%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP018_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 07:35:42 AM UTC 2026
% Result : Theorem 6.97s 3.24s
% Output : Refutation 7.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 47
% Syntax : Number of formulae : 96 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 173 ( 74 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1637 ( 10 ~; 8 |; 19 &;1550 @)
% ( 14 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 21 con; 0-2 aty)
% Number of variables : 190 ( 0 ^; 187 !; 3 ?; 190 :)
% 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_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Erealax_2Ereal_type,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(tyop_2Ebinary__ieee_2Efloat_decl,type,
tyop_2Ebinary__ieee_2Efloat: d > d > d ).
thf(tyop_2Ebool_2Eitself_decl,type,
tyop_2Ebool_2Eitself: 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_2Epair_2Eprod_decl,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(tyop_2Erealax_2Ereal_decl,type,
tyop_2Erealax_2Ereal: 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_2Ebinary__ieee_2Efloat__negate_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__negate_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__negate_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__negate_2E1: du > u ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1: du > u ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0: u ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).
thf(c_2Ebool_2Ethe__value_2E0_decl,type,
c_2Ebool_2Ethe__value_2E0: u ).
thf(c_2Ebinary__ieee_2Eulp_2E0_decl,type,
c_2Ebinary__ieee_2Eulp_2E0: u ).
thf(c_2Ebinary__ieee_2Eulp_2E1_decl,type,
c_2Ebinary__ieee_2Eulp_2E1: 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_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
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_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_2Erealax_2Ereal__neg_2E0_decl,type,
mono_2Ec_2Erealax_2Ereal__neg_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(mono_2Ec_2Erealax_2Ereal__neg_2E1_decl,type,
mono_2Ec_2Erealax_2Ereal__neg_2E1: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
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_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
thf(i_mono_2Etyop_2Erealax_2Ereal_decl,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > 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_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(j_mono_2Etyop_2Erealax_2Ereal_decl,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
thf(9,axiom,
mono_2Ec_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(88,plain,
mono_2Ec_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(170,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)],[27]) ).
thf(23,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( A @ mono_2Ec_2Erealax_2Ereal__neg_2E1 )
= ( A @ ( mono_2Ec_2Erealax_2Ereal__neg_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Erealax_2Ereal__neg_2E1) ).
thf(153,plain,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( A @ mono_2Ec_2Erealax_2Ereal__neg_2E1 )
= ( A @ ( mono_2Ec_2Erealax_2Ereal__neg_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(185,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)],[32]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(52,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)],[3]) ).
thf(30,axiom,
! [A: u] :
( ( A @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) )
= ( A @ ( tyop_2Erealax_2Ereal @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Erealax_2Ereal) ).
thf(179,plain,
! [A: u] :
( ( A @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) )
= ( A @ ( tyop_2Erealax_2Ereal @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(46,axiom,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ebinary__ieee_2Eulp_2E0 @ ( tyop_2Erealax_2Ereal @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(230,plain,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ebinary__ieee_2Eulp_2E0 @ ( tyop_2Erealax_2Ereal @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) ).
thf(126,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)],[16]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(200,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)],[37]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(61,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)],[5]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(221,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)],[43]) ).
thf(18,axiom,
! [A: d,B: u] :
( ( ( B @ ( A @ s ) )
= ( B @ ( A @ s ) ) )
<=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(132,plain,
mono_2Ec_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__to__real_2E0 @ ( tyop_2Erealax_2Ereal @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(206,plain,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__to__real_2E0 @ ( tyop_2Erealax_2Ereal @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(10,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
<=> ~ ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(89,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)],[10]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(133,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)],[19]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(233,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)],[47]) ).
thf(4,axiom,
mono_2Ec_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(60,plain,
mono_2Ec_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
~ ( mono_2Ec_2Ebool_2EF_2E0 @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(102,plain,
~ ( mono_2Ec_2Ebool_2EF_2E0 @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(197,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)],[36]) ).
thf(44,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( A @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Erealax_2Ereal) ).
thf(224,plain,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( A @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(24,axiom,
! [A: u] :
( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) ).
thf(156,plain,
! [A: u] :
( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) )
= ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(188,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)],[33]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).
thf(141,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)],[20]) ).
thf(7,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2EF_2E0 )
| ( A = mono_2Ec_2Ebool_2ET_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(77,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)],[7]) ).
thf(40,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) ).
thf(212,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(173,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)],[28]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(129,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)],[17]) ).
thf(29,axiom,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) )
= ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E0 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(176,plain,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) )
= ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E0 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E0 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(191,plain,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E0 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(118,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)],[15]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(144,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)],[21]) ).
thf(1,conjecture,
! [A: d,B: d] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Erealax_2Ereal__neg_2E1 )
= ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(2,negated_conjecture,
~ ! [A: d,B: d] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Erealax_2Ereal__neg_2E1 )
= ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(49,plain,
~ ! [A: d,B: d] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Erealax_2Ereal__neg_2E1 )
= ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__to__real_2E0 @ ( tyop_2Erealax_2Ereal @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(236,plain,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__to__real_2E0 @ ( tyop_2Erealax_2Ereal @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(159,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)],[25]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(80,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)],[8]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(167,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)],[26]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(209,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)],[39]) ).
thf(35,axiom,
! [A: d,B: d] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
thf(194,plain,
! [A: d,B: d] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(150,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)],[22]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(95,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)],[11]) ).
thf(6,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( A @ p )
<=> ( B @ p ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(67,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)],[6]) ).
thf(31,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) )
= ( B @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal) ).
thf(182,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) )
= ( B @ i_mono_2Etyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(42,axiom,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E0 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(218,plain,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E0 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(104,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)],[13]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(111,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)],[14]) ).
thf(45,axiom,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Erealax_2Ereal__neg_2E1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(227,plain,
! [A: d,B: d,C: u] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ j_mono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Erealax_2Ereal__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).
thf(215,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)],[41]) ).
thf(243,plain,
$false,
inference(e,[status(thm)],[88,170,153,185,52,179,230,126,200,61,221,132,206,89,133,233,60,102,197,224,156,188,141,77,212,173,129,176,191,118,144,49,236,159,80,167,209,194,150,95,67,182,218,104,111,227,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n015.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 17:29:12 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.26 % [INFO] Parsing done (274ms).
% 1.49/1.27 % [INFO] Running in sequential loop mode.
% 2.37/1.67 % [INFO] eprover registered as external prover.
% 2.37/1.68 % [INFO] Scanning for conjecture ...
% 2.81/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 46 axioms. Running axiom selection ...
% 3.00/1.94 % [INFO] Axiom selection finished. Selected 46 axioms (removed 0 axioms).
% 3.33/2.06 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.33/2.07 % [INFO] Type checking passed.
% 3.33/2.08 % [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 ...
% 4.20/2.41 % [INFO] [Domain constraints] Detected constraint on mono_2Etyop_2Emin_2Ebool
% 4.20/2.41 % [INFO] [Domain constraints] dom(mono_2Etyop_2Emin_2Ebool) ⊆ {mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2EF_2E0}
% 6.97/3.23 % External prover 'e' found a proof!
% 6.97/3.23 % [INFO] Killing All external provers ...
% 6.97/3.24 % Time passed: 2695ms (effective reasoning time: 1955ms)
% 6.97/3.24 % 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)>
% 6.97/3.24 % Axioms used in derivation (46): reserved_2Eho_2Enotfalse, thm_2Ebool_2EREFL__CLAUSE, arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, ij_2Emono_2Etyop_2Erealax_2Ereal, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, ij_2Emono_2Etyop_2Emin_2Ebool, thm_2Ebinary__ieee_2Eulp, ji_2Emono_2Etyop_2Emin_2Ebool, arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w, reserved_2Equant_2E_21, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b, reserved_2Equant_2E_3F, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal, reserved_2Elogic_2E_3D, arityeq1_2Ec_2Erealax_2Ereal__neg_2E1, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ebinary__ieee_2Efloat__to__real__negate, thm_2Ebool_2ETRUTH, ji_2Emono_2Etyop_2Erealax_2Ereal, 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, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, reserved_2Eho_2Eboolext, reserved_2Eho_2Ebool__cases__ax, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, reserved_2Eho_2Eeq__ext, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w, 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
% 6.97/3.24 % No. of inferences in proof: 96
% 6.97/3.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2695 ms resp. 1955 ms w/o parsing
% 7.34/3.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.34/3.35 % [INFO] Killing All external provers ...
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