%------------------------------------------------------------------------------
% 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 : n016.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 07:35:41 AM UTC 2026
% Result : Theorem 6.23s 3.12s
% Output : Refutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 70 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 48 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1691 ( 10 ~; 8 |; 19 &;1604 @)
% ( 14 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 21 con; 0-2 aty)
% Number of variables : 158 ( 0 ^; 155 !; 3 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(s_decl,type,
s: $i > $i > $i ).
thf(tyop_2Erealax_2Ereal_decl,type,
tyop_2Erealax_2Ereal: $i ).
thf(c_2Erealax_2Ereal__neg_2E1_decl,type,
c_2Erealax_2Ereal__neg_2E1: $i > $i ).
thf(c_2Ebinary__ieee_2Eulp_2E1_decl,type,
c_2Ebinary__ieee_2Eulp_2E1: $i > $i ).
thf(tyop_2Ebool_2Eitself_decl,type,
tyop_2Ebool_2Eitself: $i > $i ).
thf(tyop_2Epair_2Eprod_decl,type,
tyop_2Epair_2Eprod: $i > $i > $i ).
thf(c_2Ebool_2Ethe__value_2E0_decl,type,
c_2Ebool_2Ethe__value_2E0: $i ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1: $i > $i ).
thf(tyop_2Ebinary__ieee_2Efloat_decl,type,
tyop_2Ebinary__ieee_2Efloat: $i > $i > $i ).
thf(c_2Ebinary__ieee_2Efloat__negate_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__negate_2E1: $i > $i ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1: $i > $i ).
thf(p_decl,type,
p: $i > $o ).
thf(tyop_2Emin_2Ebool_decl,type,
tyop_2Emin_2Ebool: $i ).
thf(c_2Ebool_2E_3F_2E1_decl,type,
c_2Ebool_2E_3F_2E1: $i > $i ).
thf(tyop_2Emin_2Efun_decl,type,
tyop_2Emin_2Efun: $i > $i > $i ).
thf(app_2E2_decl,type,
app_2E2: $i > $i > $i ).
thf(c_2Ebool_2E_7E_2E0_decl,type,
c_2Ebool_2E_7E_2E0: $i ).
thf(c_2Ebool_2E_7E_2E1_decl,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
thf(c_2Ebool_2ET_2E0_decl,type,
c_2Ebool_2ET_2E0: $i ).
thf(c_2Ebool_2EF_2E0_decl,type,
c_2Ebool_2EF_2E0: $i ).
thf(c_2Ebool_2E_5C_2F_2E2_decl,type,
c_2Ebool_2E_5C_2F_2E2: $i > $i > $i ).
thf(combin_k_2E0_decl,type,
combin_k_2E0: $i ).
thf(c_2Ebinary__ieee_2Efloat__negate_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__negate_2E0: $i ).
thf(c_2Erealax_2Ereal__neg_2E0_decl,type,
c_2Erealax_2Ereal__neg_2E0: $i ).
thf(c_2Ebool_2E_3F_2E0_decl,type,
c_2Ebool_2E_3F_2E0: $i ).
thf(c_2Ebool_2E_21_2E1_decl,type,
c_2Ebool_2E_21_2E1: $i > $i ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0: $i ).
thf(c_2Emin_2E_3D_3D_3E_2E0_decl,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(c_2Ebool_2E_5C_2F_2E0_decl,type,
c_2Ebool_2E_5C_2F_2E0: $i ).
thf(c_2Ebool_2E_2F_5C_2E2_decl,type,
c_2Ebool_2E_2F_5C_2E2: $i > $i > $i ).
thf(c_2Emin_2E_3D_3D_3E_2E2_decl,type,
c_2Emin_2E_3D_3D_3E_2E2: $i > $i > $i ).
thf(c_2Ebinary__ieee_2Eulp_2E0_decl,type,
c_2Ebinary__ieee_2Eulp_2E0: $i ).
thf(combin_s_2E0_decl,type,
combin_s_2E0: $i ).
thf(c_2Ebool_2E_2F_5C_2E0_decl,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
thf(c_2Ebool_2E_21_2E0_decl,type,
c_2Ebool_2E_21_2E0: $i ).
thf(combin_i_2E0_decl,type,
combin_i_2E0: $i ).
thf(c_2Emin_2E_3D_2E2_decl,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(c_2Emin_2E_3D_2E0_decl,type,
c_2Emin_2E_3D_2E0: $i ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E0: $i ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(88,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[13]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(184,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[35]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_5C_2F_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_5C_2F_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_5C_2F_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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(165,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[32]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ! [C: $i] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(97,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ! [C: $i] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( 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 ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( 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 ) @ 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 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( 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(144,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( 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)],[26]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ? [C: $i] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ? [C: $i] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_2F_5C_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_2F_5C_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_2F_5C_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( 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 ) )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ c_2Erealax_2Ereal__neg_2E1 @ ( tyop_2Erealax_2Ereal @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(72,plain,
! [A: $i,B: $i,C: $i] :
( ( 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 ) )
= ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ c_2Erealax_2Ereal__neg_2E1 @ ( tyop_2Erealax_2Ereal @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
= ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
= ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ s ) )
= ( B @ ( A @ s ) ) )
<=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(57,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(31,axiom,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(164,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(147,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( 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(61,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( 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)],[8]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Emin_2E_3D_3D_3E_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Emin_2E_3D_3D_3E_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Emin_2E_3D_3D_3E_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(116,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( 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 ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(124,plain,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(45,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( 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(161,plain,
! [A: $i,B: $i] :
( ( 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)],[30]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_5C_2F_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_5C_2F_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_5C_2F_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ tyop_2Ebinary__ieee_2Efloat ) @ s ) @ c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( tyop_2Erealax_2Ereal @ s ) @ c_2Erealax_2Ereal__neg_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( A @ ( tyop_2Erealax_2Ereal @ s ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Erealax_2Ereal__neg_2E1) ).
thf(91,plain,
! [A: $i] :
( ( A @ ( tyop_2Erealax_2Ereal @ s ) @ c_2Erealax_2Ereal__neg_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( A @ ( tyop_2Erealax_2Ereal @ s ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Erealax_2Ereal @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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(75,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( 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)],[11]) ).
thf(7,axiom,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(58,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ c_2Erealax_2Ereal__neg_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ c_2Erealax_2Ereal__neg_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ! [A: $i,B: $i] :
( ( c_2Ebool_2Ethe__value_2E0 @ ( B @ ( A @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ s ) @ c_2Ebinary__ieee_2Eulp_2E1 @ ( tyop_2Erealax_2Ereal @ s ) @ c_2Erealax_2Ereal__neg_2E1 @ ( tyop_2Erealax_2Ereal @ s ) )
= ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
=> ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(51,plain,
! [A: $i] :
( ( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_2F_5C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(126,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_2F_5C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_2F_5C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
= ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
= ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(187,plain,
$false,
inference(e,[status(thm)],[88,184,117,165,97,141,176,144,39,150,72,158,57,78,164,106,147,61,133,116,109,124,45,161,64,103,91,75,58,36,168,51,126,94]) ).
%------------------------------------------------------------------------------
%----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
% 0.16/0.41 % Computer : n016.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 17:30:59 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.27 % [INFO] Parsing done (264ms).
% 1.44/1.29 % [INFO] Running in sequential loop mode.
% 2.51/1.70 % [INFO] eprover registered as external prover.
% 2.51/1.71 % [INFO] Scanning for conjecture ...
% 2.73/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 33 axioms. Running axiom selection ...
% 2.92/1.93 % [INFO] Axiom selection finished. Selected 33 axioms (removed 0 axioms).
% 2.92/2.03 % [INFO] Problem is first-order (TPTP FOF).
% 3.27/2.04 % [INFO] Type checking passed.
% 3.27/2.05 % [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 ...
% 6.23/3.11 % External prover 'e' found a proof!
% 6.23/3.11 % [INFO] Killing All external provers ...
% 6.23/3.11 % Time passed: 2541ms (effective reasoning time: 1811ms)
% 6.23/3.11 % 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)>
% 6.23/3.11 % Axioms used in derivation (33): arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w, 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, reserved_2Equant_2E_3F, arityeq1_2Ec_2Erealax_2Ereal__neg_2E1, reserved_2Eho_2Ebool__cases__ax, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, thm_2Ebinary__ieee_2Eulp, 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_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, reserved_2Elogic_2E_3D, 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, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, reserved_2Elogic_2E_7E, reserved_2Eho_2Eboolext, 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
% 6.23/3.11 % No. of inferences in proof: 70
% 6.23/3.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2541 ms resp. 1811 ms w/o parsing
% 6.77/3.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.77/3.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------