%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP013_1 : 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 : n011.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 07:35:35 AM UTC 2026
% Result : Theorem 29.24s 6.43s
% Output : Refutation 25.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 71
% Syntax : Number of formulae : 216 ( 133 unt; 0 typ; 3 def)
% Number of atoms : 515 ( 212 equ; 0 cnn)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 3670 ( 100 ~; 66 |; 68 &;3302 @)
% ( 26 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 27 con; 0-4 aty)
% Number of variables : 385 ( 0 ^; 379 !; 3 ?; 385 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(mono_2Etyop_2Emin_2Ebool_type,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Enum_2Enum_type,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(tyop_2Efcp_2Ecart_decl,type,
tyop_2Efcp_2Ecart: d > d > d ).
thf(tyop_2Emin_2Ebool_decl,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun_decl,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum_decl,type,
tyop_2Enum_2Enum: d ).
thf(s_decl,type,
s: d > u > du ).
thf(app_2E2_decl,type,
app_2E2: du > du > u ).
thf(p_decl,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
thf(combin_i_2E0_decl,type,
combin_i_2E0: u ).
thf(combin_k_2E0_decl,type,
combin_k_2E0: u ).
thf(combin_s_2E0_decl,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0_decl,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1_decl,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Emin_2E_3D_2E0_decl,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2_decl,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0_decl,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1_decl,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Ebool_2ECOND_2E0_decl,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3_decl,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Ewords_2En2w_2E0_decl,type,
c_2Ewords_2En2w_2E0: u ).
thf(c_2Ewords_2En2w_2E1_decl,type,
c_2Ewords_2En2w_2E1: du > u ).
thf(c_2Ewords_2Eword__2comp_2E0_decl,type,
c_2Ewords_2Eword__2comp_2E0: u ).
thf(c_2Ewords_2Eword__2comp_2E1_decl,type,
c_2Ewords_2Eword__2comp_2E1: du > u ).
thf(c_2Ewords_2Eword__add_2E0_decl,type,
c_2Ewords_2Eword__add_2E0: u ).
thf(c_2Ewords_2Eword__add_2E2_decl,type,
c_2Ewords_2Eword__add_2E2: du > du > u ).
thf(c_2Ewords_2Eword__sub_2E0_decl,type,
c_2Ewords_2Eword__sub_2E0: u ).
thf(c_2Ewords_2Eword__sub_2E2_decl,type,
c_2Ewords_2Eword__sub_2E2: du > du > u ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2B_2E0_decl,type,
mono_2Ec_2Earithmetic_2E_2B_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).
thf(mono_2Ec_2Earithmetic_2E_2B_2E2_decl,type,
mono_2Ec_2Earithmetic_2E_2B_2E2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2D_2E0_decl,type,
mono_2Ec_2Earithmetic_2E_2D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).
thf(mono_2Ec_2Earithmetic_2E_2D_2E2_decl,type,
mono_2Ec_2Earithmetic_2E_2D_2E2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_2F_5C_2E0_decl,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(mono_2Ec_2Ebool_2E_2F_5C_2E2_decl,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Earithmetic_2E_3C_3D_2E0_decl,type,
mono_2Ec_2Earithmetic_2E_3C_3D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).
thf(mono_2Ec_2Earithmetic_2E_3C_3D_2E2_decl,type,
mono_2Ec_2Earithmetic_2E_3C_3D_2E2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E0_decl,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E2_decl,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2EF_2E0_decl,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2ET_2E0_decl,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2E_5C_2F_2E0_decl,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(mono_2Ec_2Ebool_2E_5C_2F_2E2_decl,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2E_7E_2E0_decl,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Ec_2Ebool_2E_7E_2E1_decl,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(i_mono_2Etyop_2Emin_2Ebool_decl,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_decl,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_decl,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_decl,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_decl,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_decl,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_decl,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).
thf(i_mono_2Etyop_2Enum_2Enum_decl,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(j_mono_2Etyop_2Emin_2Ebool_decl,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_decl,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_decl,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_decl,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_decl,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_decl,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_decl,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Enum_2Enum_decl,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(sk1_decl,type,
sk1: d ).
thf(sk2_decl,type,
sk2: mono_2Etyop_2Enum_2Enum ).
thf(sk3_decl,type,
sk3: mono_2Etyop_2Enum_2Enum ).
thf(sk5_decl,type,
sk5: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: d] :
~ ! [B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( C @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( C @ ( B @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: mono_2Etyop_2Enum_2Enum] :
~ ! [B: mono_2Etyop_2Enum_2Enum] :
( ( A @ ( B @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: mono_2Etyop_2Enum_2Enum] :
~ ( ( sk2 @ ( A @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( A @ ( sk2 @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ) ) ) ).
thf(5,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
<=> ( ( A @ p )
=> ( B @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(81,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p ) )
& ( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(82,plain,
( ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p ) )
& ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) ) ),
inference(miniscope,[status(thm)],[81]) ).
thf(83,plain,
! [D: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( ( D @ ( C @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
| ~ ( D @ p ) )
& ( ( D @ ( C @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
| ( C @ p ) )
& ( ( B @ p )
| ~ ( A @ p )
| ~ ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(86,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
| ~ ( B @ p ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(88,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
| ~ ( B @ p ) ),
inference(simp,[status(thm)],[86]) ).
thf(15,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) ).
thf(140,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(141,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 )
= A ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 )
= A ),
inference(lifteq,[status(thm)],[141]) ).
thf(64,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
<=> ~ ( A @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(393,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ~ ( A @ p )
=> ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) )
& ( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
=> ~ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(20,axiom,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Enum_2Enum) ).
thf(159,plain,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(59,axiom,
! [A: d] :
( ! [B: u,C: u] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2EF_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
& ! [B: u,C: u] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2ET_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(370,plain,
! [A: d] :
( ! [B: u,C: u] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2EF_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
& ! [B: u,C: u] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2ET_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a) ).
thf(143,plain,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,D: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( ( A @ p )
=> ( C @ p ) )
<=> ( ( B @ p )
=> ( D @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG) ).
thf(122,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,D: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( ( ( B @ p )
=> ( D @ p ) )
=> ( ( A @ p )
=> ( C @ p ) ) )
& ( ( ( A @ p )
=> ( C @ p ) )
=> ( ( B @ p )
=> ( D @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(123,plain,
! [D: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( ( C @ p )
| ~ ( A @ p )
| ~ ( D @ p )
| ~ ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) ) )
& ( ( C @ p )
| ~ ( A @ p )
| ( B @ p )
| ~ ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) ) )
& ( ( D @ p )
| ~ ( B @ p )
| ~ ( C @ p )
| ~ ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) ) )
& ( ( D @ p )
| ~ ( B @ p )
| ( A @ p )
| ~ ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) ) )
& ( ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) )
| ( C != D )
| ( A != B ) )
& ( ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) )
| ( B @ p )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(129,plain,
! [D: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) )
| ( C != D )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[123]) ).
thf(130,plain,
! [D: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( D @ ( B @ ( C @ ( A @ sk5 ) ) ) )
| ( C != D )
| ( A != B ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(131,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] : ( B @ ( A @ ( B @ ( A @ sk5 ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(68,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) ).
thf(408,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(40,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) ).
thf(269,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(62,axiom,
! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
( ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
thf(389,plain,
! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
( ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(9,axiom,
! [A: d,B: u] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
<=> ! [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(110,plain,
! [A: d,B: u] :
( ( ! [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
=> ! [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( A @ p )
<=> ( A @ ( mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(189,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ ( mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
=> ~ ( A @ p ) )
& ( ~ ( A @ p )
=> ( A @ ( mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(49,axiom,
! [A: d,B: u] :
( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b) ).
thf(325,plain,
! [A: d,B: u] :
( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(19,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( B @ p )
| ( A @ p ) )
<=> ( B @ ( A @ ( mono_2Ec_2Ebool_2E_5C_2F_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(152,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( mono_2Ec_2Ebool_2E_5C_2F_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
=> ( ( B @ p )
| ( A @ p ) ) )
& ( ( ( B @ p )
| ( A @ p ) )
=> ( B @ ( A @ ( mono_2Ec_2Ebool_2E_5C_2F_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(228,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(45,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ ( A @ p ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = A )
<=> ~ ( A @ p ) )
& ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
<=> ( A @ p ) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = A )
<=> ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(289,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ~ ( A @ p )
=> ( A = mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
=> ~ ( A @ p ) )
& ( ~ ( A @ p )
=> ( mono_2Ec_2Ebool_2EF_2E0 = A ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = A )
=> ~ ( A @ p ) )
& ( ( A @ p )
=> ( A = mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
=> ( A @ p ) )
& ( ( A @ p )
=> ( mono_2Ec_2Ebool_2ET_2E0 = A ) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 = A )
=> ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(46,axiom,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
thf(316,plain,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4,axiom,
! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_2B_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_2B_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_2B_2E2) ).
thf(78,plain,
! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_2B_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_2B_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) ).
thf(216,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29) ).
thf(253,plain,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(53,axiom,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) ).
thf(348,plain,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(84,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( B @ p )
| ~ ( A @ p )
| ~ ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(42,axiom,
! [A: d,B: d,C: u,D: u] :
( ( D @ ( B @ s ) @ ( C @ ( A @ s ) @ ( combin_k_2E0 @ ( A @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(280,plain,
! [A: d,B: d,C: u,D: u] :
( ( D @ ( B @ s ) @ ( C @ ( A @ s ) @ ( combin_k_2E0 @ ( A @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(394,plain,
( ! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( A @ p )
=> ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) )
& ! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
=> ~ ( A @ p ) ) ),
inference(miniscope,[status(thm)],[393]) ).
thf(395,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( ( B @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
| ( B @ p ) )
& ( ~ ( A @ p )
| ~ ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( A @ p )
| ~ ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) ),
inference(cnfConj,[status(thm)],[395]) ).
thf(6,axiom,
! [A: d,B: u,C: u] :
( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
<=> ( ( C @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__SYM__EQ) ).
thf(89,plain,
! [A: d,B: u,C: u] :
( ( ( ( C @ ( A @ s ) )
= ( B @ ( A @ s ) ) )
=> ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) ) )
& ( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
=> ( ( C @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(69,axiom,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__sub_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a) ).
thf(411,plain,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__sub_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1,conjecture,
! [A: d,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( C @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( C @ ( B @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
thf(2,negated_conjecture,
~ ! [A: d,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( C @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( C @ ( B @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(70,plain,
~ ! [A: d,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( C @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
=> ( ( C @ ( B @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(71,plain,
( ( ( sk3 @ ( sk2 @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( sk3 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
& ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p ) ),
inference(cnf,[status(esa)],[70]) ).
thf(73,plain,
( ( sk3 @ ( sk2 @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( sk3 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(74,plain,
( ( sk3 @ ( sk2 @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( sk3 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(10,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) ).
thf(116,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(33,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).
thf(241,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(242,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= A ),
inference(cnf,[status(esa)],[241]) ).
thf(243,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= A ),
inference(lifteq,[status(thm)],[242]) ).
thf(32,axiom,
! [A: d,B: d] :
( ! [C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
( ( D @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( D @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( D @ ( C @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( D @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
& ! [C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
( ( D @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( C @ mono_2Ec_2Earithmetic_2E_2B_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
thf(233,plain,
! [A: d,B: d] :
( ! [C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
( ( D @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( D @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( D @ ( C @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( D @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
& ! [C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
( ( D @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( C @ mono_2Ec_2Earithmetic_2E_2B_2E2 ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(61,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( B @ p )
& ( A @ p ) )
<=> ( B @ ( A @ ( mono_2Ec_2Ebool_2E_2F_5C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(381,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( mono_2Ec_2Ebool_2E_2F_5C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) )
& ( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( mono_2Ec_2Ebool_2E_2F_5C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(29,axiom,
! [A: d,B: u,C: u] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
<=> ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(220,plain,
! [A: d,B: u,C: u] :
( ( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
=> ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) )
& ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
=> ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(63,axiom,
mono_2Ec_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(392,plain,
mono_2Ec_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(14,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) ).
thf(137,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(250,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(251,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
inference(lifteq,[status(thm)],[251]) ).
thf(24,axiom,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).
thf(195,plain,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(196,plain,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(56,axiom,
! [A: d,B: u] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(361,plain,
! [A: d,B: u] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,axiom,
mono_2Ec_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(97,plain,
mono_2Ec_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,axiom,
! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) ).
thf(322,plain,
! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(323,plain,
! [B: mono_2Etyop_2Enum_2Enum,A: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) ) ),
inference(cnf,[status(esa)],[322]) ).
thf(324,plain,
! [B: mono_2Etyop_2Enum_2Enum,A: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) ) ),
inference(lifteq,[status(thm)],[323]) ).
thf(43,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29) ).
thf(283,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(284,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
inference(cnf,[status(esa)],[283]) ).
thf(285,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 )
= A ),
inference(lifteq,[status(thm)],[284]) ).
thf(3,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2EF_2E0 )
| ( A = mono_2Ec_2Ebool_2ET_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(75,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2EF_2E0 )
| ( A = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(76,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2EF_2E0 )
| ( A = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2EF_2E0 )
| ( A = mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(72,plain,
sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p,
inference(cnfConj,[status(thm)],[71]) ).
thf(753,plain,
sk2 @ ( sk3 @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) @ p,
inference(rewrite,[status(thm)],[72,324]) ).
thf(50,axiom,
! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,D: u,E: u,F: u,G: u] :
( ( ( ~ ( C @ p )
=> ( ( F @ ( A @ s ) )
= ( G @ ( A @ s ) ) ) )
& ( ( C @ p )
=> ( ( D @ ( A @ s ) )
= ( E @ ( A @ s ) ) ) )
& ( B = C ) )
=> ( ( F @ ( A @ s ) @ ( D @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( G @ ( A @ s ) @ ( E @ ( A @ s ) @ ( C @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(328,plain,
! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,D: u,E: u,F: u,G: u] :
( ( ( ~ ( C @ p )
=> ( ( F @ ( A @ s ) )
= ( G @ ( A @ s ) ) ) )
& ( ( C @ p )
=> ( ( D @ ( A @ s ) )
= ( E @ ( A @ s ) ) ) )
& ( B = C ) )
=> ( ( F @ ( A @ s ) @ ( D @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( G @ ( A @ s ) @ ( E @ ( A @ s ) @ ( C @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(37,axiom,
! [A: d,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).
thf(256,plain,
! [A: d,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) ).
thf(134,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(34,axiom,
! [A: d,B: u] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
<=> ? [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(244,plain,
! [A: d,B: u] :
( ( ? [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
=> ? [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(39,axiom,
! [A: mono_2Etyop_2Enum_2Enum] :
( ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Enum_2Enum) ).
thf(266,plain,
! [A: mono_2Etyop_2Enum_2Enum] :
( ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(160,plain,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(cnf,[status(esa)],[159]) ).
thf(161,plain,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(lifteq,[status(thm)],[160]) ).
thf(430,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
!= ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
| ~ ( A @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,396]) ).
thf(431,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
!= ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
| ~ ( A @ p ) ),
inference(simp,[status(thm)],[430]) ).
thf(444,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 )
!= mono_2Ec_2Ebool_2ET_2E0 )
| ~ ( A @ p ) ),
inference(simp,[status(thm)],[431]) ).
thf(18,axiom,
! [A: d,B: u] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(149,plain,
! [A: d,B: u] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
= ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(66,axiom,
! [A: d,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b) ).
thf(402,plain,
! [A: d,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(44,axiom,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(286,plain,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(38,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( B @ p ) )
<=> ( B @ ( A @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(259,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) )
& ( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(28,axiom,
! [A: d,B: u] :
( ( ( B @ ( A @ s ) )
= ( B @ ( A @ s ) ) )
<=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(219,plain,
mono_2Ec_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(437,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( A @ p ) )
| ~ $true
| ~ ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) ),
inference(paramod_ordered,[status(thm)],[72,396]) ).
thf(438,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( A @ p ) )
| ~ ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) ),
inference(simp,[status(thm)],[437]) ).
thf(439,plain,
~ ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ),
inference(pattern_uni,[status(thm)],[438:[bind(A,$thf( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) ))]]) ).
thf(455,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A
!= ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ mono_2Ec_2Ebool_2E_7E_2E1 ) )
| ~ ( mono_2Ec_2Ebool_2ET_2E0 @ p )
| ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[77,439]) ).
thf(456,plain,
( ~ ( mono_2Ec_2Ebool_2ET_2E0 @ p )
| ( ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ mono_2Ec_2Ebool_2E_7E_2E1 )
= mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(pattern_uni,[status(thm)],[455:[bind(A,$thf( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ mono_2Ec_2Ebool_2E_7E_2E1 ))]]) ).
thf(783,plain,
( ~ $true
| ( ( sk2 @ ( sk3 @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) @ mono_2Ec_2Ebool_2E_7E_2E1 )
= mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(rewrite,[status(thm)],[456,97,324]) ).
thf(784,plain,
( ( sk2 @ ( sk3 @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) @ mono_2Ec_2Ebool_2E_7E_2E1 )
= mono_2Ec_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[783]) ).
thf(229,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 )
= A ),
inference(cnf,[status(esa)],[228]) ).
thf(230,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 )
= A ),
inference(lifteq,[status(thm)],[229]) ).
thf(8,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) )
<=> ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(98,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) )
=> ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) ) )
& ( ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) )
=> ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(270,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 )
= A ),
inference(cnf,[status(esa)],[269]) ).
thf(271,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 )
= A ),
inference(lifteq,[status(thm)],[270]) ).
thf(26,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Ebool_2E_5C_2F_2E2 ) @ p )
<=> ( ( B @ p )
| ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(208,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( B @ p )
| ( A @ p ) )
=> ( B @ ( A @ mono_2Ec_2Ebool_2E_5C_2F_2E2 ) @ p ) )
& ( ( B @ ( A @ mono_2Ec_2Ebool_2E_5C_2F_2E2 ) @ p )
=> ( ( B @ p )
| ( A @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(25,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ p )
<=> ( B @ p ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(198,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( B @ p )
=> ( A @ p ) )
& ( ( A @ p )
=> ( B @ p ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(52,axiom,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) ).
thf(345,plain,
! [A: u] :
( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(58,axiom,
! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_2D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_2D_2E2) ).
thf(367,plain,
! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_2D_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_2D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(65,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29) ).
thf(399,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(79,plain,
! [B: mono_2Etyop_2Enum_2Enum,A: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_2B_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_2B_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
inference(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [B: mono_2Etyop_2Enum_2Enum,A: mono_2Etyop_2Enum_2Enum] :
( ( B @ ( A @ mono_2Ec_2Earithmetic_2E_2B_2E2 ) )
= ( B @ ( A @ ( mono_2Ec_2Earithmetic_2E_2B_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(21,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( A @ p )
=> ( mono_2Ec_2Ebool_2EF_2E0 @ p ) )
<=> ~ ( A @ p ) )
& ( ( ( A @ p )
=> ( A @ p ) )
<=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
& ( ( ( mono_2Ec_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) )
<=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
& ( ( ( A @ p )
=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
<=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
& ( ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
=> ( A @ p ) )
<=> ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(162,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ~ ( A @ p )
=> ( ( A @ p )
=> ( mono_2Ec_2Ebool_2EF_2E0 @ p ) ) )
& ( ( ( A @ p )
=> ( mono_2Ec_2Ebool_2EF_2E0 @ p ) )
=> ~ ( A @ p ) )
& ( mono_2Ec_2Ebool_2ET_2E0 @ p )
& ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
=> ( ( mono_2Ec_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) ) )
& ( ( ( mono_2Ec_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) )
=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
& ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
=> ( ( A @ p )
=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) ) )
& ( ( ( A @ p )
=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
& ( ( A @ p )
=> ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
=> ( A @ p ) ) )
& ( ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
=> ( A @ p ) )
=> ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(51,axiom,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29) ).
thf(342,plain,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(85,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
| ( A @ p ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(87,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
| ( A @ p ) ),
inference(simp,[status(thm)],[85]) ).
thf(31,axiom,
~ ( mono_2Ec_2Ebool_2EF_2E0 @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(231,plain,
~ ( mono_2Ec_2Ebool_2EF_2E0 @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [A: d,B: d,C: d,D: u,E: u,F: u] :
( ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( combin_s_2E0 @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) )
= ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) @ ( F @ ( A @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(319,plain,
! [A: d,B: d,C: d,D: u,E: u,F: u] :
( ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( combin_s_2E0 @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) )
= ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) @ ( F @ ( A @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(54,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Ec_2Ebool_2E_2F_5C_2E2 ) @ p )
<=> ( ( B @ p )
& ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(351,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ mono_2Ec_2Ebool_2E_2F_5C_2E2 ) @ p ) )
& ( ( B @ ( A @ mono_2Ec_2Ebool_2E_2F_5C_2E2 ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
! [A: d,B: u] :
( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).
thf(186,plain,
! [A: d,B: u] :
( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(400,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 )
= A ),
inference(cnf,[status(esa)],[399]) ).
thf(401,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 )
= A ),
inference(lifteq,[status(thm)],[400]) ).
thf(232,plain,
~ ( mono_2Ec_2Ebool_2EF_2E0 @ p ),
inference(polarity_switch,[status(thm)],[231]) ).
thf(416,plain,
( ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
!= ( mono_2Ec_2Ebool_2EF_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,232]) ).
thf(417,plain,
( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
!= ( mono_2Ec_2Ebool_2EF_2E0 @ p ) ),
inference(simp,[status(thm)],[416]) ).
thf(418,plain,
mono_2Ec_2Ebool_2ET_2E0 != mono_2Ec_2Ebool_2EF_2E0,
inference(simp,[status(thm)],[417]) ).
thf(41,axiom,
! [A: d,B: u,C: u] :
( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
<=> ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(272,plain,
! [A: d,B: u,C: u] :
( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
=> ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) ) )
& ( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
=> ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(11,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
= ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(119,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
= ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(60,axiom,
! [A: d,B: u] :
( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(378,plain,
! [A: d,B: u] :
( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(422,plain,
( ( ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( mono_2Ec_2Ebool_2EF_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,232]) ).
thf(423,plain,
( ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) @ p )
!= ( mono_2Ec_2Ebool_2EF_2E0 @ p ) ),
inference(simp,[status(thm)],[422]) ).
thf(424,plain,
( ( sk2 @ ( sk3 @ mono_2Ec_2Earithmetic_2E_3C_3D_2E2 ) )
!= mono_2Ec_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[423]) ).
thf(752,plain,
( ( sk2 @ ( sk3 @ ( mono_2Ec_2Earithmetic_2E_3C_3D_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) )
!= mono_2Ec_2Ebool_2EF_2E0 ),
inference(rewrite,[status(thm)],[424,324]) ).
thf(17,axiom,
! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
( ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29) ).
thf(146,plain,
! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
( ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(816,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
!= ( B @ p ) )
| ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,88]) ).
thf(817,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
!= ( B @ p ) )
| ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p ) ),
inference(simp,[status(thm)],[816]) ).
thf(818,plain,
! [A: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Ebool_2ET_2E0 @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p ),
inference(pattern_uni,[status(thm)],[817:[bind(A,$thf( A )),bind(B,$thf( mono_2Ec_2Ebool_2ET_2E0 ))]]) ).
thf(67,axiom,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b) ).
thf(405,plain,
! [A: d,B: u,C: u] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(267,plain,
! [A: mono_2Etyop_2Enum_2Enum] :
( ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
= A ),
inference(cnf,[status(esa)],[266]) ).
thf(268,plain,
! [A: mono_2Etyop_2Enum_2Enum] :
( ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
= A ),
inference(lifteq,[status(thm)],[267]) ).
thf(55,axiom,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(358,plain,
! [A: u] :
( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(432,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ $true
| ~ ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) ),
inference(paramod_ordered,[status(thm)],[97,396]) ).
thf(433,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) ),
inference(simp,[status(thm)],[432]) ).
thf(434,plain,
~ ( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ),
inference(pattern_uni,[status(thm)],[433:[bind(A,$thf( mono_2Ec_2Ebool_2ET_2E0 ))]]) ).
thf(482,plain,
( ( ( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
!= ( mono_2Ec_2Ebool_2ET_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,434]) ).
thf(483,plain,
( ( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
!= ( mono_2Ec_2Ebool_2ET_2E0 @ p ) ),
inference(simp,[status(thm)],[482]) ).
thf(492,plain,
( ( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 )
!= mono_2Ec_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[483]) ).
thf(494,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A
!= ( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 ) )
| ( mono_2Ec_2Ebool_2ET_2E0 != mono_2Ec_2Ebool_2ET_2E0 )
| ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[77,492]) ).
thf(495,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A
!= ( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 ) )
| ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[494]) ).
thf(496,plain,
( ( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 )
= mono_2Ec_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[495:[bind(A,$thf( mono_2Ec_2Ebool_2ET_2E0 @ mono_2Ec_2Ebool_2E_7E_2E1 ))]]) ).
thf(57,axiom,
! [A: d,B: d,C: u,D: u] :
( ! [E: u] :
( ( E @ ( A @ s ) @ ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) )
= ( E @ ( A @ s ) @ ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) ) )
=> ( ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) )
= ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(364,plain,
! [A: d,B: d,C: u,D: u] :
( ! [E: u] :
( ( E @ ( A @ s ) @ ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) )
= ( E @ ( A @ s ) @ ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) ) )
=> ( ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) )
= ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(3721,plain,
$false,
inference(e,[status(thm)],[88,142,393,159,370,143,131,408,269,389,110,189,325,152,228,289,316,78,216,253,348,84,280,396,89,411,74,116,243,233,381,220,392,70,137,252,197,361,97,324,285,77,753,328,256,134,244,266,161,444,149,402,286,259,219,784,81,230,98,271,208,140,198,345,367,399,241,80,162,342,87,250,231,319,351,186,401,418,75,272,119,378,752,146,818,405,268,358,195,283,322,122,496,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013_1 : 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
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 17:17:43 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.71/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.96/0.88 % [INFO] Parsing done (175ms).
% 0.96/0.89 % [INFO] Running in sequential loop mode.
% 1.87/1.11 % [INFO] eprover registered as external prover.
% 1.87/1.12 % [INFO] Scanning for conjecture ...
% 2.24/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ...
% 2.45/1.39 % [INFO] Axiom selection finished. Selected 67 axioms (removed 0 axioms).
% 3.15/1.51 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.15/1.53 % [INFO] Type checking passed.
% 3.15/1.53 % [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 ...
% 3.86/1.79 % [INFO] [Domain constraints] Detected constraint on mono_2Etyop_2Emin_2Ebool
% 3.86/1.80 % [INFO] [Domain constraints] dom(mono_2Etyop_2Emin_2Ebool) ⊆ {mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2EF_2E0}
% 29.24/6.42 % External prover 'e' found a proof!
% 29.24/6.42 % [INFO] Killing All external provers ...
% 29.24/6.42 % Time passed: 5930ms (effective reasoning time: 5529ms)
% 29.24/6.42 % 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)>
% 29.24/6.42 % Axioms used in derivation (67): ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29, ji_2Emono_2Etyop_2Emin_2Ebool, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool, reserved_2Eho_2Ebool__cases__ax, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b, ij_2Emono_2Etyop_2Emin_2Ebool, ji_2Emono_2Etyop_2Enum_2Enum, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b, reserved_2Eho_2Enotfalse, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29, thm_2Ewords_2Eword__sub__def, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum, arityeq2_2Ec_2Earithmetic_2E_2D_2E2, thm_2Ebool_2EREFL__CLAUSE, reserved_2Equant_2E_21, thm_2Ebool_2EEQ__CLAUSES, arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2, thm_2Ebool_2EIMP__CONG, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29, thm_2Ewords_2EWORD__LITERAL__ADD, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29, reserved_2Equant_2E_3F, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, reserved_2Elogic_2E_3D, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, reserved_2Elogic_2E_7E, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, reserved_2Eho_2Eboolext, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, reserved_2Eho_2Eeq__ext, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29, arityeq2_2Ec_2Earithmetic_2E_2B_2E2, reserved_2Elogic_2E_3D_3D_3E, ij_2Emono_2Etyop_2Enum_2Enum, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29, thm_2Ebool_2EEQ__SYM__EQ, reserved_2Elogic_2E_5C_2F, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a, thm_2Ebool_2Ebool__case__thm, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29
% 29.24/6.42 % No. of inferences in proof: 213
% 29.24/6.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5930 ms resp. 5529 ms w/o parsing
% 25.81/6.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.81/6.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------