%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP012^4 : 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 : n002.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 : Wed Sep 30 08:06:20 AM UTC 2026
% Result : Theorem 23.74s 10.21s
% Output : Refutation 24.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 46
% Syntax : Number of formulae : 94 ( 75 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 111 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 587 ( 2 ~; 0 |; 6 &; 564 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 53 ( 52 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 225 ( 0 ^; 223 !; 2 ?; 225 :)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(mono_2Etyop_2Emin_2Eind_type,type,
mono_2Etyop_2Emin_2Eind: $tType ).
thf(mono_2Etyop_2Enum_2Enum_type,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Eone_2Eone_type,type,
mono_2Etyop_2Eone_2Eone: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Estring_2Echar_type,type,
mono_2Etyop_2Estring_2Echar: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Esum_2Esum_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Esum_2Esum_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2EternaryComparisons_2Eordering_type,type,
mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ehrat_2Ehrat_type,type,
mono_2Etyop_2Ehrat_2Ehrat: $tType ).
thf(mono_2Etyop_2Einteger_2Eint_type,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(mono_2Ec_2Einteger_2Eint__add_decl,type,
mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__divides_decl,type,
mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__mul_decl,type,
mono_2Ec_2Einteger_2Eint__mul: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__neg_decl,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__sub_decl,type,
mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(8,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__ASSOC) ).
thf(69,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LDISTRIB) ).
thf(120,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD) ).
thf(157,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(13,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LDISTRIB) ).
thf(84,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).
thf(133,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(45,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__TRIANGLE) ).
thf(188,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(17,axiom,
! [A: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEGNEG) ).
thf(96,plain,
! [A: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).
thf(105,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(46,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB) ).
thf(191,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(3,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__COMM) ).
thf(54,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SYM) ).
thf(81,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB2) ).
thf(130,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RNEG) ).
thf(75,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
& ( mono_2Ec_2Einteger_2Eint__divides @ B @ C ) )
=> ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__TRANS) ).
thf(163,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
& ( mono_2Ec_2Einteger_2Eint__divides @ B @ C ) )
=> ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
& ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MUL) ).
thf(174,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
& ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(44,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
= C )
= ( A
= ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__RADD) ).
thf(185,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
= C )
= ( A
= ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(16,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__ASSOC) ).
thf(93,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LMUL) ).
thf(57,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB2) ).
thf(78,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__RMUL) ).
thf(102,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ C )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RDISTRIB) ).
thf(60,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ C )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__MUL2) ).
thf(117,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(36,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ A )
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB) ).
thf(160,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ A )
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(30,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ B @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD2) ).
thf(137,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ B @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint,D: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__add @ C @ D ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD2__SUB2) ).
thf(165,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint,D: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__add @ C @ D ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(42,axiom,
! [A: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__divides @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__REFL) ).
thf(180,plain,
! [A: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__divides @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(34,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).
thf(149,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(31,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( A
= ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__LADD) ).
thf(140,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( A
= ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__COMM) ).
thf(66,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__NEG) ).
thf(108,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LSUB) ).
thf(123,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(47,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LADD) ).
thf(194,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1,conjecture,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).
thf(2,negated_conjecture,
~ ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SYM) ).
thf(63,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
= ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RMUL) ).
thf(182,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(27,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
= ( ? [C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ C @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES) ).
thf(127,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
= ( ? [C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ C @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LNEG) ).
thf(72,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(32,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RDISTRIB) ).
thf(143,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__ADD) ).
thf(99,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ B )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LADD) ).
thf(87,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ B )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ A ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIFFSQ) ).
thf(114,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ A ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SUB) ).
thf(171,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(39,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__NEG2) ).
thf(168,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LMUL) ).
thf(146,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
= ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RADD) ).
thf(90,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
= ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
= B )
= ( A
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ) ).
thf(111,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
= B )
= ( A
= ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(198,plain,
$false,
inference(e,[status(thm)],[69,120,157,84,133,188,96,105,191,54,81,130,75,163,174,185,93,57,78,102,60,117,160,137,165,180,149,140,66,108,123,194,48,63,182,127,72,143,99,87,114,171,168,146,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP012^4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % 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
% 0.09/0.21 % Computer : n002.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 19:28:55 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 12.70/6.45 % [INFO] Parsing done (5638ms).
% 12.70/6.48 % [INFO] Running in sequential loop mode.
% 13.27/6.86 % [INFO] eprover registered as external prover.
% 13.27/6.86 % [INFO] Scanning for conjecture ...
% 18.56/8.65 % [INFO] Found a conjecture (or negated_conjecture) and 18501 axioms. Running axiom selection ...
% 19.36/8.92 % [INFO] Axiom selection finished. Selected 45 axioms (removed 18456 axioms).
% 19.36/8.98 % [INFO] Problem is higher-order (TPTP THF).
% 19.36/8.99 % [INFO] Type checking passed.
% 19.36/9.00 % [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 ...
% 23.74/10.20 % External prover 'e' found a proof!
% 23.74/10.21 % [INFO] Killing All external provers ...
% 23.74/10.21 % Time passed: 9849ms (effective reasoning time: 3715ms)
% 23.74/10.21 % 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)>
% 23.74/10.21 % Axioms used in derivation (45): thm_2Einteger_2EINT__NEG__RMUL, thm_2Einteger_2EINT__ADD__ASSOC, thm_2Einteger_2EINT__NEG__SUB, thm_2Einteger_2EINT__EQ__NEG, thm_2Einteger_2EINT__SUB__NEG2, thm_2Einteger_2EINT__DIVIDES__RADD, thm_2Einteger_2EINT__DIVIDES__RMUL, thm_2Einteger_2EINT__DIVIDES__NEG, thm_2Einteger_2EINT__NEGNEG, thm_2Einteger_2EINT__RDISTRIB, thm_2Einteger_2EINT__SUB__LNEG, thm_2Einteger_2EINT__ADD__SYM, thm_2Einteger_2EINT__SUB__SUB, thm_2Einteger_2EINT__EQ__LADD, thm_2Einteger_2EINT__DIVIDES__MUL, thm_2Einteger_2Eint__sub, thm_2Einteger_2EINT__DIVIDES__LSUB, thm_2Einteger_2EINT__DIVIDES__REFL, thm_2Einteger_2EINT__SUB__TRIANGLE, thm_2Einteger_2EINT__MUL__SYM, thm_2Einteger_2EINT__SUB__SUB2, thm_2Einteger_2EINT__ADD__SUB2, thm_2Einteger_2EINT__DIVIDES, thm_2Einteger_2EINT__MUL__COMM, thm_2Einteger_2EINT__SUB__RNEG, thm_2Einteger_2EINT__DIVIDES__LMUL, thm_2Einteger_2EINT__NEG__EQ, thm_2Einteger_2EINT__DIVIDES__LADD, thm_2Einteger_2EINT__ADD__COMM, thm_2Einteger_2EINT__DIVIDES__TRANS, thm_2Einteger_2EINT__ADD2__SUB2, thm_2Einteger_2EINT__NEG__MUL2, thm_2Einteger_2EINT__SUB__RDISTRIB, thm_2Einteger_2EINT__LDISTRIB, thm_2Einteger_2EINT__SUB__LDISTRIB, thm_2Einteger_2EINT__MUL__ASSOC, thm_2Einteger_2EINT__SUB__ADD, thm_2Einteger_2EINT__EQ__RADD, thm_2Einteger_2EINT__NEG__LMUL, thm_2Einteger_2EINT__NEG__ADD, thm_2Einteger_2EINT__EQ__SUB__RADD, thm_2Einteger_2EINT__EQ__SUB__LADD, thm_2Einteger_2EINT__ADD__SUB, thm_2Einteger_2EINT__DIFFSQ, thm_2Einteger_2EINT__SUB__ADD2
% 23.74/10.21 % No. of inferences in proof: 94
% 23.74/10.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9849 ms resp. 3715 ms w/o parsing
% 24.11/10.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.11/10.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------