thf(4446,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).
thf(4927,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(825,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
thf(4025,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(2648,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Rings_Oordered__semiring )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(710,axiom,
tc_RealDef_Oreal @ class_Rings_Osemiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(3585,plain,
tc_RealDef_Oreal @ class_Rings_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
thf(1777,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
& ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(985,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(4591,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1030,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(4774,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(716,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__iff) ).
thf(3598,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(1294,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A ) )
& ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
= A )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(3896,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(2198,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Ocomm__monoid__mult )
=> ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(5072,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(1513,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Groups_Oordered__ab__group__add )
=> ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
=> ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(332,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(2230,plain,
! [A: $i] :
( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != E )
=> ( ( A @ ( D @ ( F @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) @ ( E @ ( D @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) @ ( D @ ( F @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) )
= ( A @ ( E @ ( F @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__triple) ).
thf(2036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != E )
=> ( ( A @ ( D @ ( F @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) @ ( E @ ( D @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) @ ( D @ ( F @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) )
= ( A @ ( E @ ( F @ ( B @ ( C @ c_Fun_Oswap ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= B )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).
thf(4570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Fun_Ocomp ) ) ) @ hAPP ) )
= B )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
thf(1442,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( ( B @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).
thf(4869,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( ( B @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= A )
& ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(926,axiom,
! [A: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).
thf(4372,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(1161,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
& ( ( A
= ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(3420,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__ring )
=> ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(391,axiom,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle__0) ).
thf(2421,plain,
! [A: $i] : ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2123,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Ometric__space )
=> ( ( B @ ( C @ c_SEQ_OCauchy ) )
=> ( ( A @ c_SEQ_Osubseq )
=> ( A @ ( B @ ( tc_Nat_Onat @ ( C @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_SEQ_OCauchy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cauchy__subseq__Cauchy) ).
thf(4378,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_RealVector_Ometric__space )
=> ( ( B @ ( C @ c_SEQ_OCauchy ) )
=> ( ( A @ c_SEQ_Osubseq )
=> ( A @ ( B @ ( tc_Nat_Onat @ ( C @ ( tc_Nat_Onat @ c_Fun_Ocomp ) ) ) @ hAPP ) @ ( C @ c_SEQ_OCauchy ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(744,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ c_Transcendental_Oln )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__eq__zero__iff) ).
thf(3733,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
=> ( ( A @ c_Transcendental_Oln )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ c_Transcendental_Oln )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(969,axiom,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(4523,plain,
tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(271,axiom,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(2050,plain,
tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1000,axiom,
! [A: $i] :
~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
thf(4663,plain,
! [A: $i] :
~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(1480,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(603,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
thf(3203,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(591,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq) ).
thf(3164,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= ( A @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
thf(1116,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
thf(2142,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(2374,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(82,axiom,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
thf(1348,plain,
( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
= ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( c_Int_Onat @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(290,axiom,
( ( tc_Nat_Onat @ c_RealDef_Oreal )
= ( tc_RealDef_Oreal @ c_Nat_Osemiring__1__class_Oof__nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__def) ).
thf(2102,plain,
( ( tc_Nat_Onat @ c_RealDef_Oreal )
= ( tc_RealDef_Oreal @ c_Nat_Osemiring__1__class_Oof__nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).
thf(4816,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(2302,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1034,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(4794,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(735,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) )
& ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
thf(3705,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) ) ) )
& ( ( C
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oring )
=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(1578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(251,axiom,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1957,plain,
! [A: $i] :
( ( A @ class_Rings_Olinordered__semidom )
=> ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(853,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(4114,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(956,axiom,
tc_Nat_Onat @ class_Groups_Omonoid__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(4472,plain,
tc_Nat_Onat @ class_Groups_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1006,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4687,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).
thf(2385,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(4706,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(628,axiom,
tc_RealDef_Oreal @ class_SEQ_Ocomplete__space,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__SEQ_Ocomplete__space) ).
thf(3291,plain,
tc_RealDef_Oreal @ class_SEQ_Ocomplete__space,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(815,axiom,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(3997,plain,
tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(4809,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
& ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(3865,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(3882,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( B
= ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__power) ).
thf(3987,plain,
! [A: $i,B: $i] :
( ( B
= ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_RComplete_Onatfloor )
= ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(649,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(3373,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(1593,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(771,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
thf(3837,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
thf(1380,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(460,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__ge__zero__iff) ).
thf(2736,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(1033,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(4787,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3790,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(642,axiom,
! [A: $i] :
( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).
thf(3337,plain,
! [A: $i] :
( ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(15,axiom,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1148,plain,
tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(482,axiom,
tc_Int_Oint @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
thf(2800,plain,
tc_Int_Oint @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(2201,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).
thf(1363,plain,
! [A: $i,B: $i] :
( ( B @ class_Divides_Osemiring__div )
=> ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(881,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ c_RComplete_Onatceiling )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
thf(4210,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ c_RComplete_Onatceiling )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(759,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(3804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Olinordered__semiring__1 )
=> ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( F @ c_Groups_Oone__class_Oone ) )
=> ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(784,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2) ).
thf(3875,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Divides_Osemiring__div )
=> ( ( C
!= ( D @ c_Groups_Ozero__class_Ozero ) )
=> ( ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Divides_Odiv__class_Odiv ) ) )
= ( C @ ( B @ ( D @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1091,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(5019,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
thf(2704,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ class_Rings_Oring )
=> ( ( ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(200,axiom,
tc_Int_Oint @ class_Rings_Olinordered__ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1789,plain,
tc_Int_Oint @ class_Rings_Olinordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__iff) ).
thf(2366,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__idom )
=> ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( B @ ( C @ c_Int_Oring__1__class_Oof__int ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(2404,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(3030,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Omult__zero )
=> ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(1473,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__semiring__strict )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(664,axiom,
! [A: $i] :
( ! [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
<=> ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat) ).
thf(3424,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) )
=> ! [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL ) )
& ( ! [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
=> ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2340,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(475,axiom,
tc_Int_Oint @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(2783,plain,
tc_Int_Oint @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(912,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(4318,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(919,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(4350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(1816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(121,axiom,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
thf(1495,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__Suc) ).
thf(1657,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Osemiring__1 )
=> ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(2334,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
thf(2186,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(645,axiom,
tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(3347,plain,
tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(4286,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__ring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(3479,plain,
! [A: $i,B: $i,C: $i] :
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2417,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(2714,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).
thf(3196,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(5036,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(3045,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Ominus )
=> ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(3506,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(774,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(3843,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C
= ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(1346,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
=> ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__zle__neg) ).
thf(1610,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(3244,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(2810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(858,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(4129,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(17,axiom,
tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
thf(1152,plain,
tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(405,axiom,
! [A: $i] :
( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).
thf(2467,plain,
! [A: $i] :
( ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(837,axiom,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
thf(4066,plain,
! [A: $i] :
( ( A @ c_Nat_OSuc )
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(3489,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1044,axiom,
! [A: $i] :
( ( A @ c_SEQ_Osubseq )
<=> ! [B: $i] : ( B @ c_Nat_OSuc @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).
thf(4831,plain,
! [A: $i] :
( ( ! [B: $i] : ( B @ c_Nat_OSuc @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_SEQ_Osubseq ) )
& ( ( A @ c_SEQ_Osubseq )
=> ! [B: $i] : ( B @ c_Nat_OSuc @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).
thf(5046,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) @ ( D @ ( B @ ( C @ ( C @ c_Nat_Ocompow ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Oordered__ab__group__add )
=> ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
<=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(1236,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Olinordered__ab__group__add )
=> ( ( ( A
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ c_Groups_Ozero__class_Ozero ) )
=> ( A
= ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).
thf(2241,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Int_Onat @ hAPP ) @ ( B @ ( c_Int_Onat @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( c_Int_Onat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Ocomm__semiring__1 )
=> ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(700,axiom,
! [A: $i] :
( ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
thf(3543,plain,
! [A: $i] :
( ( ! [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
=> ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) )
=> ! [B: $i] : ( B @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(130,axiom,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(1532,plain,
tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1036,axiom,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
thf(4799,plain,
! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(2847,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(2600,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
thf(3570,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(659,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
thf(3411,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
!= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(340,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(2265,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) ) )
& ( ( ( B @ c_Nat_OSuc )
= ( A @ c_Nat_OSuc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(781,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
thf(3869,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(1976,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(135,axiom,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1550,plain,
tc_Int_Oint @ class_Rings_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(764,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
<=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(3817,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Oone )
=> ( ( ( A
= ( B @ c_Groups_Oone__class_Oone ) )
=> ( ( B @ c_Groups_Oone__class_Oone )
= A ) )
& ( ( ( B @ c_Groups_Oone__class_Oone )
= A )
=> ( A
= ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(5060,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Oab__semigroup__idem__mult )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
thf(3020,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(2864,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).
thf(3740,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ c_Nat__Transfer_Otsub ) )
= ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__natfloor) ).
thf(1880,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_RComplete_Onatfloor @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
<=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
thf(1431,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
=> ( ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
| ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(564,axiom,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(3076,plain,
( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
!= ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
thf(1902,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
thf(2484,plain,
! [A: $i,B: $i] :
( ( B @ class_Groups_Omonoid__mult )
=> ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ c_Groups_Oone__class_Oone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(237,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
thf(1885,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
!= ( A @ c_Nat_OSuc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(2699,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Oordered__cancel__semiring )
=> ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) )
=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(72,axiom,
tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(1320,plain,
tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(4520,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
thf(1945,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3854,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Olinordered__ring__strict )
=> ( ( ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( C @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Transcendental_Oln )
= ( B @ c_Transcendental_Oln @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__realpow) ).
thf(3405,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ c_Transcendental_Oln )
= ( B @ c_Transcendental_Oln @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
thf(1848,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(3432,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(401,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(2453,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(636,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power__div__base) ).
thf(3316,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(283,axiom,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
thf(2087,plain,
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) )
= ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(748,axiom,
tc_Int_Oint @ class_Power_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(3753,plain,
tc_Int_Oint @ class_Power_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(974,axiom,
! [A: $i,B: $i] :
( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
thf(4533,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_RComplete_Onatfloor )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__eq) ).
thf(3901,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ c_RComplete_Onatfloor )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(542,axiom,
tc_Int_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(3013,plain,
tc_Int_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(3526,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__add) ).
thf(3528,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal @ hAPP ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_RComplete_Onatceiling )
= ( A @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(2754,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Ono__zero__divisors )
=> ( ( B
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
!= ( C @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
!= ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(2672,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(2640,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(510,axiom,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natfloor__zero) ).
thf(2866,plain,
( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatfloor )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(867,axiom,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).
thf(4161,plain,
! [A: $i,B: $i] :
( ( B @ class_Rings_Olinordered__semidom )
=> ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__gt__zero) ).
thf(1490,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(4742,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(2297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Groups_Oordered__comm__monoid__add )
=> ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(398,axiom,
! [A: $i] :
( ? [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat) ).
thf(2438,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
=> ? [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL ) )
& ( ? [B: $i] : ( B @ ( A @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( B @ ( c_Int_Onat @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
thf(2238,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(4977,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semidom )
=> ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__power) ).
thf(4423,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) )
= ( A @ ( B @ ( C @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
thf(2993,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Divides_Odiv__class_Odiv ) ) )
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
=> ( ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
& ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
| ( A
= ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
thf(3200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
= ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1052,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(4858,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
thf(3047,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Groups_Omonoid__mult )
=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
<=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
thf(1912,plain,
! [A: $i,B: $i] :
( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(2980,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
=> ( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) )
& ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
= ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(550,axiom,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__int) ).
thf(3035,plain,
! [A: $i] :
( ( A @ ( tc_Int_Oint @ c_Nat_Osemiring__1__class_Oof__nat @ hAPP ) @ ( c_Int_Onat @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(2177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Olinordered__semiring__strict )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(817,axiom,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ln__less__zero) ).
thf(4002,plain,
! [A: $i] :
( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Transcendental_Oln @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(5492,plain,
$false,
inference(e,[status(thm)],[1168,4262,2876,2463,3969,4015,4877,1554,3873,4188,2094,3944,2744,1369,1823,2336,2131,4909,4022,3666,4729,3434,3167,3698,3979,2595,1315,3863,5028,4728,1686,2250,4931,3072,1882,2622,1522,2062,2776,1401,3910,1205,2837,4215,4623,1173,1211,3990,4714,1158,2117,2104,3040,4391,3153,1422,4697,2248,1793,3402,1533,3382,4479,1655,1137,2740,1999,1327,4247,3313,2042,4980,3848,2195,4234,1671,4575,1310,4839,4647,4110,1867,4220,2184,4856,4440,2168,1260,3414,4294,3481,3895,3717,4941,1196,2723,2046,3994,4079,3777,1359,1366,2516,4156,4948,1623,4386,1746,3103,3236,3629,1243,1127,2763,4496,2227,1576,3730,5056,1601,3281,4198,3898,2082,4137,1475,2400,4760,4963,2825,3878,2136,4524,3938,3644,2039,3689,3342,1871,4761,5064,2217,3653,1511,2682,1832,4766,2745,2703,4637,1628,4539,3442,3263,1287,4563,4422,3131,1660,4070,2667,1455,3280,1992,4568,2466,2126,1545,1922,3998,3840,2857,1890,2767,4270,3835,4265,3231,3099,1800,4194,1247,4358,1479,1609,2635,4675,4368,3014,2730,3951,2158,4383,1815,4460,1494,3602,3557,1232,3268,3258,4411,1415,2616,2794,3966,4173,4297,2650,1418,3702,2880,1828,5032,3300,1581,3851,3075,1811,2090,3393,5013,4454,4600,1858,3438,1864,1383,4134,4783,3152,1283,2073,2058,4504,4087,1394,3327,1697,3184,2508,2964,4055,1377,4033,2833,2281,4842,1215,3808,1796,2002,3756,3243,2809,1345,2286,4038,3226,1943,2154,3906,4588,4082,4483,3510,1564,2922,3097,3567,3720,3984,5017,1153,1470,1783,1311,4910,2496,3550,3418,1730,4853,3582,3450,3503,4323,2910,4407,2473,3531,1199,1768,2382,5049,1900,1255,4252,4344,3239,4499,3814,3664,3514,3339,4044,3827,2428,1519,4397,5002,1174,2133,3233,4204,2414,3250,3948,2445,4140,2670,1920,4725,1178,2179,4979,2327,1195,3727,4063,4280,2758,4585,2433,2332,2820,3297,3499,3065,3750,4776,1457,3144,4746,1836,2181,4417,3050,2345,1392,4732,3647,2112,4080,3931,3033,3408,1740,3595,5066,4027,4316,1983,4974,4486,1970,4636,4233,3518,4095,4883,4012,2638,4123,1350,3699,2300,2498,3782,2157,2840,5053,1762,3254,2100,1851,1772,1259,2946,2990,4668,2801,4512,2685,3218,4429,4525,1425,1878,3386,1138,4930,1719,1755,3941,3440,3205,3018,4898,4049,1964,2323,3846,4772,1182,3714,2868,4750,2053,2613,2085,3723,4530,4320,1683,3775,3141,3094,4167,4191,1584,4861,4648,1889,3555,4457,3294,1155,4736,4804,3541,1451,3222,1947,2862,4953,2140,2370,1825,1324,2968,5063,1263,3611,3486,1588,2487,3059,3354,1231,2153,2900,2355,1192,4231,2813,3628,1874,3692,4902,1246,2788,4644,4288,4081,3587,3173,2748,1286,2402,4448,4036,2189,3841,2423,4995,3476,1333,4148,4184,1202,4352,2408,2089,3190,4004,1996,4308,4550,3807,3660,2677,2904,1959,3042,1273,3111,4365,3158,1251,3130,4470,4380,2275,2149,4613,3871,2717,1219,3491,1483,3079,4412,2941,1301,4340,1595,3396,2376,1154,4041,4662,3319,2859,4494,3811,2789,1620,1652,4801,4465,2806,3590,2817,5022,2827,4998,3187,4159,2849,3086,1752,3266,2674,1124,4946,1428,1503,4485,3773,3964,1707,1733,3594,4764,3487,3416,1258,3091,3302,1638,3170,1675,1669,2193,1786,4796,2308,4837,3208,4236,1865,3832,1765,3579,3719,2358,1356,2079,3101,2679,3155,2415,4620,3779,3384,3996,1853,1408,3038,4305,2774,4828,2097,3270,1492,2299,3106,3468,1722,4805,1771,2943,4213,4616,4073,2802,3500,1690,3586,3066,2896,4477,1307,2065,4388,2824,4401,1471,2812,2742,4009,1731,3932,4181,4850,1149,4296,3483,2278,2928,4684,1820,3027,1339,4420,2343,3668,4462,2111,1630,4818,2446,2757,2410,3614,1460,2647,4726,2252,2664,2461,2974,4990,1112,1171,1926,1699,2171,3110,4362,3325,4304,1250,4196,4626,3348,2069,2770,4844,2051,2481,2931,2288,3953,2797,1775,2244,2207,4890,1694,2693,1973,4158,1805,2506,4473,4084,2005,1626,4405,2952,1662,2784,2652,3161,4529,1134,4292,2629,1990,2597,3292,1181,1551,4426,1948,3444,4741,1304,3193,2107,1758,4901,3576,4868,4260,5025,3981,2878,2503,1277,4052,4319,1145,2256,1547,1798,3376,2863,1961,4864,3112,2661,2977,3082,3833,2518,2720,4593,2882,1845,4255,1743,4366,1566,3904,1605,3260,3754,4950,2732,3462,5074,1368,3228,2821,4754,3058,4894,4961,1230,2850,2160,2831,2689,2656,2092,1186,3722,4549,1869,1235,2337,3127,1285,1336,1220,3642,4561,4346,1790,2224,3305,3885,1813,3114,3063,2920,5030,2128,4132,2322,5001,2903,4982,3564,3329,2044,1130,4117,2948,1543,4959,2379,3356,1284,1140,3024,4093,2939,3961,3256,3520,4257,3288,4217,2056,1404,2113,3829,1141,3124,2426,1802,3493,1353,4748,2357,2843,2320,2711,1506,1749,4046,4267,1717,4111,4414,1966,2347,4738,4078,2643,2658,1108,3797,2435,2760,3946,4289,1839,3139,1918,1316,4698,2352,2696,1553,2870,4165,2828,3171,2960,4944,1321,1834,4656,3533,3447,2310,1844,2611,2325,4185,1781,2209,4102,4006,2110,2305,4170,2907,4310,2792,1646,4121,2594,1341,1674,3825,4089,4126,3748,2971,1854,2608,5010,3331,2152,3465,1590,2174,2283,2389,4666,2406,4681,1508,4010,3516,1523,4745,1861,1689,3181,2399,3497,2330,2362,3793,4404,2120,4446,4927,4025,2648,3585,1777,4591,4774,3598,1294,3896,2198,5072,1513,2230,2036,4570,1442,4869,4372,1161,3420,2421,2123,4378,3733,4523,2050,4663,1480,3203,3164,1116,2142,2374,1348,2102,4816,2302,4794,3705,1280,1578,1957,4114,4472,4687,2385,4706,3291,3997,4809,3865,3882,3987,3373,1593,3837,1380,2736,4787,3790,3337,1148,2800,2201,1363,4210,3804,3875,5019,2704,1789,2366,2404,3030,1473,3424,2340,2783,4318,4350,1816,1495,1657,2334,2186,3347,4286,3479,2417,2714,3196,5036,3045,3506,3843,1346,1610,3244,2810,4129,1152,2467,4066,3489,4831,5046,1120,1236,2241,2430,3543,1532,4799,2847,2600,3570,1384,3411,2265,3869,1976,1550,3817,5060,3020,2864,3740,1880,1431,3076,1902,2484,1885,2699,1320,4520,1945,3854,3405,1848,3432,2453,3316,2087,3753,4533,3901,3013,3526,3528,2754,2672,2640,2866,4161,1490,4742,2297,2438,2238,4977,4423,2993,3200,4858,3047,1912,2980,3035,2177,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.14 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/5.52 % Computer : n014.cluster.edu
% 0.24/5.52 % Model : x86_64 x86_64
% 0.24/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.52 % Memory : 8046.5625MB
% 0.24/5.52 % OS : Linux 6.8.0-71-generic
% 0.24/5.52 % CPULimit : 300
% 0.24/5.52 % WCLimit : 300
% 0.24/5.52 % DateTime : Sat Sep 26 15:28:37 UTC 2026
% 0.24/5.53 % CPUTime :
% 0.24/5.53 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.30/6.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.01/6.52 % [INFO] Parsing done (507ms).
% 3.01/6.53 % [INFO] Running in sequential loop mode.
% 4.53/7.09 % [INFO] eprover registered as external prover.
% 4.53/7.10 % [INFO] Scanning for conjecture ...
% 5.92/7.51 % [INFO] Found a conjecture (or negated_conjecture) and 1160 axioms. Running axiom selection ...
% 8.70/8.18 % [INFO] Axiom selection finished. Selected 1105 axioms (removed 55 axioms).
% 11.95/9.17 % [INFO] Problem is first-order (TPTP FOF).
% 12.15/9.27 % [INFO] Type checking passed.
% 12.15/9.28 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 43.06/17.12 % External prover 'e' found a proof!
% 43.06/17.12 % [INFO] Killing All external provers ...
% 43.06/17.13 % Time passed: 11467ms (effective reasoning time: 10591ms)
% 43.06/17.13 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 42.64/17.14 % Axioms used in derivation (1105): fact_all__nat, arity_fun__Orderings_Oorder, fact_nat_Osimps_I3_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, arity_Int__Oint__Rings_Ocomm__semiring, fact_natfloor__power, fact_zle__refl, fact_transfer__nat__int__numerals_I1_J, fact_minus__mult__left, fact_neg__le__0__iff__le, fact_add__le__less__mono, fact_zadd__int, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_real__squared__diff__one__factored, fact_int__mult, fact_xt1_I1_J, fact_div__mult__mult1, fact_le__SucI, fact_real__le__refl, fact_int__0, fact_of__int__minus, fact_le__imp__diff__is__add, fact_real__less__def, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_power__strict__decreasing, fact_natfloor__real__of__nat, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, arity_RealDef__Oreal__Orderings_Oord, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_natfloor__add, fact_mult__1__left, fact_diff__0__eq__0, fact_nat__power__eq, fact_of__nat__add, fact_mult__less__cancel__left__disj, fact_diff__add__inverse, fact_Suc__lessE, fact_of__int__power, fact_power__inject__base, fact_le__eq__less__or__eq, fact_xt1_I4_J, fact_termination__basic__simps_I5_J, fact_odd__nonzero, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_q__pos__lemma, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_order__le__less__trans, fact_lift__Suc__mono__less, fact_transfer__morphism__nat__int, fact_zdiv__eq__0__iff, fact_power__power__power, fact_real__of__nat__zero, fact_mult__left_Ominus, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_of__int__int__eq, fact_zero__less__int__conv, fact_one__is__add, fact_diff__le__mono2, arity_Int__Oint__Rings_Olinordered__semiring__strict, fact_minus__mult__right, fact_real__of__nat__diff, fact_transfer__int__nat__quantifiers_I2_J, fact_zminus__zminus, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_add__leD1, fact_split__mult__neg__le, fact_zmult__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_zero__less__power, fact_add__less__mono, fact_mult__eq__0__iff, fact_zpower__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_Suc__nat__eq__nat__zadd1, fact_zless__nat__conj, arity_RealDef__Oreal__Groups_Ominus, arity_Nat__Onat__Orderings_Oorder, fact_mult__right__less__imp__less, fact_n__less__m__mult__n, fact_ln__eq__zero__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_of__int__add, arity_Int__Oint__Rings_Osemiring__1, fact_ln__inj__iff, fact_Suc__mono, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, arity_RealDef__Oreal__Rings_Osemiring__0, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_linorder__not__le, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_mult__le__less__imp__less, fact_zadd__commute, fact_zless__int, fact_natceiling__le, fact_ln__less__cancel__iff, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_diff__Suc__less, fact_transfer__int__nat__numerals_I2_J, fact_real__add__le__0__iff, fact_mult__0, fact_real__0__less__add__iff, fact_convergent__subseq__convergent, fact_int__eq__iff, fact_order__less__asym_H, fact_not__zle__0__negative, arity_Nat__Onat__Rings_Ozero__neq__one, fact_div__nonpos__pos__le0, fact_linorder__antisym__conv2, fact_zero__less__diff, fact_diff__diff__cancel, fact_mult__mono, fact_gr0__conv__Suc, fact_leI, fact_field__power__not__zero, fact_natceiling__le__eq__one, arity_RealDef__Oreal__Rings_Oidom, fact_Suc__le__mono, fact_zero__le__natfloor, fact_order__eq__refl, fact_add__right__imp__eq, fact_realpow__two__diff, fact_funpow__add, fact_nat__add__right__cancel, fact_neg__le__iff__le, fact_linorder__neqE, fact_o__eq__elim, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_div__le__dividend, fact_mult__le__mono2, fact_Suc__diff__diff, fact_le__neq__implies__less, fact_mult__left__le__imp__le, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_add__pos__nonneg, fact_transfer__nat__int__numerals_I2_J, fact_zero__le__one, arity_Int__Oint__Orderings_Oord, fact_nat__add__left__cancel__less, fact_int__0__less__1, fact_le__minus__iff, fact_o__apply, fact_lift__Suc__mono__less__iff, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_swap__triple, fact_le__add__iff2, fact_mult__eq__self__implies__10, fact_of__int__1, fact_zle__linear, fact_nat__add__distrib, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_linorder__antisym__conv3, fact_add__strict__increasing2, fact_order__less__imp__not__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_of__nat__less__imp__less, fact_linorder__neqE__linordered__idom, fact_lemma__realpow__diff, fact_ex__nat, fact_neg__less__0__iff__less, fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J, fact_mult__strict__left__mono, fact_zero__le__mult__iff, arity_Int__Oint__Groups_Ozero, fact_swap__commute, fact_real__of__nat__zero__iff, fact_seq__suble, fact_div__1, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, fact_div__if, fact_transfer__nat__int__relations_I1_J, fact_zadd__left__mono, fact_sum__squares__le__zero__iff, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_minus__real__def, fact_add__le__imp__le__left, fact_nat__mult__distrib__neg, fact_sum__squares__ge__zero, fact_add__increasing2, fact_split__div_H, fact_natceiling__mono, fact_linorder__antisym__conv1, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, fact_add__nonneg__eq__0__iff, fact_lessE, fact_zdiv__zero, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_real__mult__commute, fact_split__div__lemma, fact_gr0I, arity_Int__Oint__Rings_Olinordered__ring, fact_le__funD, fact_add__right__mono, fact_le__fun__def, fact_reals__Archimedean4, fact_power__minus, fact_of__nat__mult, fact_of__nat__aux_Osimps_I1_J, fact_real__of__nat__less__iff, fact_one__less__power, fact_power__strict__increasing, fact_one__le__power, fact_mult__eq__1__iff, fact_even__less__0__iff, fact_self__quotient__aux1, fact_power__commutes, fact_power__real__of__nat, fact_le__natfloor__eq__one, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__0__left, fact_add__mono, fact_nonneg1__imp__zdiv__pos__iff, fact_add__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_add__0__iff, fact_int__int__eq, fact_zero__less__imp__eq__int, fact_nat__less__real__le, fact_funpow__code__def, fact_real__mult__assoc, fact_nat__0, arity_Nat__Onat__Rings_Osemiring__0, fact_diff__le__self, fact_nat__diff__distrib, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_power__eq__0__iff, fact_diff__Suc__eq__diff__pred, fact_nat__mult__1__right, fact_mult__left_Odiff, fact_zero__le__natceiling, arity_Int__Oint__Rings_Oidom, fact_ord__less__eq__trans, fact_zero__reorient, fact_mult__right_Odiff, fact_le__iff__add, fact_one__reorient, fact_diff__commute, fact_minus__less__iff, fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J, fact_xt1_I9_J, fact_less__add__eq__less, fact_minus__mult__commute, fact_linorder__less__linear, fact_natceiling__zero, fact_order__less__imp__not__less, fact_int__zle__neg, fact_add__lessD1, fact_div__mult__self1__is__id, fact_add__le__mono1, fact_LIMSEQ__inverse__realpow__zero__lemma, fact_less__eq__nat_Osimps_I1_J, fact_strict__monoI, fact_lessI, fact_zero__le__square, fact_transfer__int__nat__numerals_I1_J, fact_pos__imp__zdiv__neg__iff, arity_Int__Oint__Groups_Oordered__ab__group__add, arity_RealDef__Oreal__Rings_Olinordered__idom, fact_termination__basic__simps_I4_J, fact_minus__le__iff, fact_of__int__mult, arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, fact_add__0__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_split__mult__pos__le, fact_div__nonneg__neg__le0, fact_nat_Oinject, fact_mult__left__le__one__le, arity_Int__Oint__Rings_Oring__no__zero__divisors, fact_nat__le__real__less, fact_not__add__less2, fact_decseq__def, fact_less__or__eq__imp__le, fact_Suc__less__SucD, fact_power__strict__mono, fact_int__div__less__self, fact_div__neg__neg__trivial, arity_Int__Oint__Rings_Oordered__cancel__semiring, fact_real__add__minus__iff, fact_zadd__strict__right__mono, fact_q__neg__lemma, fact_minus__apply, fact_zadd__zless__mono, fact_split__div, fact_mult__pos__neg, fact_power__gt1__lemma, fact_funpow__swap1, fact_nat__eq__add__iff2, fact_real__le__eq__diff, fact_mult__less__mono1, fact_Suc__leI, fact_add__neg__nonpos, fact_split__zdiv, fact_pos__imp__zdiv__pos__iff, fact_unique__quotient__lemma__neg, arity_RealDef__Oreal__Rings_Ozero__neq__one, fact_diff__less, fact_convex__bound__lt, fact_comp__cong, fact_mult__right__mono__neg, fact_zpower__zadd__distrib, fact_div__mult2__eq, fact_le__add2, fact_minus__nat_Odiff__0, fact_zadd__assoc, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J, arity_Nat__Onat__Orderings_Opreorder, fact_div__mult__self2, fact_mult__pos__neg2, fact_nat__0__le, arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, fact_not__less__less__Suc__eq, fact_power__Suc2, fact_comp__funpow, 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fact_real__natceiling__ge, fact_order__less__le, fact_nat__le__0, fact_diff__diff__right, fact_of__int__of__nat__eq, fact_nat__div__distrib, fact_power__le__imp__le__exp, fact_power__one__right, fact_add__nonneg__pos, fact_mult__less__cancel__right__disj, arity_RealDef__Oreal__Groups_Oab__semigroup__add, fact_add__less__cancel__right, fact_Suc__mult__cancel1, fact_mult__strict__right__mono, arity_Nat__Onat__Groups_Ocomm__monoid__mult, fact_real__of__nat__ge__zero, fact_add__nonpos__nonpos, arity_Int__Oint__Groups_Omonoid__mult, arity_RealDef__Oreal__Rings_Olinordered__semiring__strict, fact_Suc__le__lessD, arity_RealDef__Oreal__Rings_Oordered__ring, fact_add__increasing, fact_not__add__less1, fact_int__Suc0__eq__1, fact_mult__idem, fact_div__pos__pos__trivial, fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J, arity_fun__Orderings_Oord, fact_less__diff__conv, fact_le__imp__neg__le, fact_zless__imp__add1__zle, fact_mult__le__cancel__left__pos, fact_eq__diff__iff, fact_zero__less__double__add__iff__zero__less__single__add, fact_div__mult__mult2, fact_zero__le__power, fact_transfer__nat__int__relations_I3_J, fact_real__mult__less__iff1, fact_nat__le__add__iff2, arity_RealDef__Oreal__Rings_Olinordered__ring__strict, fact_negD, fact_Suc__inject, fact_of__nat__le__iff, fact_ext, fact_order__less__not__sym, fact_crossproduct__noteq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_Nat__Onat__Rings_Olinordered__semiring, fact_zle__trans, arity_RealDef__Oreal__Groups_Oordered__ab__group__add, fact_natceiling__neg, fact_less__add__iff1, fact_div__mult__mult1__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_mult_Oadd__left, fact_of__nat__nat, fact_nat__power__less__imp__less, fact_linorder__le__less__linear, fact_nat__lt__two__imp__zero__or__one, fact_Suc__neq__Zero, fact_zdiv__mono1, fact_g_I1_J, fact_power__strict__increasing__iff, fact_diff__less__Suc, fact_add__eq__self__zero, fact_funpow__mult, fact_mult__le__cancel2, arity_Int__Oint__Rings_Omult__zero, fact_real__le__antisym, fact_div__less__dividend, fact_mult__le__mono, arity_Nat__Onat__Orderings_Olinorder, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, arity_Int__Oint__Rings_Oring, fact_mult__le__0__iff, fact_le__iff__diff__le__0, fact_mult__is__0, fact_nat__add__left__cancel, fact_Suc__diff__1, fact_of__nat__less__0__iff, fact_less__le__not__le, fact_n__not__Suc__n, fact_nat__le__linear, fact_natceiling__eq, fact_transfer__int__nat__quantifiers_I1_J, fact_linorder__le__cases, fact_mult__zero__right, fact_nat__less__add__iff1, arity_RealDef__Oreal__RealVector_Ometric__space, fact_real__natfloor__add__one__gt, fact_div__by__0, fact_zminus__0, fact_order__less__le__trans, fact_power__less__imp__less__exp, arity_Nat__Onat__Rings_Omult__zero, arity_RealDef__Oreal__Groups_Ocomm__monoid__add, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_of__nat__0, fact_less__minus__self__iff, 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fact_Zero__not__Suc, arity_RealDef__Oreal__Rings_Olinordered__semiring__1, fact_div__geq, fact_zero__less__one, fact_power__0__left, fact_real__diff__def, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_div__add__self2, arity_Nat__Onat__Rings_Oordered__cancel__semiring, fact_decr__mult__lemma, fact_diff__mult__distrib, fact_int__0__neq__1, fact_le__natfloor__eq, fact_add__less__imp__less__right, fact_le__Suc__ex__iff, arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, fact_zdiff__zmult__distrib, fact_subseq__def, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, fact_zless__nat__eq__int__zless, fact_mult__strict__mono, fact_diff__less__mono, fact_Suc__leD, fact_not__real__of__nat__less__zero, fact_power__0, fact_neg__equal__zero, fact_power__mult, fact_real__of__nat__1, fact_add_Ocomm__neutral, fact_strict__monoD, fact_realpow__pos__nth, fact_mult__Suc, fact_less__trans__Suc, fact_xt1_I6_J, fact_le__minus__self__iff, fact_less__not__refl2, 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fact_strict__mono__less__eq, fact_Suc__mult__le__cancel1, fact_ln__less__zero, fact_less__fun__def, fact_One__nat__def, fact_update__accessor__noopE, fact_comm__semiring__class_Odistrib, fact_update__accessor__noop__compE, fact_div__mult__self__is__m, fact_square__eq__iff, fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096, fact_neg__imp__zdiv__nonneg__iff, fact_nat__diff__add__eq1, fact_termination__basic__simps_I3_J, fact_swap__nilpotent, arity_Int__Oint__Rings_Oordered__ring, fact_o__eq__dest__lhs, fact_nat__eq__iff, fact_add__0, fact_nat__less__add__iff2, fact_Cauchy__convergent__iff, fact_power__mono, fact_diff__self__eq__0, fact_Divides_Otransfer__nat__int__function__closures_I1_J, fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J, fact_diff__add__0, fact_mult__nonpos__nonneg, fact_Zero__neq__Suc, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, fact_add__nonneg__nonneg, fact_nat__eq__add__iff1, arity_RealDef__Oreal__Power_Opower, fact_Suc__eq__plus1, fact_real__of__nat__power, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, fact_mult__le__mono1, fact_Divides_Otransfer__int__nat__functions_I1_J, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_self__quotient__aux2, arity_RealDef__Oreal__Rings_Olinordered__semidom, fact_realpow__two__disj, fact_div__neg__pos__less0, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_nat__mult__div__cancel1, fact_Suc__diff__le, fact_of__int__diff, fact_order__eq__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, fact_int__less__0__conv, arity_Nat__Onat__Groups_Oab__semigroup__add, arity_Int__Oint__Groups_Ocomm__monoid__mult, fact_power__mult__distrib, fact_ord__eq__less__trans, fact_less__1__mult, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_square__eq__1__iff, fact_le__trans, fact_Suc__pred, fact_ge__natfloor__plus__one__imp__gt, arity_fun__Groups_Ominus, fact_of__int__le__0__iff, arity_Int__Oint__Groups_Oone, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, fact_add__left__mono, fact_real__add__eq__0__iff, fact_power__Suc__0, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_mult__right_Ominus, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_le0, fact_power__one, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, arity_Int__Oint__Orderings_Oorder, fact_int__eq__0__conv, fact_le__diff__conv2, fact_mult__pos__pos, fact_minus__mult__minus, fact_ex__least__nat__less, fact_crossproduct__eq, fact_zmult__zless__mono2, fact_zdiff__int__split, fact_diff__Suc__diff__eq1, fact_comm__mult__left__mono, arity_Int__Oint__Groups_Oab__semigroup__add, fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_zdiv__zminus__zminus, fact_le__mult__natfloor, fact_less__add__one, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_add__leE, fact_natceiling__subtract, arity_Int__Oint__Rings_Oring__1, arity_RealDef__Oreal__Rings_Osemiring__1, fact_diff__Suc__1, fact_add__less__le__mono, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_real__of__nat__Suc__gt__zero, fact_real__two__squares__add__zero__iff, fact_power__less__power__Suc, fact_int__one__le__iff__zero__less, fact_Cauchy__subseq__Cauchy, fact_zdiv__mono2, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_nat__less__eq__zless, fact_natfloor__add__one, fact_power__eq__imp__eq__base, fact_less__Suc__eq, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_diff__eq__diff__less__eq, fact_swap__self, fact_of__nat__eq__iff, fact_Suc__less__eq, fact_mult__neg__neg, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, fact_neg__0__le__iff__le, fact_mult_Odiff__left, fact_ln__realpow, fact_zdiv__mono2__lemma, fact_zmult__zminus, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Oring__1, fact_zdiv__zminus2, fact_zle__iff__zadd, fact_zero__less__Suc, fact_add1__zle__eq, fact_eq__imp__le, fact_nat__le__eq__zle, fact_ln__less__zero__iff, fact_div__self, fact_mult_Ocomm__neutral, fact_real__add__left__mono, fact_add__strict__increasing, fact_real__mult__order, arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_zmult__zless__mono2__lemma, fact_zdiv__self, arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_le__less__Suc__eq, fact_pos__imp__zdiv__nonneg__iff, fact_nat__power__eq__Suc__0__iff, fact_nat__1, fact_nat__mult__commute, fact_diff__add__inverse2, arity_Int__Oint__Rings_Olinordered__semiring__1, fact_plus__nat_Oadd__0, fact_subseq__Suc__iff, fact_order__le__imp__less__or__eq, fact_of__nat__Suc, fact_minus__le__self__iff, fact_eq__nat__nat__iff, fact_add__nonpos__neg, fact_mult__left__idem, fact_div__le__mono, fact_Suc__n__not__n, fact_comp__swap, fact_mult__left__mono__neg, fact_le__antisym, fact_zadd__0__right, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_diff__le__mono, fact_zero__less__mult__pos, fact_order__antisym__conv, fact_neq0__conv, fact_real__of__nat__gt__zero__cancel__iff, fact_mult__0__right, fact_real__add__less__0__iff, fact_zless__linear, fact_mult__less__cancel__left__pos, fact_real__mult__le__cancel__iff2, fact_trans__le__add1, fact_zless__iff__Suc__zadd, arity_Int__Oint__Groups_Ominus, fact_zmult__1__right, fact_double__eq__0__iff, fact_le__0__eq, fact_mult__Suc__right, fact_realpow__pos__nth__unique, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_mult__less__cancel2, fact_zle__add1__eq__le, fact_mult__1__right, fact_add__le__imp__le__right, fact_order__less__irrefl, fact_less__Suc0, fact_order__le__less, fact_zero__zle__int, fact_less__iff__Suc__add, fact_order__less__imp__le, fact_termination__basic__simps_I1_J, fact_real__0__le__add__iff, fact_order__less__trans, fact_negative__eq__positive, fact_zero__less__two, fact_nat__int, fact_diff__is__0__eq, fact_real__of__nat__one, fact_rp, fact_real__of__nat__le__iff, fact_real__mult__less__mono2, fact_sum__squares__eq__zero__iff, fact_le__add__diff__inverse, fact_nat__zero__less__power__iff, fact_of__nat__1, fact_of__int__0__less__iff, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, fact_add__diff__inverse, fact_convex__bound__le, arity_Nat__Onat__Rings_Osemiring, fact_int__le__0__conv, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_nat__mult__eq__cancel__disj, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_mult__less__imp__less__left, fact_le__diff__iff, arity_Nat__Onat__Groups_Oone, fact_diff__Suc__Suc, fact_add__imp__eq, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_no__zero__divisors, fact_le__square, fact_divisors__zero, fact_reals__Archimedean6a, fact_div__mult__self2__is__id, fact_realpow__Suc__le__self, arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_RealDef__Oreal__Groups_Oab__semigroup__mult, arity_Int__Oint__Rings_Ozero__neq__one, fact_ln__gt__zero, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_transfer__nat__int__relations_I2_J, fact_power__gt1, fact_power__0__Suc, fact_nat__less__le, fact_less__iff__diff__less__0, fact_mult__eq__if, fact_split__nat, fact_zadd__zmult__distrib, fact_less__SucE, fact_le__cube, fact_zless__add1__eq, fact_linorder__cases, fact_real__natfloor__le, fact_xt1_I11_J, fact_add__less__mono1, fact_add__le__cancel__left, fact_real__le__linear, fact_ord__eq__le__trans, fact_f_I1_J, fact_zadd__zminus__inverse2, fact_o__assoc, fact_double__add__less__zero__iff__single__add__less__zero, fact_less__diff__iff, fact_real__natfloor__gt__diff__one, fact_odd__less__0, arity_Int__Oint__Groups_Omonoid__add, fact_order__trans, fact_power__le__imp__le__base, fact_mult__1, fact_real__eq__of__nat, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, arity_Int__Oint__Orderings_Opreorder, fact_real__of__nat__inject, fact_reals__Archimedean3, fact_negative__zless__0, fact_add__Suc__shift, fact_less__SucI, fact_Suc__not__Zero, fact_real__of__nat__add, fact_ln__gt__zero__iff, fact_xt1_I7_J, fact_not__square__less__zero, fact_Suc__lessI, fact_negative__zle__0, fact_add__Suc__right, fact_less__bin__lemma, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_zdiv__mono2__neg__lemma, fact_ln__one, fact_nat__0__iff, fact_natfloor__mono, fact_ln__ge__zero__iff
% 42.64/17.14 % No. of inferences in proof: 2214
% 42.64/17.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11467 ms resp. 10591 ms w/o parsing
% 47.02/18.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.02/18.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------