%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP018_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 : n012.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 07:35:44 AM UTC 2026
% Result : Theorem 19.04s 7.48s
% Output : Refutation 19.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 433 ( 176 equ; 0 cnn)
% Maximal formula atoms : 35 ( 6 avg)
% Number of connectives : 2167 ( 131 ~; 2 |; 106 &;1922 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 6 avg)
% Number of types : 21 ( 21 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 7 con; 0-7 aty)
% Number of variables : 173 ( 0 ^; 173 !; 0 ?; 173 :)
% 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(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(c_2Ebool_2Eitself__case_2E2_decl,type,
c_2Ebool_2Eitself__case_2E2:
!>[TA: $tType,TB: $tType] : ( ( TB @ tyop_2Ebool_2Eitself ) > TA > TA ) ).
thf(c_2Ebool_2Ethe__value_2E0_decl,type,
c_2Ebool_2Ethe__value_2E0:
!>[TA: $tType] : ( TA @ tyop_2Ebool_2Eitself ) ).
thf(c_2EerrorStateMonad_2EMCOMP_2E2_decl,type,
c_2EerrorStateMonad_2EMCOMP_2E2:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( ( TC @ tyop_2Eoption_2Eoption @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ tyop_2Emin_2Efun ) ) > ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Eoption_2Eoption @ ( TD @ tyop_2Emin_2Efun ) @ ( TE @ tyop_2Emin_2Efun ) ) > ( TC @ tyop_2Eoption_2Eoption @ ( TD @ tyop_2Emin_2Efun ) @ ( TE @ tyop_2Emin_2Efun ) ) ) ).
thf(c_2Erealax_2Ereal__neg_2E1_decl,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Etransc_2Etan_2E1_decl,type,
c_2Etransc_2Etan_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ebinary__ieee_2Efloat__bottom_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__bottom_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__minus__infinity_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__minus__infinity_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__minus__min_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__minus__min_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__minus__zero_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__minus__zero_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__negate_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__negate_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__plus__infinity_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__plus__infinity_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__plus__zero_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__plus__zero_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__some__qnan_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__some__qnan_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op ) ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) > tyop_2Erealax_2Ereal ) ).
thf(c_2Ebinary__ieee_2Efloat__top_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__top_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Eulp_2E1_decl,type,
c_2Ebinary__ieee_2Eulp_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > tyop_2Erealax_2Ereal ) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ! [A: TC @ ( TD @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TC @ ( TD @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) )
!= A )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__distinct) ).
thf(27,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ! [A: TC @ ( TD @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TC @ ( TD @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) )
!= A )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) )
& ! [A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) )
& ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,I: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ),H: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op ),G: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op ),F: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op ),E: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op ),D: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op ),C: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op ),B: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op ),A: TD @ ( TC @ tyop_2Ebinary__ieee_2Efp__op )] :
( ( ( I @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) )
!= I )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) )
!= ( H @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
!= ( G @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
!= ( F @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( E @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( D @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( C @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( B @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( A @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__some__qnan_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) )
& ( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(61,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(68,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(69,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(7,axiom,
! [TA: $tType,A: TA @ tyop_2Ebool_2Eitself] :
( A
= ( TA @ c_2Ebool_2Ethe__value_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EITSELF__UNIQUE) ).
thf(140,plain,
! [TA: $tType,A: TA @ tyop_2Ebool_2Eitself] :
( A
= ( TA @ c_2Ebool_2Ethe__value_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(141,plain,
! [TA: $tType,A: TA @ tyop_2Ebool_2Eitself] :
( A
= ( TA @ c_2Ebool_2Ethe__value_2E0 ) ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [TA: $tType,A: TA @ tyop_2Ebool_2Eitself] :
( A
= ( TA @ c_2Ebool_2Ethe__value_2E0 ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(15,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= B )
<=> ( A
= ( B @ c_2Erealax_2Ereal__neg_2E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__EQ) ).
thf(164,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( A
= ( B @ c_2Erealax_2Ereal__neg_2E1 ) )
=> ( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= B ) )
& ( ( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= B )
=> ( A
= ( B @ c_2Erealax_2Ereal__neg_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TA] :
( ( A @ ( TB @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebool_2Eitself__case_2E2 ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Eitself__case__thm) ).
thf(137,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( A @ ( TB @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebool_2Eitself__case_2E2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(56,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(64,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(65,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__minus__zero__def) ).
thf(173,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__zero_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(60,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(70,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(71,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__zero_2E1 ) ) )
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(52,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(66,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(67,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(143,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 @ c_2Etransc_2Etan_2E1 )
= ( A @ c_2Etransc_2Etan_2E1 @ c_2Erealax_2Ereal__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Etransc_2ETAN__NEG) ).
thf(146,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 @ c_2Etransc_2Etan_2E1 )
= ( A @ c_2Etransc_2Etan_2E1 @ c_2Erealax_2Ereal__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__minus__infinity__def) ).
thf(134,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(135,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(19,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 @ c_2Erealax_2Ereal__neg_2E1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEGNEG) ).
thf(189,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 @ c_2Erealax_2Ereal__neg_2E1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__minus__min__def) ).
thf(152,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(53,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(72,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(73,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) )
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__minus__min_2E1 ) ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Eoption_2Eoption @ ( TF @ tyop_2Emin_2Efun ) @ ( TG @ tyop_2Emin_2Efun ),B: TC @ ( TD @ tyop_2Epair_2Eprod ) @ tyop_2Eoption_2Eoption @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ tyop_2Emin_2Efun ),C: TE @ tyop_2Eoption_2Eoption @ ( TC @ tyop_2Emin_2Efun ) @ ( TD @ tyop_2Emin_2Efun )] :
( ( A @ ( B @ ( TA @ ( TB @ ( TC @ ( TD @ tyop_2Epair_2Eprod ) @ ( TF @ ( TG @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) @ ( C @ ( TC @ ( TD @ ( TE @ ( TF @ ( TG @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( TC @ ( TD @ ( TE @ ( TA @ ( TB @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) @ ( TA @ ( TB @ ( TE @ ( TF @ ( TG @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EerrorStateMonad_2EMCOMP__ASSOC) ).
thf(161,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Eoption_2Eoption @ ( TF @ tyop_2Emin_2Efun ) @ ( TG @ tyop_2Emin_2Efun ),B: TC @ ( TD @ tyop_2Epair_2Eprod ) @ tyop_2Eoption_2Eoption @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ tyop_2Emin_2Efun ),C: TE @ tyop_2Eoption_2Eoption @ ( TC @ tyop_2Emin_2Efun ) @ ( TD @ tyop_2Emin_2Efun )] :
( ( A @ ( B @ ( TA @ ( TB @ ( TC @ ( TD @ tyop_2Epair_2Eprod ) @ ( TF @ ( TG @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) @ ( C @ ( TC @ ( TD @ ( TE @ ( TF @ ( TG @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( TC @ ( TD @ ( TE @ ( TA @ ( TB @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) @ ( TA @ ( TB @ ( TE @ ( TF @ ( TG @ c_2EerrorStateMonad_2EMCOMP_2E2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 @ c_2Erealax_2Ereal__neg_2E1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__NEG) ).
thf(149,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 @ c_2Erealax_2Ereal__neg_2E1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= ( B @ c_2Erealax_2Ereal__neg_2E1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__NEG) ).
thf(176,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( A = B )
=> ( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= ( B @ c_2Erealax_2Ereal__neg_2E1 ) ) )
& ( ( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= ( B @ c_2Erealax_2Ereal__neg_2E1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__negate__negate) ).
thf(155,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
~ ( ( A
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) )
& ( A
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__infinities__distinct) ).
thf(23,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
~ ( ( A
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) )
& ( A
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) )
| ( A
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) )
| ( A
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(26,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 ) ) )
!= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
thf(158,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__bottom__def) ).
thf(186,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__bottom_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__top_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(292,plain,
$false,
inference(e,[status(thm)],[69,142,164,137,65,173,71,67,143,146,136,189,20,152,134,73,161,149,176,22,27,140,155,26,158,186,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018_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
% 0.14/0.40 % Computer : n012.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 17:27:41 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.88/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 11.89/5.21 % [INFO] Parsing done (4286ms).
% 11.89/5.23 % [INFO] Running in sequential loop mode.
% 12.05/5.39 % [INFO] eprover registered as external prover.
% 12.05/5.39 % [INFO] Scanning for conjecture ...
% 15.46/6.39 % [INFO] Found a conjecture (or negated_conjecture) and 23089 axioms. Running axiom selection ...
% 16.06/6.68 % [INFO] Axiom selection finished. Selected 17 axioms (removed 23072 axioms).
% 16.28/6.72 % [INFO] Problem is typed first-order (TPTP TFF).
% 16.28/6.73 % [INFO] Type checking passed.
% 16.28/6.73 % [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 ...
% 17.29/7.06 % [INFO] [Domain constraints] Detected constraint on tyop_2Ebool_2Eitself(1)
% 17.29/7.06 % [INFO] [Domain constraints] dom(tyop_2Ebool_2Eitself(1)) ⊆ {c_2Ebool_2Ethe__value_2E0 ⋅ (1;⊥)}
% 19.04/7.47 % External prover 'e' found a proof!
% 19.04/7.47 % [INFO] Killing All external provers ...
% 19.04/7.47 % Time passed: 6947ms (effective reasoning time: 2244ms)
% 19.04/7.47 % 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)>
% 19.04/7.48 % Axioms used in derivation (17): thm_2Ebinary__ieee_2Efloat__distinct, thm_2Ebinary__ieee_2Efloat__minus__infinity__def, thm_2Ebinary__ieee_2Efloat__to__real__negate, thm_2Ebinary__ieee_2Efloat__minus__min__def, thm_2Ebool_2Eitself__case__thm, thm_2Ebool_2EITSELF__UNIQUE, thm_2EerrorStateMonad_2EMCOMP__ASSOC, thm_2Ereal_2EREAL__EQ__NEG, thm_2Ebinary__ieee_2Eulp, thm_2Ebinary__ieee_2Efloat__minus__zero__def, thm_2Ereal_2EREAL__NEGNEG, thm_2Ereal_2EREAL__NEG__NEG, thm_2Ebinary__ieee_2Efloat__negate__negate, thm_2Ebinary__ieee_2Efloat__bottom__def, thm_2Ereal_2EREAL__NEG__EQ, thm_2Ebinary__ieee_2Efloat__infinities__distinct, thm_2Etransc_2ETAN__NEG
% 19.04/7.48 % No. of inferences in proof: 63
% 19.04/7.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6947 ms resp. 2244 ms w/o parsing
% 19.57/7.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.57/7.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------