%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP019_7 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : n009.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 07:35:46 AM UTC 2026
% Result : Theorem 27.14s 9.91s
% Output : Refutation 27.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 88
% Syntax : Number of formulae : 178 ( 121 unt; 0 typ; 0 def)
% Number of atoms : 295 ( 294 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1518 ( 24 ~; 11 |; 31 &;1377 @)
% ( 20 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 19 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 5 con; 0-3 aty)
% Number of variables : 329 ( 0 ^; 325 !; 4 ?; 329 :)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Eind_type,type,
tyop_2Emin_2Eind: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone_type,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Estring_2Echar_type,type,
tyop_2Estring_2Echar: $tType ).
thf(tyop_2EternaryComparisons_2Eordering_type,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
thf(tyop_2Ehrat_2Ehrat_type,type,
tyop_2Ehrat_2Ehrat: $tType ).
thf(tyop_2Einteger_2Eint_type,type,
tyop_2Einteger_2Eint: $tType ).
thf(tyop_2Equote_2Eindex_type,type,
tyop_2Equote_2Eindex: $tType ).
thf(tyop_2Etoto_2Enum__dt_type,type,
tyop_2Etoto_2Enum__dt: $tType ).
thf(tyop_2Ehreal_2Ehreal_type,type,
tyop_2Ehreal_2Ehreal: $tType ).
thf(tyop_2EDeepSyntax_2Edeep__form_type,type,
tyop_2EDeepSyntax_2Edeep__form: $tType ).
thf(tyop_2Erealax_2Ereal_type,type,
tyop_2Erealax_2Ereal: $tType ).
thf(tyop_2Efrac_2Efrac_type,type,
tyop_2Efrac_2Efrac: $tType ).
thf(tyop_2Erat_2Erat_type,type,
tyop_2Erat_2Erat: $tType ).
thf(tyop_2Ebinary__ieee_2Eflags_type,type,
tyop_2Ebinary__ieee_2Eflags: $tType ).
thf(tyop_2Ebinary__ieee_2Efloat__compare_type,type,
tyop_2Ebinary__ieee_2Efloat__compare: $tType ).
thf(tyop_2Ebinary__ieee_2Efloat__value_type,type,
tyop_2Ebinary__ieee_2Efloat__value: $tType ).
thf(tyop_2Ebinary__ieee_2Erounding_type,type,
tyop_2Ebinary__ieee_2Erounding: $tType ).
thf(c_2Enum_2E0_2E0_decl,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
thf(c_2EbasicSize_2Ebool__size_2E1_decl,type,
c_2EbasicSize_2Ebool__size_2E1: tyop_2Emin_2Ebool > tyop_2Enum_2Enum ).
thf(c_2EbasicSize_2Eone__size_2E1_decl,type,
c_2EbasicSize_2Eone__size_2E1: tyop_2Eone_2Eone > tyop_2Enum_2Enum ).
thf(c_2Egcd_2Elcm_2E2_decl,type,
c_2Egcd_2Elcm_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enumpair_2Encons_2E2_decl,type,
c_2Enumpair_2Encons_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebag_2EEMPTY__BAG_2E1_decl,type,
c_2Ebag_2EEMPTY__BAG_2E1:
!>[TA: $tType] : ( TA > tyop_2Enum_2Enum ) ).
thf(c_2Estring_2Echar__size_2E1_decl,type,
c_2Estring_2Echar__size_2E1: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).
thf(c_2EternaryComparisons_2Eordering__size_2E1_decl,type,
c_2EternaryComparisons_2Eordering__size_2E1: tyop_2EternaryComparisons_2Eordering > tyop_2Enum_2Enum ).
thf(c_2Ewords_2Ebit__count__upto_2E2_decl,type,
c_2Ewords_2Ebit__count__upto_2E2:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > tyop_2Enum_2Enum ) ).
thf(c_2Ealignment_2Ealign_2E2_decl,type,
c_2Ealignment_2Ealign_2E2:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Ebitstring_2Eshiftr_2E2_decl,type,
c_2Ebitstring_2Eshiftr_2E2: ( tyop_2Emin_2Ebool @ tyop_2Elist_2Elist ) > tyop_2Enum_2Enum > ( tyop_2Emin_2Ebool @ tyop_2Elist_2Elist ) ).
thf(c_2Esptree_2Espt__acc_2E2_decl,type,
c_2Esptree_2Espt__acc_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ereal_2Ereal__of__num_2E1_decl,type,
c_2Ereal_2Ereal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
thf(c_2Ebinary__ieee_2Efloat__compare__size_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__compare__size_2E1: tyop_2Ebinary__ieee_2Efloat__compare > tyop_2Enum_2Enum ).
thf(c_2Ebinary__ieee_2Erounding__size_2E1_decl,type,
c_2Ebinary__ieee_2Erounding__size_2E1: tyop_2Ebinary__ieee_2Erounding > tyop_2Enum_2Enum ).
thf(c_2Ecomplex_2EIM_2E1_decl,type,
c_2Ecomplex_2EIM_2E1: ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > tyop_2Erealax_2Ereal ).
thf(c_2Ecomplex_2Ecomplex__add_2E2_decl,type,
c_2Ecomplex_2Ecomplex__add_2E2: ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(c_2Ecomplex_2Ecomplex__div_2E2_decl,type,
c_2Ecomplex_2Ecomplex__div_2E2: ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(c_2Ecomplex_2Ecomplex__inv_2E1_decl,type,
c_2Ecomplex_2Ecomplex__inv_2E1: ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(c_2Ecomplex_2Ecomplex__mul_2E2_decl,type,
c_2Ecomplex_2Ecomplex__mul_2E2: ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(c_2Ecomplex_2Ecomplex__neg_2E1_decl,type,
c_2Ecomplex_2Ecomplex__neg_2E1: ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(c_2Ecomplex_2Ecomplex__of__num_2E1_decl,type,
c_2Ecomplex_2Ecomplex__of__num_2E1: tyop_2Enum_2Enum > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(c_2Ecomplex_2Ecomplex__of__real_2E1_decl,type,
c_2Ecomplex_2Ecomplex__of__real_2E1: tyop_2Erealax_2Ereal > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(c_2Ecomplex_2Ecomplex__sub_2E2_decl,type,
c_2Ecomplex_2Ecomplex__sub_2E2: ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) > ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) ) ).
thf(87,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__INV) ).
thf(472,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(46,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LNEG) ).
thf(288,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(35,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= C )
<=> ( A
= ( B @ ( C @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__SUB__RADD) ).
thf(243,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A
= ( B @ ( C @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= C ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= C )
=> ( A
= ( B @ ( C @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(62,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
!= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__not__nnil) ).
thf(360,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
!= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(85,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2Ebit__count__upto_2E2 ) ) )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ebit__count__upto__0) ).
thf(466,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2Ebit__count__upto_2E2 ) ) )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(73,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__RZERO) ).
thf(406,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( A @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__DIFFSQ) ).
thf(255,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( A @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LADD) ).
thf(104,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B = C )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(72,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
<=> ( ( B
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
| ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ENTIRE) ).
thf(395,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( B
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
| ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( B
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
| ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(19,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__COMM) ).
thf(170,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(49,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= B )
<=> ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LID__UNIQ) ).
thf(308,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= B ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= B )
=> ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(81,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
<=> ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__EQ0) ).
thf(449,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
& ( ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(30,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RINV) ).
thf(217,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(42,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__NEG2) ).
thf(276,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(70,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( A @ c_2EbasicSize_2Ebool__size_2E1 )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Ebool__size__def) ).
thf(389,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A @ c_2EbasicSize_2Ebool__size_2E1 )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(58,axiom,
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__0) ).
thf(344,plain,
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(61,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__div_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__div) ).
thf(357,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__div_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(83,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__0) ).
thf(460,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(76,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
<=> ( ( A = B )
| ( C
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RMUL) ).
thf(421,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( A = B )
| ( C
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ) )
& ( ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
=> ( ( A = B )
| ( C
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(53,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ c_2Ebag_2EEMPTY__BAG_2E1 ) )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebag_2EEMPTY__BAG__alt) ).
thf(325,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ c_2Ebag_2EEMPTY__BAG_2E1 ) )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__SUB) ).
thf(152,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(50,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RID) ).
thf(316,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(88,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
<=> ( ( B = C )
| ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL) ).
thf(475,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( B = C )
| ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
=> ( ( B = C )
| ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(17,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RNEG) ).
thf(164,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__LMUL) ).
thf(179,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(79,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__INV) ).
thf(443,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(67,axiom,
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__0) ).
thf(376,plain,
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(6,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( A @ c_2Ereal_2Ereal__of__num_2E1 )
= ( B @ c_2Ereal_2Ereal__of__num_2E1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__OF__NUM__EQ) ).
thf(117,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( A = B )
=> ( ( A @ c_2Ereal_2Ereal__of__num_2E1 )
= ( B @ c_2Ereal_2Ereal__of__num_2E1 ) ) )
& ( ( ( A @ c_2Ereal_2Ereal__of__num_2E1 )
= ( B @ c_2Ereal_2Ereal__of__num_2E1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__ASSOC) ).
thf(270,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(27,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__COMM) ).
thf(201,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(31,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) )
<=> ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD) ).
thf(220,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= B )
=> ( A
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ) )
& ( ( A
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) )
=> ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(71,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__REFL) ).
thf(392,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(24,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LDISTRIB) ).
thf(192,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LINV) ).
thf(137,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__SUB2) ).
thf(229,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(36,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__SUB) ).
thf(252,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(78,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__0) ).
thf(435,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A = B )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(45,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Ecomplex_2Ecomplex__of__real_2E1 @ c_2Ecomplex_2EIM_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ereal_2Ereal__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2EIM__COMPLEX__OF__REAL) ).
thf(285,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Ecomplex_2Ecomplex__of__real_2E1 @ c_2Ecomplex_2EIM_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ereal_2Ereal__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(54,axiom,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
= c_2Enum_2E0_2E0 )
& ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
= c_2Enum_2E0_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__0) ).
thf(328,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
= c_2Enum_2E0_2E0 )
& ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
= c_2Enum_2E0_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(56,axiom,
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ereal_2Ereal__of__num_2E1 @ c_2Ecomplex_2Ecomplex__of__real_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__0) ).
thf(339,plain,
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ereal_2Ereal__of__num_2E1 @ c_2Ecomplex_2Ecomplex__of__real_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(3,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
<=> ( B
= ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__RNEG__UNIQ) ).
thf(96,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B
= ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( B
= ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(82,axiom,
! [A: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
( ( c_2Enum_2E0_2E0 @ ( A @ c_2Ebitstring_2Eshiftr_2E2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Eshiftr__0) ).
thf(457,plain,
! [A: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
( ( c_2Enum_2E0_2E0 @ ( A @ c_2Ebitstring_2Eshiftr_2E2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(20,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__MUL2) ).
thf(173,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(75,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( B = C )
<=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL2) ).
thf(412,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(16,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__ADD) ).
thf(161,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(43,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LDISTRIB) ).
thf(279,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(12,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__ASSOC) ).
thf(149,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__sub) ).
thf(176,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(47,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
= ( C @ ( D @ c_2Enumpair_2Encons_2E2 ) ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__11) ).
thf(291,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( ( A = C )
& ( B = D ) )
=> ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
= ( C @ ( D @ c_2Enumpair_2Encons_2E2 ) ) ) )
& ( ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
= ( C @ ( D @ c_2Enumpair_2Encons_2E2 ) ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(28,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__align) ).
thf(204,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
= ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(64,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INVINV) ).
thf(367,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(9,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Egcd_2Elcm_2E2 ) )
= ( B @ ( A @ c_2Egcd_2Elcm_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__COMM) ).
thf(140,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A @ ( B @ c_2Egcd_2Elcm_2E2 ) )
= ( B @ ( A @ c_2Egcd_2Elcm_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__ADD) ).
thf(155,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__RNEG) ).
thf(198,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(39,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RDISTRIB) ).
thf(267,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(18,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__LNEG) ).
thf(167,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(44,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEGNEG) ).
thf(282,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(74,axiom,
! [A: tyop_2Ebinary__ieee_2Efloat__compare] :
( ( A @ c_2Ebinary__ieee_2Efloat__compare__size_2E1 )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__compare__size__def) ).
thf(409,plain,
! [A: tyop_2Ebinary__ieee_2Efloat__compare] :
( ( A @ c_2Ebinary__ieee_2Efloat__compare__size_2E1 )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(23,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__NEG) ).
thf(182,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A = B )
=> ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) )
& ( ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(65,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LZERO) ).
thf(370,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(84,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
& ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__MUL) ).
thf(463,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
& ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(7,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RADD) ).
thf(127,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A = B )
=> ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ) )
& ( ( ( C @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(55,axiom,
! [A: tyop_2Enum_2Enum] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Esptree_2Espt__acc_2E2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esptree_2Espt__acc__0) ).
thf(336,plain,
! [A: tyop_2Enum_2Enum] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Esptree_2Espt__acc_2E2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(69,axiom,
! [A: tyop_2Estring_2Echar] :
( ( A @ c_2Estring_2Echar__size_2E1 )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Echar__size__def) ).
thf(386,plain,
! [A: tyop_2Estring_2Echar] :
( ( A @ c_2Estring_2Echar__size_2E1 )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(80,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LID) ).
thf(446,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(10,axiom,
! [A: tyop_2Enum_2Enum] :
( ( A @ c_2Ecomplex_2Ecomplex__of__num_2E1 )
= ( A @ c_2Ereal_2Ereal__of__num_2E1 @ c_2Ecomplex_2Ecomplex__of__real_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__of__num) ).
thf(143,plain,
! [A: tyop_2Enum_2Enum] :
( ( A @ c_2Ecomplex_2Ecomplex__of__num_2E1 )
= ( A @ c_2Ereal_2Ereal__of__num_2E1 @ c_2Ecomplex_2Ecomplex__of__real_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,axiom,
! [A: tyop_2Eone_2Eone] :
( ( A @ c_2EbasicSize_2Eone__size_2E1 )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Eone__size__def) ).
thf(319,plain,
! [A: tyop_2Eone_2Eone] :
( ( A @ c_2EbasicSize_2Eone__size_2E1 )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(38,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= B )
<=> ( A
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__EQ) ).
thf(258,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= B ) )
& ( ( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= B )
=> ( A
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__TRIANGLE) ).
thf(158,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RDISTRIB) ).
thf(114,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( C @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(68,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
<=> ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(378,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
& ( ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( A
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(34,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
<=> ( A
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__LNEG__UNIQ) ).
thf(235,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( A
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( A
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( A @ c_2Ereal_2Ereal__of__num_2E1 )
= ( B @ c_2Ereal_2Ereal__of__num_2E1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__INJ) ).
thf(207,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( A = B )
=> ( ( A @ c_2Ereal_2Ereal__of__num_2E1 )
= ( B @ c_2Ereal_2Ereal__of__num_2E1 ) ) )
& ( ( ( A @ c_2Ereal_2Ereal__of__num_2E1 )
= ( B @ c_2Ereal_2Ereal__of__num_2E1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(59,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A )
<=> ( B
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ) ).
thf(346,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( B
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ) )
& ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A )
=> ( B
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(77,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
& ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL__IMP) ).
thf(432,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( C @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
& ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(11,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__ADD2) ).
thf(146,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( B @ c_2Ecomplex_2Ecomplex__add_2E2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(41,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__SUB) ).
thf(273,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( A @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(66,axiom,
! [A: tyop_2EternaryComparisons_2Eordering] :
( ( A @ c_2EternaryComparisons_2Eordering__size_2E1 )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Eordering__size__def) ).
thf(373,plain,
! [A: tyop_2EternaryComparisons_2Eordering] :
( ( A @ c_2EternaryComparisons_2Eordering__size_2E1 )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(48,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__RMUL) ).
thf(305,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) @ c_2Ecomplex_2Ecomplex__neg_2E1 )
= ( B @ c_2Ecomplex_2Ecomplex__neg_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(57,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RZERO) ).
thf(341,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(25,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),D: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( D @ ( C @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( D @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( C @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD2__SUB2) ).
thf(195,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),D: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( D @ ( C @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ ( B @ ( A @ c_2Ecomplex_2Ecomplex__add_2E2 ) @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= ( D @ ( B @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( C @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ c_2Ecomplex_2Ecomplex__add_2E2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,conjecture,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 )
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 )
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(90,plain,
~ ! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 )
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NEG) ).
thf(322,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ c_2Ecomplex_2Ecomplex__neg_2E1 @ c_2Ecomplex_2Ecomplex__inv_2E1 )
= ( A @ c_2Ecomplex_2Ecomplex__inv_2E1 @ c_2Ecomplex_2Ecomplex__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(89,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( A @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( A @ ( C @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
& ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RMUL__IMP) ).
thf(486,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),C: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( ( ( A @ ( B @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( A @ ( C @ c_2Ecomplex_2Ecomplex__mul_2E2 ) ) )
& ( A
!= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(86,axiom,
! [A: tyop_2Enum_2Enum] :
( ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( A
= ( C @ ( B @ c_2Enumpair_2Encons_2E2 ) ) )
| ( A = c_2Enum_2E0_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__cases) ).
thf(469,plain,
! [A: tyop_2Enum_2Enum] :
( ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( A
= ( C @ ( B @ c_2Enumpair_2Encons_2E2 ) ) )
| ( A = c_2Enum_2E0_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(60,axiom,
! [A: tyop_2Ebinary__ieee_2Erounding] :
( ( A @ c_2Ebinary__ieee_2Erounding__size_2E1 )
= c_2Enum_2E0_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Erounding__size__def) ).
thf(354,plain,
! [A: tyop_2Ebinary__ieee_2Erounding] :
( ( A @ c_2Ebinary__ieee_2Erounding__size_2E1 )
= c_2Enum_2E0_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(63,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__LZERO) ).
thf(364,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( A @ ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ c_2Ecomplex_2Ecomplex__mul_2E2 ) )
= ( c_2Enum_2E0_2E0 @ c_2Ecomplex_2Ecomplex__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(33,axiom,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__SUB2) ).
thf(232,plain,
! [A: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ),B: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod )] :
( ( B @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) @ ( A @ c_2Ecomplex_2Ecomplex__sub_2E2 ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(490,plain,
$false,
inference(e,[status(thm)],[472,288,243,360,466,406,255,104,395,170,308,449,217,276,389,344,357,460,421,325,152,316,475,164,179,443,376,117,270,201,220,392,192,137,229,252,435,285,328,339,96,457,173,412,161,279,149,176,291,204,367,140,155,198,267,167,282,409,182,370,463,127,336,386,446,143,319,258,158,114,378,235,207,346,432,146,273,373,305,341,195,90,322,486,469,354,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019_7 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % 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
% 0.15/0.50 % Computer : n009.cluster.edu
% 0.15/0.50 % Model : x86_64 x86_64
% 0.15/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.50 % Memory : 8046.5625MB
% 0.15/0.50 % OS : Linux 6.8.0-71-generic
% 0.15/0.50 % CPULimit : 300
% 0.15/0.51 % WCLimit : 300
% 0.15/0.51 % DateTime : Fri Sep 25 17:29:19 UTC 2026
% 0.15/0.51 % CPUTime :
% 0.15/0.51 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
% 0.69/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 12.26/5.47 % [INFO] Parsing done (4600ms).
% 12.37/5.51 % [INFO] Running in sequential loop mode.
% 12.80/5.89 % [INFO] eprover registered as external prover.
% 12.80/5.89 % [INFO] Scanning for conjecture ...
% 19.66/7.76 % [INFO] Found a conjecture (or negated_conjecture) and 23398 axioms. Running axiom selection ...
% 20.65/8.10 % [INFO] Axiom selection finished. Selected 87 axioms (removed 23311 axioms).
% 21.09/8.16 % [INFO] Problem is typed first-order (TPTP TFF).
% 21.09/8.16 % [INFO] Type checking passed.
% 21.09/8.17 % [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 ...
% 27.14/9.90 % External prover 'e' found a proof!
% 27.14/9.90 % [INFO] Killing All external provers ...
% 27.14/9.90 % Time passed: 9302ms (effective reasoning time: 4384ms)
% 27.14/9.90 % 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)>
% 27.14/9.91 % Axioms used in derivation (87): thm_2Egcd_2ELCM__COMM, thm_2Enumpair_2Encons__not__nnil, thm_2Ecomplex_2ECOMPLEX__NEG__EQ, thm_2Ebinary__ieee_2Efloat__compare__size__def, thm_2Ecomplex_2ECOMPLEX__MUL__RNEG, thm_2Ecomplex_2ECOMPLEX__EQ__RMUL, thm_2Ecomplex_2ECOMPLEX__SUB__TRIANGLE, thm_2Ecomplex_2ECOMPLEX__ADD__ASSOC, thm_2Ecomplex_2ECOMPLEX__ADD__RINV, thm_2Ecomplex_2ECOMPLEX__ADD__COMM, thm_2Ecomplex_2ECOMPLEX__EQ__LMUL2, thm_2Ecomplex_2ECOMPLEX__SUB__0, thm_2Ewords_2Ebit__count__upto__0, thm_2Ecomplex_2ECOMPLEX__EQ__RMUL__IMP, thm_2Ecomplex_2ECOMPLEX__INV__MUL, thm_2Ecomplex_2ECOMPLEX__SUB__ADD, thm_2Enumpair_2Enlist__cases, thm_2Ecomplex_2ECOMPLEX__ADD__RDISTRIB, thm_2Ecomplex_2ECOMPLEX__NEG__SUB, thm_2Ereal_2EREAL__OF__NUM__EQ, thm_2Ecomplex_2ECOMPLEX__MUL__RZERO, thm_2Ecomplex_2ECOMPLEX__SUB__SUB2, thm_2Ecomplex_2ECOMPLEX__EQ__RADD, thm_2Ecomplex_2ECOMPLEX__SUB__RDISTRIB, thm_2Ecomplex_2ECOMPLEX__SUB__RZERO, thm_2Ecomplex_2ECOMPLEX__SUB__NEG2, thm_2Ecomplex_2ECOMPLEX__SUB__RNEG, thm_2Ebinary__ieee_2Erounding__size__def, thm_2Ecomplex_2ECOMPLEX__NEG__INV, thm_2Ecomplex_2ECOMPLEX__LNEG__UNIQ, thm_2Ecomplex_2ECOMPLEX__EQ__LMUL, thm_2Ecomplex_2ECOMPLEX__NEG__RMUL, thm_2Ecomplex_2ECOMPLEX__SUB__SUB, thm_2EternaryComparisons_2Eordering__size__def, thm_2EbasicSize_2Eone__size__def, thm_2Ecomplex_2ECOMPLEX__SUB__ADD2, thm_2Ealignment_2Ealign__0, thm_2Ecomplex_2ECOMPLEX__ADD2__SUB2, thm_2Ecomplex_2Ecomplex__of__num, thm_2Egcd_2ELCM__0, thm_2Ecomplex_2ECOMPLEX__NEG__ADD, thm_2Ecomplex_2ECOMPLEX__INVINV, thm_2Ebitstring_2Eshiftr__0, thm_2Ereal_2EREAL__INJ, thm_2Ecomplex_2ECOMPLEX__NEG__0, thm_2Ecomplex_2ECOMPLEX__0, thm_2Estring_2Echar__size__def, thm_2Ecomplex_2ECOMPLEX__ADD__LID, thm_2Ecomplex_2ECOMPLEX__EQ__SUB__RADD, thm_2Ecomplex_2ECOMPLEX__ADD__SUB, thm_2Ecomplex_2ECOMPLEX__EQ__LADD, thm_2Ecomplex_2ECOMPLEX__DIFFSQ, thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD, thm_2Ecomplex_2ECOMPLEX__MUL__LZERO, thm_2Ecomplex_2ECOMPLEX__INV__EQ__0, thm_2Ecomplex_2ECOMPLEX__NEG__MUL2, thm_2Ealignment_2Ealign__align, thm_2Ecomplex_2ECOMPLEX__EQ__NEG, thm_2EbasicSize_2Ebool__size__def, thm_2Ecomplex_2ECOMPLEX__SUB__LZERO, thm_2Ecomplex_2ECOMPLEX__ADD__LDISTRIB, thm_2Ecomplex_2ECOMPLEX__SUB__LNEG, thm_2Ecomplex_2ECOMPLEX__MUL__LNEG, thm_2Ecomplex_2ECOMPLEX__ENTIRE, thm_2Enumpair_2Encons__11, thm_2Ecomplex_2ECOMPLEX__SUB__LDISTRIB, thm_2Ecomplex_2ECOMPLEX__MUL__COMM, thm_2Ecomplex_2ECOMPLEX__INV__INV, thm_2Ebag_2EEMPTY__BAG__alt, thm_2Ecomplex_2ECOMPLEX__RNEG__UNIQ, thm_2Ecomplex_2ECOMPLEX__INV__0, thm_2Ecomplex_2ECOMPLEX__ADD__RID, thm_2Ecomplex_2ECOMPLEX__NEGNEG, thm_2Ecomplex_2ECOMPLEX__EQ__LMUL__IMP, thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ, thm_2Ecomplex_2Ecomplex__div, thm_2Ecomplex_2EIM__COMPLEX__OF__REAL, thm_2Ecomplex_2ECOMPLEX__MUL__ASSOC, thm_2Ecomplex_2Ecomplex__sub, thm_2Ecomplex_2ECOMPLEX__NEG__EQ0, thm_2Ecomplex_2ECOMPLEX__NEG__LMUL, thm_2Ecomplex_2ECOMPLEX__SUB__REFL, thm_2Ecomplex_2ECOMPLEX__ADD__SUB2, thm_2Ecomplex_2ECOMPLEX__ADD__LINV, thm_2Ecomplex_2ECOMPLEX__ADD__LID__UNIQ, thm_2Esptree_2Espt__acc__0, thm_2Ecomplex_2ECOMPLEX__INV__NEG
% 27.14/9.91 % No. of inferences in proof: 178
% 27.14/9.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9302 ms resp. 4384 ms w/o parsing
% 27.62/10.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.62/10.05 % [INFO] Killing All external provers ...
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