%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP013+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:35:35 AM UTC 2026
% Result : Theorem 21.25s 5.52s
% Output : Refutation 21.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 50
% Syntax : Number of formulae : 195 ( 83 unt; 0 typ; 4 def)
% Number of atoms : 595 ( 245 equ; 0 cnn)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 5147 ( 193 ~; 114 |; 100 &;4582 @)
% ( 26 <=>; 132 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 27 con; 0-3 aty)
% Number of variables : 398 ( 2 ^; 385 !; 7 ?; 398 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(p_decl,type,
p: $i > $o ).
thf(s_decl,type,
s: $i > $i > $i ).
thf(tyop_2Emin_2Ebool_decl,type,
tyop_2Emin_2Ebool: $i ).
thf(c_2Earithmetic_2E_3C_3D_2E2_decl,type,
c_2Earithmetic_2E_3C_3D_2E2: $i > $i > $i ).
thf(tyop_2Enum_2Enum_decl,type,
tyop_2Enum_2Enum: $i ).
thf(tyop_2Efcp_2Ecart_decl,type,
tyop_2Efcp_2Ecart: $i > $i > $i ).
thf(c_2Ewords_2En2w_2E1_decl,type,
c_2Ewords_2En2w_2E1: $i > $i ).
thf(c_2Earithmetic_2E_2D_2E2_decl,type,
c_2Earithmetic_2E_2D_2E2: $i > $i > $i ).
thf(c_2Ewords_2Eword__sub_2E2_decl,type,
c_2Ewords_2Eword__sub_2E2: $i > $i > $i ).
thf(c_2Ebool_2ET_2E0_decl,type,
c_2Ebool_2ET_2E0: $i ).
thf(c_2Ebool_2EF_2E0_decl,type,
c_2Ebool_2EF_2E0: $i ).
thf(c_2Ebool_2E_3F_2E1_decl,type,
c_2Ebool_2E_3F_2E1: $i > $i ).
thf(tyop_2Emin_2Efun_decl,type,
tyop_2Emin_2Efun: $i > $i > $i ).
thf(app_2E2_decl,type,
app_2E2: $i > $i > $i ).
thf(c_2Ebool_2E_7E_2E0_decl,type,
c_2Ebool_2E_7E_2E0: $i ).
thf(c_2Ebool_2E_7E_2E1_decl,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
thf(c_2Ewords_2Eword__add_2E2_decl,type,
c_2Ewords_2Eword__add_2E2: $i > $i > $i ).
thf(c_2Ewords_2Eword__add_2E0_decl,type,
c_2Ewords_2Eword__add_2E0: $i ).
thf(c_2Ewords_2Eword__2comp_2E1_decl,type,
c_2Ewords_2Eword__2comp_2E1: $i > $i ).
thf(c_2Earithmetic_2E_2B_2E2_decl,type,
c_2Earithmetic_2E_2B_2E2: $i > $i > $i ).
thf(c_2Ebool_2ECOND_2E3_decl,type,
c_2Ebool_2ECOND_2E3: $i > $i > $i > $i ).
thf(c_2Ewords_2Eword__2comp_2E0_decl,type,
c_2Ewords_2Eword__2comp_2E0: $i ).
thf(c_2Emin_2E_3D_3D_3E_2E0_decl,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(c_2Earithmetic_2E_2B_2E0_decl,type,
c_2Earithmetic_2E_2B_2E0: $i ).
thf(combin_k_2E0_decl,type,
combin_k_2E0: $i ).
thf(c_2Ebool_2ECOND_2E0_decl,type,
c_2Ebool_2ECOND_2E0: $i ).
thf(c_2Ewords_2En2w_2E0_decl,type,
c_2Ewords_2En2w_2E0: $i ).
thf(c_2Ebool_2E_21_2E1_decl,type,
c_2Ebool_2E_21_2E1: $i > $i ).
thf(c_2Ebool_2E_21_2E0_decl,type,
c_2Ebool_2E_21_2E0: $i ).
thf(c_2Emin_2E_3D_2E0_decl,type,
c_2Emin_2E_3D_2E0: $i ).
thf(c_2Earithmetic_2E_3C_3D_2E0_decl,type,
c_2Earithmetic_2E_3C_3D_2E0: $i ).
thf(c_2Ebool_2E_3F_2E0_decl,type,
c_2Ebool_2E_3F_2E0: $i ).
thf(c_2Ewords_2Eword__sub_2E0_decl,type,
c_2Ewords_2Eword__sub_2E0: $i ).
thf(c_2Earithmetic_2E_2D_2E0_decl,type,
c_2Earithmetic_2E_2D_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(combin_s_2E0_decl,type,
combin_s_2E0: $i ).
thf(c_2Ebool_2E_2F_5C_2E0_decl,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
thf(combin_i_2E0_decl,type,
combin_i_2E0: $i ).
thf(c_2Emin_2E_3D_2E2_decl,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( C @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( 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_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Enum_2Enum @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [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(46,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(308,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)],[46]) ).
thf(38,axiom,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(257,plain,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,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(305,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)],[45]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a) ).
thf(240,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,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(77,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)],[4]) ).
thf(78,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)],[77]) ).
thf(79,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 @ sk4 ) @ ( 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)],[78]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( 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)],[79]) ).
thf(19,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_27b_29) ).
thf(175,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)],[19]) ).
thf(13,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(146,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)],[13]) ).
thf(32,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(234,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)],[32]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( C @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( 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_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( C @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( 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_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( C @ ( tyop_2Enum_2Enum @ s ) @ ( B @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( 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_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
( ( ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
& ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(cnfConj,[status(thm)],[49]) ).
thf(258,plain,
~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(polarity_switch,[status(thm)],[257]) ).
thf(329,plain,
( ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,258]) ).
thf(330,plain,
( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[329]) ).
thf(331,plain,
( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(332,plain,
( ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[331]) ).
thf(333,plain,
( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[332]) ).
thf(36,axiom,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(249,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(11,axiom,
! [A: $i] :
( ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
<=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
<=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
<=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
<=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(110,plain,
! [A: $i] :
( ( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(111,plain,
( ! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ! [A: $i] :
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ! [A: $i] :
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(miniscope,[status(thm)],[110]) ).
thf(112,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( H @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( H @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ~ ( G @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( G @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( F @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( F @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ~ ( E @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( E @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( ( D @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ~ ( D @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( C @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( C @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Emin_2Ebool @ s ) ) )
| ~ ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ) ),
inference(cnf,[status(esa)],[111]) ).
thf(117,plain,
! [A: $i] :
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(cnfConj,[status(thm)],[112]) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(lifteq,[status(thm)],[117]) ).
thf(123,plain,
! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(1160,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(paramod_ordered,[status(thm)],[123,331]) ).
thf(1225,plain,
! [A: $i] :
( ( A != sk2 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[1160]) ).
thf(1327,plain,
( ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 )
| ( sk2 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[1225]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2B_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2E_2B_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_2E_2B_2E2) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2B_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2E_2B_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)],[14]) ).
thf(51,plain,
( ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(52,plain,
( ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
!= ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(25,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(196,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)],[25]) ).
thf(3,axiom,
! [A: $i] :
( ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(53,plain,
! [A: $i] :
( ( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,plain,
( ! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ! [A: $i] : ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ? [A: $i] : ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ? [A: $i] : ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ! [A: $i] : ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ! [A: $i] :
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(55,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( H @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( H @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ~ ( G @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ~ ( G @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( G @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
& ( ( F @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( E @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( D @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( B @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(67,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(cnfConj,[status(thm)],[55]) ).
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(89,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(90,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)],[89]) ).
thf(91,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)],[90]) ).
thf(92,plain,
! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(941,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_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(paramod_ordered,[status(thm)],[67,92]) ).
thf(942,plain,
! [A: $i] :
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[941]) ).
thf(943,plain,
~ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(pattern_uni,[status(thm)],[942:[bind(A,$thf( c_2Ebool_2ET_2E0 ))]]) ).
thf(1057,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[123,943]) ).
thf(1058,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(simp,[status(thm)],[1057]) ).
thf(1059,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
thf(189,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( B @ ( A @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[307,331]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) ) )
| ( A != tyop_2Emin_2Ebool )
| ( B != c_2Ebool_2EF_2E0 )
| ( A != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[356]) ).
thf(421,plain,
( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(30,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(228,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)],[30]) ).
thf(47,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(316,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)],[47]) ).
thf(44,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(293,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)],[44]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__sub_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a) ).
thf(243,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__sub_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,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(192,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)],[23]) ).
thf(18,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(165,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)],[18]) ).
thf(322,plain,
( ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,258]) ).
thf(323,plain,
( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[322]) ).
thf(324,plain,
( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(43,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(285,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)],[43]) ).
thf(21,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(181,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)],[21]) ).
thf(182,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 ) ) )
& ! [A: $i,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(miniscope,[status(thm)],[181]) ).
thf(183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( D @ s ) @ ( E @ ( D @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( D @ s ) )
= ( F @ ( D @ s ) ) )
& ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( B @ ( A @ s ) ) ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [C: $i,B: $i,A: $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(cnfConj,[status(thm)],[183]) ).
thf(186,plain,
! [C: $i,B: $i,A: $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(lifteq,[status(thm)],[184]) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( B @ ( A @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,324]) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 )
| ( A != tyop_2Emin_2Ebool )
| ( B != c_2Ebool_2ET_2E0 )
| ( A != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[485]) ).
thf(578,plain,
! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[530]) ).
thf(15,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(156,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)],[15]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) ),
inference(lifteq,[status(thm)],[185]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
= ( C @ ( A @ s ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2E_3C_3D_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_2Earithmetic_2E_3C_3D_2E2) ).
thf(225,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2E_3C_3D_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)],[29]) ).
thf(27,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(212,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)],[27]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__add_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(114,plain,
! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(cnfConj,[status(thm)],[112]) ).
thf(128,plain,
! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(129,plain,
! [A: $i] :
( ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(972,plain,
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[67,943]) ).
thf(973,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[972]) ).
thf(976,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[973]) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( B @ ( A @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[307,976]) ).
thf(1574,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 ) )
| ( A != tyop_2Emin_2Ebool )
| ( B != c_2Ebool_2ET_2E0 )
| ( A != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[1540]) ).
thf(1599,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 ) ),
inference(simp,[status(thm)],[1574]) ).
thf(936,plain,
! [A: $i] :
( ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ $true
| ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(paramod_ordered,[status(thm)],[50,92]) ).
thf(937,plain,
! [A: $i] :
( ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ p )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
| ~ ( A @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[936]) ).
thf(938,plain,
~ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ p ),
inference(pattern_uni,[status(thm)],[937:[bind(A,$thf( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) ))]]) ).
thf(40,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(266,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)],[40]) ).
thf(26,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(204,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)],[26]) ).
thf(39,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(259,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)],[39]) ).
thf(334,plain,
( ( ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) )
!= ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( 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)],[52]) ).
thf(335,plain,
( ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( sk1 @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__sub_2E2 ) )
!= ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 ) ),
inference(simp,[status(thm)],[334]) ).
thf(5,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(83,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)],[5]) ).
thf(84,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)],[83]) ).
thf(85,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)],[84]) ).
thf(86,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)],[85]) ).
thf(16,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(159,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)],[16]) ).
thf(41,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(274,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)],[41]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( B @ ( A @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[307,324]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= c_2Ebool_2EF_2E0 )
| ( A != tyop_2Emin_2Ebool )
| ( B != c_2Ebool_2ET_2E0 )
| ( A != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[346]) ).
thf(434,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( combin_i_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[381]) ).
thf(711,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( C @ ( A @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[188,324]) ).
thf(801,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 )
| ( A != tyop_2Emin_2Ebool )
| ( C != c_2Ebool_2ET_2E0 )
| ( A != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[711]) ).
thf(855,plain,
! [A: $i] :
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[801]) ).
thf(1689,plain,
! [A: $i] :
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[1059,855]) ).
thf(1690,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[1689:[bind(A,$thf( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 ))]]) ).
thf(17,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(162,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)],[17]) ).
thf(42,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(282,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)],[42]) ).
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(95,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( B @ ( A @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[307,331]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= sk2 )
| ( A != tyop_2Enum_2Enum )
| ( ( B @ ( A @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[358]) ).
thf(409,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Enum_2Enum @ s ) @ ( combin_i_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) )
!= sk2 )
| ( ( A @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[395]) ).
thf(1700,plain,
( ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[1059,331]) ).
thf(1701,plain,
( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) ) ),
inference(simp,[status(thm)],[1700]) ).
thf(1762,plain,
( ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 ) )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[1701]) ).
thf(1830,plain,
( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 ) ),
inference(simp,[status(thm)],[1762]) ).
thf(1678,plain,
! [A: $i] :
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 @ ( tyop_2Emin_2Ebool @ s ) )
!= ( A @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[1059,578]) ).
thf(1679,plain,
( ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[1678:[bind(A,$thf( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( D @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( tyop_2Enum_2Enum @ s ) @ ( D @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( D @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ ( D @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
& ! [C: $i,D: $i] :
( ( D @ ( 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 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2B_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
thf(99,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( D @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( C @ ( tyop_2Enum_2Enum @ s ) @ ( D @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( D @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ ( D @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( B @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
& ! [C: $i,D: $i] :
( ( D @ ( 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 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__add_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
= ( D @ ( tyop_2Enum_2Enum @ s ) @ ( C @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2B_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1539,plain,
( ( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[976]) ).
thf(1575,plain,
( ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[1539]) ).
thf(37,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(250,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)],[37]) ).
thf(31,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_27b) ).
thf(231,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)],[31]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2E_2D_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_2E_2D_2E2) ).
thf(246,plain,
! [A: $i,B: $i] :
( ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_2D_2E2 ) @ ( tyop_2Enum_2Enum @ s ) )
= ( B @ ( tyop_2Enum_2Enum @ s ) @ ( A @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Earithmetic_2E_2D_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)],[35]) ).
thf(81,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)],[79]) ).
thf(82,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)],[81]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( C @ ( tyop_2Emin_2Ebool @ s ) )
= ( D @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Emin_2Ebool @ s ) ) ) )
=> ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
<=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( D @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG) ).
thf(136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( ( C @ ( tyop_2Emin_2Ebool @ s ) )
= ( D @ ( tyop_2Emin_2Ebool @ s ) ) ) )
& ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
= ( B @ ( tyop_2Emin_2Ebool @ s ) ) ) )
=> ( ( ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( D @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) )
& ( ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( C @ ( tyop_2Emin_2Ebool @ s ) @ p ) )
=> ( ( B @ ( tyop_2Emin_2Ebool @ s ) @ p )
=> ( D @ ( tyop_2Emin_2Ebool @ s ) @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(195,plain,
c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(325,plain,
( ( c_2Ebool_2EF_2E0 != c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
c_2Ebool_2EF_2E0 != c_2Ebool_2ET_2E0,
inference(simp,[status(thm)],[325]) ).
thf(10,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(107,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)],[10]) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( ( B @ ( A @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,331]) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) ) )
| ( A != tyop_2Emin_2Ebool )
| ( B != c_2Ebool_2EF_2E0 )
| ( A != tyop_2Emin_2Ebool ) ),
inference(simp,[status(thm)],[502]) ).
thf(596,plain,
! [A: $i] :
( ( A @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ET_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) )
!= ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( sk3 @ ( tyop_2Enum_2Enum @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) ) ),
inference(simp,[status(thm)],[548]) ).
thf(20,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_27b) ).
thf(178,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)],[20]) ).
thf(1159,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Emin_2Ebool @ s ) )
!= ( sk3 @ ( tyop_2Enum_2Enum @ s ) ) )
| ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) )
!= ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) ) )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(paramod_ordered,[status(thm)],[123,331]) ).
thf(1217,plain,
! [A: $i] :
( ( A != sk3 )
| ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool )
| ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( A @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[1159]) ).
thf(1320,plain,
( ( tyop_2Enum_2Enum != tyop_2Emin_2Ebool )
| ( ( sk2 @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ebool_2EF_2E0 @ ( tyop_2Emin_2Ebool @ s ) @ c_2Earithmetic_2E_3C_3D_2E2 ) )
!= c_2Ebool_2EF_2E0 )
| ( sk3 @ ( tyop_2Emin_2Ebool @ s ) @ p ) ),
inference(simp,[status(thm)],[1217]) ).
thf(28,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(222,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)],[28]) ).
thf(5273,plain,
$false,
inference(e,[status(thm)],[308,257,307,240,80,175,146,234,333,249,1327,153,52,110,196,1059,189,421,228,316,293,89,243,192,165,92,324,285,578,156,188,53,225,77,212,96,129,1599,938,266,204,259,335,181,86,159,274,434,1690,162,123,48,855,282,95,409,50,67,331,1830,1679,99,1575,250,231,258,186,246,82,305,136,195,326,107,596,178,1320,83,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP013+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % 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
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Fri Sep 25 17:17:35 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 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
% 0.38/0.60 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.73 % [INFO] Parsing done (125ms).
% 0.68/0.73 % [INFO] Running in sequential loop mode.
% 1.20/0.92 % [INFO] eprover registered as external prover.
% 1.20/0.93 % [INFO] Scanning for conjecture ...
% 1.20/1.00 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 1.46/1.06 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 1.83/1.12 % [INFO] Problem is first-order (TPTP FOF).
% 1.83/1.13 % [INFO] Type checking passed.
% 1.83/1.13 % [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 ...
% 21.25/5.52 % External prover 'e' found a proof!
% 21.25/5.52 % [INFO] Killing All external provers ...
% 21.25/5.52 % Time passed: 5132ms (effective reasoning time: 4785ms)
% 21.25/5.52 % 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)>
% 21.25/5.52 % Axioms used in derivation (45): arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, reserved_2Equant_2E_3F, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29, reserved_2Eho_2Ebool__cases__ax, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27b, reserved_2Eho_2Enotfalse, thm_2Ewords_2Eword__sub__def, arityeq2_2Ec_2Earithmetic_2E_2D_2E2, thm_2Ebool_2EREFL__CLAUSE, reserved_2Equant_2E_21, thm_2Ebool_2EEQ__CLAUSES, arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2, thm_2Ebool_2EIMP__CONG, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a, thm_2Ewords_2EWORD__LITERAL__ADD, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, reserved_2Elogic_2E_3D, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, reserved_2Elogic_2E_7E, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27b, reserved_2Eho_2Eboolext, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, reserved_2Eho_2Eeq__ext, arityeq2_2Ec_2Earithmetic_2E_2B_2E2, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Ebool_2EEQ__SYM__EQ, reserved_2Elogic_2E_5C_2F, arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a, thm_2Ebool_2Ebool__case__thm
% 21.25/5.52 % No. of inferences in proof: 191
% 21.25/5.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5132 ms resp. 4785 ms w/o parsing
% 21.68/5.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.68/5.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------