%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP015+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 : n010.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 07:35:37 AM UTC 2026
% Result : Theorem 19.61s 5.98s
% Output : Refutation 21.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 52
% Syntax : Number of formulae : 193 ( 87 unt; 0 typ; 2 def)
% Number of atoms : 450 ( 245 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 4247 ( 169 ~; 102 |; 44 &;3839 @)
% ( 18 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 31 con; 0-3 aty)
% Number of variables : 299 ( 2 ^; 289 !; 6 ?; 299 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(s_decl,type,
s: $i > $i > $i ).
thf(tyop_2Efcp_2Ecart_decl,type,
tyop_2Efcp_2Ecart: $i > $i > $i ).
thf(tyop_2Emin_2Ebool_decl,type,
tyop_2Emin_2Ebool: $i ).
thf(c_2Einteger__word_2Ei2w_2E1_decl,type,
c_2Einteger__word_2Ei2w_2E1: $i > $i ).
thf(tyop_2Einteger_2Eint_decl,type,
tyop_2Einteger_2Eint: $i ).
thf(c_2Einteger_2Eint__of__num_2E1_decl,type,
c_2Einteger_2Eint__of__num_2E1: $i > $i ).
thf(tyop_2Enum_2Enum_decl,type,
tyop_2Enum_2Enum: $i ).
thf(c_2Enum_2E0_2E0_decl,type,
c_2Enum_2E0_2E0: $i ).
thf(c_2Ewords_2En2w_2E1_decl,type,
c_2Ewords_2En2w_2E1: $i > $i ).
thf(p_decl,type,
p: $i > $o ).
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_2Einteger_2Eint__lt_2E2_decl,type,
c_2Einteger_2Eint__lt_2E2: $i > $i > $i ).
thf(c_2Eprim__rec_2E_3C_2E2_decl,type,
c_2Eprim__rec_2E_3C_2E2: $i > $i > $i ).
thf(c_2Einteger_2Eint__neg_2E1_decl,type,
c_2Einteger_2Eint__neg_2E1: $i > $i ).
thf(c_2Ebool_2EF_2E0_decl,type,
c_2Ebool_2EF_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_2Emin_2E_3D_3D_3E_2E0_decl,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(c_2Einteger_2ENum_2E1_decl,type,
c_2Einteger_2ENum_2E1: $i > $i ).
thf(c_2Ewords_2Edimword_2E1_decl,type,
c_2Ewords_2Edimword_2E1: $i > $i ).
thf(tyop_2Ebool_2Eitself_decl,type,
tyop_2Ebool_2Eitself: $i > $i ).
thf(c_2Ewords_2Edimword_2E0_decl,type,
c_2Ewords_2Edimword_2E0: $i ).
thf(c_2Einteger_2Eint__lt_2E0_decl,type,
c_2Einteger_2Eint__lt_2E0: $i ).
thf(c_2Einteger_2ENum_2E0_decl,type,
c_2Einteger_2ENum_2E0: $i ).
thf(c_2Einteger_2Eint__of__num_2E0_decl,type,
c_2Einteger_2Eint__of__num_2E0: $i ).
thf(c_2Ebool_2ECOND_2E3_decl,type,
c_2Ebool_2ECOND_2E3: $i > $i > $i > $i ).
thf(c_2Ewords_2Eword__2comp_2E1_decl,type,
c_2Ewords_2Eword__2comp_2E1: $i > $i ).
thf(c_2Earithmetic_2EMOD_2E2_decl,type,
c_2Earithmetic_2EMOD_2E2: $i > $i > $i ).
thf(c_2Earithmetic_2EMOD_2E0_decl,type,
c_2Earithmetic_2EMOD_2E0: $i ).
thf(combin_k_2E0_decl,type,
combin_k_2E0: $i ).
thf(combin_s_2E0_decl,type,
combin_s_2E0: $i ).
thf(c_2Ebool_2ECOND_2E0_decl,type,
c_2Ebool_2ECOND_2E0: $i ).
thf(c_2Eprim__rec_2E_3C_2E0_decl,type,
c_2Eprim__rec_2E_3C_2E0: $i ).
thf(c_2Einteger_2Eint__neg_2E0_decl,type,
c_2Einteger_2Eint__neg_2E0: $i ).
thf(c_2Emin_2E_3D_2E0_decl,type,
c_2Emin_2E_3D_2E0: $i ).
thf(c_2Ewords_2En2w_2E0_decl,type,
c_2Ewords_2En2w_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_2Ewords_2Eword__2comp_2E0_decl,type,
c_2Ewords_2Eword__2comp_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_2Ebool_2E_5C_2F_2E2_decl,type,
c_2Ebool_2E_5C_2F_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_2Ebool_2Ethe__value_2E0_decl,type,
c_2Ebool_2Ethe__value_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_2Einteger__word_2Ei2w_2E0_decl,type,
c_2Einteger__word_2Ei2w_2E0: $i ).
thf(c_2Emin_2E_3D_2E2_decl,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( C @ ( B @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
<=> ( ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__11) ).
thf(249,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) )
=> ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) )
& ( ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
=> ( ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Eprim__rec_2E_3C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Eprim__rec_2E_3C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
thf(302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Einteger_2Eint__of__num_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) ).
thf(139,plain,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Einteger_2Eint__of__num_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(140,plain,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Einteger_2Eint__of__num_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(141,plain,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Einteger_2Eint__of__num_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(1,conjecture,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(52,plain,
~ ! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(25,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(154,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)],[25]) ).
thf(32,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(185,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)],[32]) ).
thf(13,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(119,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)],[13]) ).
thf(120,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(cnf,[status(esa)],[119]) ).
thf(121,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(lifteq,[status(thm)],[120]) ).
thf(7,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(93,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(61,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(62,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: $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 ) ) ),
inference(miniscope,[status(thm)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ~ ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( B @ ( 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 ) @ ( 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 ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(65,plain,
! [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 ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(66,plain,
! [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 ) ),
inference(simp,[status(thm)],[65]) ).
thf(2296,plain,
! [A: $i] :
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true
| ~ ( 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(paramod_ordered,[status(thm)],[93,66]) ).
thf(2297,plain,
! [A: $i] :
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[2296]) ).
thf(2298,plain,
~ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(pattern_uni,[status(thm)],[2297:[bind(A,$thf( c_2Ebool_2ET_2E0 ))]]) ).
thf(2385,plain,
( ( ( c_2Ebool_2ET_2E0 @ ( 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 )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,2298]) ).
thf(2386,plain,
( ( c_2Ebool_2ET_2E0 @ ( 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 )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[2385]) ).
thf(2420,plain,
( ( c_2Ebool_2ET_2E0 @ ( 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 ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[2386]) ).
thf(2430,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( 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 ) ) )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,2420]) ).
thf(2431,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(simp,[status(thm)],[2430]) ).
thf(2432,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(pattern_uni,[status(thm)],[2431:[bind(A,$thf( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) ))]]) ).
thf(48,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(288,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)],[48]) ).
thf(44,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(257,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)],[44]) ).
thf(324,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) )
!= ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(345,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ),
inference(simp,[status(thm)],[324]) ).
thf(909,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) ) )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,345]) ).
thf(1038,plain,
! [A: $i] :
( ( A
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 ) )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(1177,plain,
( ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(simp,[status(thm)],[1038]) ).
thf(17,axiom,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(131,plain,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(132,plain,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(polarity_switch,[status(thm)],[131]) ).
thf(305,plain,
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,132]) ).
thf(306,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[305]) ).
thf(307,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(1317,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ) ),
inference(paramod_ordered,[status(thm)],[1177,307]) ).
thf(1318,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ) ),
inference(simp,[status(thm)],[1317]) ).
thf(1430,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ) ),
inference(simp,[status(thm)],[1318]) ).
thf(1511,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ) ),
inference(simp,[status(thm)],[1430]) ).
thf(15,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(125,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)],[15]) ).
thf(8,axiom,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
thf(94,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(95,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2ENum_2E1) ).
thf(133,plain,
! [A: $i] :
( ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(134,plain,
! [A: $i] :
( ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(cnf,[status(esa)],[133]) ).
thf(135,plain,
! [A: $i] :
( ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(12,axiom,
! [A: $i] :
~ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
thf(116,plain,
! [A: $i] :
~ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(117,plain,
~ ? [A: $i] : ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(miniscope,[status(thm)],[116]) ).
thf(118,plain,
! [A: $i] :
~ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(cnf,[status(esa)],[117]) ).
thf(384,plain,
! [A: $i] :
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,118]) ).
thf(385,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[384]) ).
thf(391,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[385]) ).
thf(397,plain,
! [A: $i] :
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[391]) ).
thf(416,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[397]) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
!= ( B @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[135,416]) ).
thf(681,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(pattern_uni,[status(thm)],[680:[bind(A,$thf( J )),bind(B,$thf( J @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) ))]]) ).
thf(801,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[681]) ).
thf(836,plain,
! [A: $i] :
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
!= ( A @ ( tyop_2Einteger_2Eint @ s ) ) )
| ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[95,801]) ).
thf(837,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
thf(103,plain,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(104,plain,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [A: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(853,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(rewrite,[status(thm)],[837,105]) ).
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(164,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(11,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Emin_2Ebool @ s ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Emin_2Ebool @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
<=> ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(265,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
=> ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(35,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(206,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)],[35]) ).
thf(41,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(233,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)],[41]) ).
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(55,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(56,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 ) )
& ! [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 ) ) ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( tyop_2Emin_2Ebool @ ( C @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( E @ ( C @ s ) @ ( D @ ( tyop_2Emin_2Ebool @ ( C @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( B @ sk2 ) @ ( 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 ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[59]) ).
thf(6,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(87,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)],[6]) ).
thf(88,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: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(miniscope,[status(thm)],[87]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(91,plain,
! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(92,plain,
! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[91]) ).
thf(47,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(285,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)],[47]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ~ ( C @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( F @ ( A @ s ) )
= ( G @ ( A @ s ) ) ) )
& ( ( C @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( D @ ( A @ s ) )
= ( E @ ( A @ s ) ) ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ s ) )
= ( C @ ( tyop_2Emin_2Ebool @ s ) ) ) )
=> ( ( F @ ( A @ s ) @ ( D @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( G @ ( A @ s ) @ ( E @ ( A @ s ) @ ( C @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(193,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ~ ( C @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( F @ ( A @ s ) )
= ( G @ ( A @ s ) ) ) )
& ( ( C @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( D @ ( A @ s ) )
= ( E @ ( A @ s ) ) ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ s ) )
= ( C @ ( tyop_2Emin_2Ebool @ s ) ) ) )
=> ( ( F @ ( A @ s ) @ ( D @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( G @ ( A @ s ) @ ( E @ ( A @ s ) @ ( C @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,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(96,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)],[9]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2Eint__neg_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__neg_2E1) ).
thf(173,plain,
! [A: $i] :
( ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
= ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2Eint__neg_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(2429,plain,
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[2420]) ).
thf(2566,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[2429]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2Eint__lt_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Einteger_2Eint__lt_2E2) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger_2Eint__lt_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(423,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,307]) ).
thf(467,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool )
| ( A != c_2Ebool_2EF_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[423]) ).
thf(508,plain,
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[467]) ).
thf(310,plain,
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[307]) ).
thf(311,plain,
c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0,
inference(simp,[status(thm)],[310]) ).
thf(23,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(148,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)],[23]) ).
thf(64,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 ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(30,axiom,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(176,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger__word_2Ei2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a) ).
thf(291,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger__word_2Ei2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(969,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,391]) ).
thf(970,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(simp,[status(thm)],[969]) ).
thf(971,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(pattern_uni,[status(thm)],[970:[bind(A,$thf( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( F @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )),bind(B,$thf( F ))]]) ).
thf(1282,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[971]) ).
thf(39,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(219,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)],[39]) ).
thf(465,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( A != c_2Ebool_2EF_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[423]) ).
thf(507,plain,
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[465]) ).
thf(871,plain,
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(rewrite,[status(thm)],[507,105]) ).
thf(873,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(paramod_ordered,[status(thm)],[105,871]) ).
thf(878,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Enum_2Enum )
| ( A != c_2Ebool_2ET_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[873]) ).
thf(890,plain,
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[878]) ).
thf(40,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(226,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)],[40]) ).
thf(457,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[105,54]) ).
thf(463,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) )
!= tyop_2Enum_2Enum )
| ( A
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 ) )
| ( ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) )
!= tyop_2Enum_2Enum ) ),
inference(simp,[status(thm)],[457]) ).
thf(505,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) )
!= tyop_2Enum_2Enum ) ),
inference(simp,[status(thm)],[463]) ).
thf(42,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(241,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)],[42]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29) ).
thf(167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,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(209,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)],[36]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2EMOD_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2EMOD_2E2) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2EMOD_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2EMOD_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(399,plain,
! [A: $i] :
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
!= ( A @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[95,391]) ).
thf(406,plain,
! [A: $i] :
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 )
!= A )
| ( tyop_2Enum_2Enum != tyop_2Einteger_2Eint )
| ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[399]) ).
thf(414,plain,
( ( tyop_2Enum_2Enum != tyop_2Einteger_2Eint )
| ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[406]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
& ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
<=> ( ( ( B @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) ) ) ) )
& ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) )
& ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
& ( ( ( ( B @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) ) ) )
=> ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( ( B @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) ) ) ) )
& ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__neg_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) )
& ( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2Eint__lt_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Eprim__rec_2E_3C_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
<=> ( ( C @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__SYM__EQ) ).
thf(177,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ s ) )
= ( B @ ( A @ s ) ) )
=> ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) ) )
& ( ( ( B @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
=> ( ( C @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(218,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk2 ) @ ( 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 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(24,axiom,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).
thf(151,plain,
! [A: $i] :
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1336,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ) ),
inference(paramod_ordered,[status(thm)],[1177,54]) ).
thf(1384,plain,
( ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 ) )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) )
!= ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ) ),
inference(simp,[status(thm)],[1336]) ).
thf(1480,plain,
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) )
| ( tyop_2Einteger_2Eint != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Einteger__word_2Ei2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(430,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 @ ( tyop_2Enum_2Enum @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
inference(paramod_ordered,[status(thm)],[105,345]) ).
thf(464,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= c_2Enum_2E0_2E0 )
| ( tyop_2Enum_2Enum != tyop_2Enum_2Enum )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
inference(simp,[status(thm)],[430]) ).
thf(506,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger_2ENum_2E1 )
!= c_2Enum_2E0_2E0 )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Einteger_2Eint__of__num_2E1 @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
inference(simp,[status(thm)],[464]) ).
thf(50,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(294,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)],[50]) ).
thf(19,axiom,
! [A: $i] :
( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(136,plain,
! [A: $i] :
( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,axiom,
! [A: $i] :
( ! [B: $i,C: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
& ! [B: $i,C: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(277,plain,
! [A: $i] :
( ! [B: $i,C: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) )
& ! [B: $i,C: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ewords_2Edimword_2E0 @ ( tyop_2Enum_2Enum @ ( A @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ewords_2Edimword_2E0 @ ( tyop_2Enum_2Enum @ ( A @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).
thf(215,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(3801,plain,
$false,
inference(e,[status(thm)],[249,170,142,302,141,54,154,185,2432,288,257,52,1511,125,853,93,416,164,106,121,61,132,133,116,265,206,307,233,60,92,285,193,96,173,2566,128,105,508,311,148,64,176,291,1282,219,890,345,103,66,1177,135,226,505,241,167,209,145,414,95,67,177,87,203,218,55,139,119,58,151,1480,506,94,294,801,136,131,277,871,122,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP015+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
% 0.14/0.41 % Computer : n010.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 17:21:10 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.27 % [INFO] Parsing done (270ms).
% 1.33/1.29 % [INFO] Running in sequential loop mode.
% 2.18/1.67 % [INFO] eprover registered as external prover.
% 2.18/1.68 % [INFO] Scanning for conjecture ...
% 2.54/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 49 axioms. Running axiom selection ...
% 2.74/1.92 % [INFO] Axiom selection finished. Selected 49 axioms (removed 0 axioms).
% 3.08/2.04 % [INFO] Problem is first-order (TPTP FOF).
% 3.08/2.05 % [INFO] Type checking passed.
% 3.08/2.06 % [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 ...
% 19.61/5.97 % External prover 'e' found a proof!
% 19.61/5.97 % [INFO] Killing All external provers ...
% 19.61/5.97 % Time passed: 5423ms (effective reasoning time: 4680ms)
% 19.61/5.97 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 19.61/5.98 % Axioms used in derivation (49): arityeq2_2Ec_2Eprim__rec_2E_3C_2E2, reserved_2Eho_2Enotfalse, thm_2Ebool_2EREFL__CLAUSE, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, reserved_2Equant_2E_3F, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a, thm_2Eprim__rec_2ENOT__LESS__0, reserved_2Eho_2Ebool__cases__ax, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, reserved_2Equant_2E_21, thm_2Ebool_2EIMP__ANTISYM__AX, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, thm_2Ebool_2EFALSITY, reserved_2Elogic_2E_3D, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Earithmetic_2EMOD_2E2, thm_2Einteger_2EINT__NEG__0, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29, thm_2Ebool_2ETRUTH, arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, reserved_2Elogic_2E_7E, thm_2Einteger_2EINT__LT__CALCULATE, reserved_2Eho_2Eboolext, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Einteger_2Eint__of__num_2E1, reserved_2Eho_2Eeq__ext, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq1_2Ec_2Einteger_2ENum_2E1, arityeq2_2Ec_2Einteger_2Eint__lt_2E2, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Einteger__word_2Ei2w__def, thm_2Ebool_2EEQ__SYM__EQ, reserved_2Elogic_2E_5C_2F, arityeq1_2Ec_2Einteger_2Eint__neg_2E1, thm_2Ewords_2EWORD__NEG__0, thm_2Einteger_2ENUM__OF__INT, thm_2Ewords_2En2w__11, thm_2Ebool_2Ebool__case__thm
% 19.61/5.98 % No. of inferences in proof: 191
% 19.61/5.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5423 ms resp. 4680 ms w/o parsing
% 21.04/6.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.04/6.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------