%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP015_3 : 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 : n005.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 07:35:38 AM UTC 2026
% Result : Theorem 24.09s 8.66s
% Output : Refutation 21.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 49
% Syntax : Number of formulae : 188 ( 98 unt; 0 typ; 0 def)
% Number of atoms : 557 ( 190 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2003 ( 123 ~; 76 |; 59 &;1653 @)
% ( 17 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 18 con; 0-4 aty)
% Number of variables : 353 ( 0 ^; 349 !; 4 ?; 353 :)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Einteger_2Eint_type,type,
tyop_2Einteger_2Eint: $tType ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(app_2E2_decl,type,
app_2E2:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Emin_2Efun ) ) > TB > TA ) ).
thf(p_decl,type,
p: tyop_2Emin_2Ebool > $o ).
thf(combin_i_2E0_decl,type,
combin_i_2E0:
!>[TA: $tType] : ( TA @ ( TA @ tyop_2Emin_2Efun ) ) ).
thf(combin_k_2E0_decl,type,
combin_k_2E0:
!>[TA: $tType,TB: $tType] : ( TB @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ tyop_2Emin_2Efun ) ) ).
thf(combin_s_2E0_decl,type,
combin_s_2E0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2E_21_2E0_decl,type,
c_2Ebool_2E_21_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2E_21_2E1_decl,type,
c_2Ebool_2E_21_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_2F_5C_2E0_decl,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Ebool_2E_2F_5C_2E2_decl,type,
c_2Ebool_2E_2F_5C_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Enum_2E0_2E0_decl,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C_2E0_decl,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ).
thf(c_2Eprim__rec_2E_3C_2E2_decl,type,
c_2Eprim__rec_2E_3C_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
thf(c_2Emin_2E_3D_2E0_decl,type,
c_2Emin_2E_3D_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) ) ).
thf(c_2Emin_2E_3D_2E2_decl,type,
c_2Emin_2E_3D_2E2:
!>[TA: $tType] : ( TA > TA > tyop_2Emin_2Ebool ) ).
thf(c_2Emin_2E_3D_3D_3E_2E0_decl,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Emin_2E_3D_3D_3E_2E2_decl,type,
c_2Emin_2E_3D_3D_3E_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_3F_2E0_decl,type,
c_2Ebool_2E_3F_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2E_3F_2E1_decl,type,
c_2Ebool_2E_3F_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2ECOND_2E0_decl,type,
c_2Ebool_2ECOND_2E0:
!>[TA: $tType] : ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebool_2ECOND_2E3_decl,type,
c_2Ebool_2ECOND_2E3:
!>[TA: $tType] : ( tyop_2Emin_2Ebool > TA > TA > TA ) ).
thf(c_2Ebool_2EF_2E0_decl,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
thf(c_2Earithmetic_2EMOD_2E0_decl,type,
c_2Earithmetic_2EMOD_2E0: tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ).
thf(c_2Earithmetic_2EMOD_2E2_decl,type,
c_2Earithmetic_2EMOD_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Einteger_2ENum_2E0_decl,type,
c_2Einteger_2ENum_2E0: tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) ).
thf(c_2Einteger_2ENum_2E1_decl,type,
c_2Einteger_2ENum_2E1: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET_2E0_decl,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_5C_2F_2E0_decl,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Ebool_2E_5C_2F_2E2_decl,type,
c_2Ebool_2E_5C_2F_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Ewords_2Edimword_2E0_decl,type,
c_2Ewords_2Edimword_2E0:
!>[TA: $tType] : ( tyop_2Enum_2Enum @ ( TA @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ewords_2Edimword_2E1_decl,type,
c_2Ewords_2Edimword_2E1:
!>[TA: $tType] : ( ( TA @ tyop_2Ebool_2Eitself ) > tyop_2Enum_2Enum ) ).
thf(c_2Einteger__word_2Ei2w_2E0_decl,type,
c_2Einteger__word_2Ei2w_2E0:
!>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) ) ).
thf(c_2Einteger__word_2Ei2w_2E1_decl,type,
c_2Einteger__word_2Ei2w_2E1:
!>[TA: $tType] : ( tyop_2Einteger_2Eint > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Einteger_2Eint__lt_2E0_decl,type,
c_2Einteger_2Eint__lt_2E0: tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) ).
thf(c_2Einteger_2Eint__lt_2E2_decl,type,
c_2Einteger_2Eint__lt_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Emin_2Ebool ).
thf(c_2Einteger_2Eint__neg_2E0_decl,type,
c_2Einteger_2Eint__neg_2E0: tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) ).
thf(c_2Einteger_2Eint__neg_2E1_decl,type,
c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__of__num_2E0_decl,type,
c_2Einteger_2Eint__of__num_2E0: tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ).
thf(c_2Einteger_2Eint__of__num_2E1_decl,type,
c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2Ewords_2En2w_2E0_decl,type,
c_2Ewords_2En2w_2E0:
!>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ewords_2En2w_2E1_decl,type,
c_2Ewords_2En2w_2E1:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Ebool_2Ethe__value_2E0_decl,type,
c_2Ebool_2Ethe__value_2E0:
!>[TA: $tType] : ( TA @ tyop_2Ebool_2Eitself ) ).
thf(c_2Ewords_2Eword__2comp_2E0_decl,type,
c_2Ewords_2Eword__2comp_2E0:
!>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ewords_2Eword__2comp_2E1_decl,type,
c_2Ewords_2Eword__2comp_2E1:
!>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).
thf(c_2Ebool_2E_7E_2E0_decl,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) ).
thf(c_2Ebool_2E_7E_2E1_decl,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(17,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( TA @ ( TA @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
thf(125,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
( ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( TA @ ( TA @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ),B: TA @ ( TB @ tyop_2Emin_2Efun )] :
( ! [C: TB] :
( ( C @ ( A @ ( TA @ ( TB @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ app_2E2 ) ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).
thf(173,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ),B: TA @ ( TB @ tyop_2Emin_2Efun )] :
( ! [C: TB] :
( ( C @ ( A @ ( TA @ ( TB @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ app_2E2 ) ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ p )
& ( A @ p ) )
<=> ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(54,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) )
& ( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).
thf(112,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ),B: TB @ ( TC @ tyop_2Emin_2Efun ),C: TC] :
( ( C @ ( B @ ( A @ ( TA @ ( TB @ ( TC @ combin_s_2E0 ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TB @ ( TC @ app_2E2 ) ) ) @ ( C @ ( A @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ app_2E2 ) ) ) @ ( TA @ ( TB @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).
thf(150,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ),B: TB @ ( TC @ tyop_2Emin_2Efun ),C: TC] :
( ( C @ ( B @ ( A @ ( TA @ ( TB @ ( TC @ combin_s_2E0 ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ tyop_2Emin_2Efun ) @ ( TB @ ( TC @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) @ ( TA @ ( TC @ app_2E2 ) ) ) )
= ( C @ ( B @ ( TB @ ( TC @ app_2E2 ) ) ) @ ( C @ ( A @ ( TA @ ( TB @ tyop_2Emin_2Efun ) @ ( TC @ app_2E2 ) ) ) @ ( TA @ ( TB @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
thf(62,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(63,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2EF_2E0 )
| ( A = c_2Ebool_2ET_2E0 ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(21,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
<=> ( c_2Ebool_2ET_2E0 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(149,plain,
c_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(369,plain,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( A @ p )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[64,149]) ).
thf(370,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A @ p )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(pattern_uni,[status(thm)],[369:[]]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(99,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( A = B )
=> ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p ) )
& ( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) @ p )
<=> ! [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(115,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( ! [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p )
=> ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) @ p ) )
& ( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) @ p )
=> ! [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(100,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
| ( A != B ) )
& ( ( A = B )
| ~ ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(102,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[100]) ).
thf(104,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
| ( A != B ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(105,plain,
! [TA: $tType,A: TA] : ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p ),
inference(simp,[status(thm)],[104]) ).
thf(25,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( A @ c_2Ebool_2E_7E_2E1 @ p )
<=> ~ ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(160,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( A @ p )
=> ( A @ c_2Ebool_2E_7E_2E1 @ p ) )
& ( ( A @ c_2Ebool_2E_7E_2E1 @ p )
=> ~ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(161,plain,
( ! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
=> ( A @ c_2Ebool_2E_7E_2E1 @ p ) )
& ! [A: tyop_2Emin_2Ebool] :
( ( A @ c_2Ebool_2E_7E_2E1 @ p )
=> ~ ( A @ p ) ) ),
inference(miniscope,[status(thm)],[160]) ).
thf(162,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( ( B @ c_2Ebool_2E_7E_2E1 @ p )
| ( B @ p ) )
& ( ~ ( A @ p )
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ) ),
inference(cnf,[status(esa)],[161]) ).
thf(163,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(cnfConj,[status(thm)],[162]) ).
thf(423,plain,
! [TA: $tType,B: tyop_2Emin_2Ebool,A: TA] :
( ( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
!= ( B @ p ) )
| ~ $true
| ~ ( B @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(paramod_ordered,[status(thm)],[105,163]) ).
thf(424,plain,
! [TA: $tType,B: tyop_2Emin_2Ebool,A: TA] :
( ( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
!= ( B @ p ) )
| ~ ( B @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(simp,[status(thm)],[423]) ).
thf(425,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ c_2Ebool_2E_7E_2E1 @ p ),
inference(pattern_uni,[status(thm)],[424:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( TA @ c_2Emin_2E_3D_2E2 ) ) ))]]) ).
thf(440,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ c_2Ebool_2E_7E_2E1 @ p ),
inference(simp,[status(thm)],[425]) ).
thf(33,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
= ( B @ ( A @ ( c_2Einteger_2Eint__lt_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Einteger_2Eint__lt_2E2) ).
thf(202,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
= ( B @ ( A @ ( c_2Einteger_2Eint__lt_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(328,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ ( A @ p )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,163]) ).
thf(329,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ ( A @ p ) ),
inference(simp,[status(thm)],[328]) ).
thf(340,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 )
| ~ ( A @ p ) ),
inference(simp,[status(thm)],[329]) ).
thf(23,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2Eint__neg_2E1 )
= ( A @ ( c_2Einteger_2Eint__neg_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__neg_2E1) ).
thf(153,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2Eint__neg_2E1 )
= ( A @ ( c_2Einteger_2Eint__neg_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
~ ( c_2Ebool_2EF_2E0 @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
thf(75,plain,
~ ( c_2Ebool_2EF_2E0 @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(76,plain,
~ ( c_2Ebool_2EF_2E0 @ p ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(419,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,76]) ).
thf(420,plain,
! [TA: $tType,A: TA] :
( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) ),
inference(simp,[status(thm)],[419]) ).
thf(436,plain,
! [TA: $tType,A: TA] :
( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[420]) ).
thf(46,axiom,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
thf(257,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(189,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(55,plain,
( ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) )
& ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [D: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( ( D @ p )
| ~ ( D @ ( C @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) )
& ( ( C @ p )
| ~ ( D @ ( C @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) )
& ( ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
| ~ ( B @ p )
| ~ ( A @ p ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
| ~ ( B @ p )
| ~ ( A @ p ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(47,axiom,
! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).
thf(259,plain,
! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(260,plain,
! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(36,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( B @ p ) )
=> ( ( ( B @ p )
=> ( A @ p ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(211,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( B @ p ) )
=> ( ( ( B @ p )
=> ( A @ p ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ( A @ p )
<=> ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(106,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ~ ( A @ p ) )
& ( ~ ( A @ p )
=> ( A @ ( c_2Ebool_2E_7E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,axiom,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).
thf(119,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(120,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(9,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ c_2Ebool_2E_5C_2F_2E2 ) @ p )
<=> ( ( B @ p )
| ( A @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(84,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
| ( A @ p ) )
=> ( B @ ( A @ c_2Ebool_2E_5C_2F_2E2 ) @ p ) )
& ( ( B @ ( A @ c_2Ebool_2E_5C_2F_2E2 ) @ p )
=> ( ( B @ p )
| ( A @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(59,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( B @ p )
| ~ ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(61,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( B @ p )
| ~ ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(simp,[status(thm)],[59]) ).
thf(37,axiom,
c_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
thf(221,plain,
c_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(291,plain,
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,76]) ).
thf(292,plain,
( ( c_2Ebool_2ET_2E0 @ p )
!= ( c_2Ebool_2EF_2E0 @ p ) ),
inference(simp,[status(thm)],[291]) ).
thf(293,plain,
c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0,
inference(simp,[status(thm)],[292]) ).
thf(43,axiom,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
= ( A @ c_2Einteger_2ENum_2E1 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2ENum_2E1 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__lt_2E2 ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
thf(248,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
= ( A @ c_2Einteger_2ENum_2E1 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2ENum_2E1 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__lt_2E2 ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(58,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( A @ p )
| ~ ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(cnfConj,[status(thm)],[56]) ).
thf(60,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( A @ p )
| ~ ( B @ ( A @ ( c_2Ebool_2E_2F_5C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
inference(simp,[status(thm)],[58]) ).
thf(42,axiom,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) @ p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
thf(245,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(246,plain,
~ ? [A: tyop_2Enum_2Enum] : ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) @ p ),
inference(miniscope,[status(thm)],[245]) ).
thf(247,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) @ p ),
inference(cnf,[status(esa)],[246]) ).
thf(297,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,247]) ).
thf(298,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) ),
inference(simp,[status(thm)],[297]) ).
thf(299,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[298]) ).
thf(359,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Enum_2E0_2E0 @ ( B @ c_2Eprim__rec_2E_3C_2E2 ) ) )
| ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[64,299]) ).
thf(360,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Enum_2E0_2E0 @ ( B @ c_2Eprim__rec_2E_3C_2E2 ) ) )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[359]) ).
thf(361,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( c_2Enum_2E0_2E0 @ ( C @ c_2Eprim__rec_2E_3C_2E2 ) )),bind(B,$thf( C ))]]) ).
thf(380,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) )
= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[361]) ).
thf(31,axiom,
! [TA: $tType,A: TA @ tyop_2Ebool_2Eitself] :
( ( A @ ( TA @ c_2Ewords_2Edimword_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Edimword_2E0 @ ( tyop_2Enum_2Enum @ ( TA @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a) ).
thf(192,plain,
! [TA: $tType,A: TA @ tyop_2Ebool_2Eitself] :
( ( A @ ( TA @ c_2Ewords_2Edimword_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2Edimword_2E0 @ ( tyop_2Enum_2Enum @ ( TA @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(10,axiom,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2EF_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= B )
& ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2ET_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(92,plain,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2EF_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= B )
& ! [A: TA,B: TA] :
( ( B @ ( A @ ( c_2Ebool_2ET_2E0 @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p )
<=> ( ( B @ p )
& ( A @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(65,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p ) )
& ( ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) @ p )
<=> ? [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(156,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( ? [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p )
=> ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) @ p ) )
& ( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) @ p )
=> ? [B: TA] : ( B @ ( A @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
c_2Ebool_2ET_2E0 @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(188,plain,
c_2Ebool_2ET_2E0 @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1,conjecture,
! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
thf(2,negated_conjecture,
~ ! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(51,plain,
~ ! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( skt1 @ c_2Einteger__word_2Ei2w_2E1 ) )
!= ( c_2Enum_2E0_2E0 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( skt1 @ c_2Einteger__word_2Ei2w_2E1 ) )
!= ( c_2Enum_2E0_2E0 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(8,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ p )
| ( A @ p ) )
<=> ( B @ ( A @ ( c_2Ebool_2E_5C_2F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(77,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( c_2Ebool_2E_5C_2F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ( ( B @ p )
| ( A @ p ) ) )
& ( ( ( B @ p )
| ( A @ p ) )
=> ( B @ ( A @ ( c_2Ebool_2E_5C_2F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2ENum_2E1 )
= ( A @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2ENum_2E1) ).
thf(122,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2ENum_2E1 )
= ( A @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(123,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2ENum_2E1 )
= ( A @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2ENum_2E1 )
= ( A @ ( c_2Einteger_2ENum_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(39,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( ~ ( B @ p )
=> ( E = F ) )
& ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( E @ ( C @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( F @ ( D @ ( B @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(225,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( ~ ( B @ p )
=> ( E = F ) )
& ( ( B @ p )
=> ( C = D ) )
& ( A = B ) )
=> ( ( E @ ( C @ ( A @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( F @ ( D @ ( B @ ( TA @ c_2Ebool_2ECOND_2E3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(18,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ c_2Emin_2E_3D_3D_3E_2E2 ) @ p )
<=> ( ( A @ p )
=> ( B @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(128,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ c_2Emin_2E_3D_3D_3E_2E2 ) @ p ) )
& ( ( B @ ( A @ c_2Emin_2E_3D_3D_3E_2E2 ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(34,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(205,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_3F_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(494,plain,
! [TA: $tType,B: tyop_2Emin_2Ebool,A: TA] :
( ( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
!= ( B @ p ) )
| ( ( B @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[105,340]) ).
thf(495,plain,
! [TA: $tType,B: tyop_2Emin_2Ebool,A: TA] :
( ( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ p )
!= ( B @ p ) )
| ( ( B @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[494]) ).
thf(496,plain,
! [TA: $tType,A: TA] :
( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 ),
inference(pattern_uni,[status(thm)],[495:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( TA @ c_2Emin_2E_3D_2E2 ) ) ))]]) ).
thf(508,plain,
! [TA: $tType,A: TA] :
( ( A @ ( A @ ( TA @ c_2Emin_2E_3D_2E2 ) ) @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[496]) ).
thf(26,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( B @ p ) )
<=> ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(166,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) )
& ( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) )
<=> ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(176,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) )
=> ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) ) )
& ( ( ( A @ p )
=> ( ( B @ p )
=> ( C @ p ) ) )
=> ( ( ( B @ p )
& ( A @ p ) )
=> ( C @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(190,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(191,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun )] :
( ( A @ ( TA @ c_2Ebool_2E_21_2E1 ) )
= ( A @ ( TA @ c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(50,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= c_2Ebool_2EF_2E0 )
& ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
<=> ( ( B != c_2Enum_2E0_2E0 )
| ( A != c_2Enum_2E0_2E0 ) ) )
& ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( A @ ( B @ c_2Eprim__rec_2E_3C_2E2 ) ) )
& ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( B @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
thf(271,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= c_2Ebool_2EF_2E0 )
& ( ( ( B != c_2Enum_2E0_2E0 )
| ( A != c_2Enum_2E0_2E0 ) )
=> ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p ) )
& ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
=> ( ( B != c_2Enum_2E0_2E0 )
| ( A != c_2Enum_2E0_2E0 ) ) )
& ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( A @ ( B @ c_2Eprim__rec_2E_3C_2E2 ) ) )
& ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( B @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(35,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29) ).
thf(208,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E3 ) ) ) )
= ( C @ ( B @ ( A @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ c_2Ebool_2ECOND_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(44,axiom,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
= ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a) ).
thf(251,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
= ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(154,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2Eint__neg_2E1 )
= ( A @ ( c_2Einteger_2Eint__neg_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(155,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A @ c_2Einteger_2Eint__neg_2E1 )
= ( A @ ( c_2Einteger_2Eint__neg_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(6,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) )
= ( B @ ( A @ ( c_2Eprim__rec_2E_3C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) ).
thf(72,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) )
= ( B @ ( A @ ( c_2Eprim__rec_2E_3C_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(330,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ $true
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(paramod_ordered,[status(thm)],[149,163]) ).
thf(331,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 @ p )
!= ( A @ p ) )
| ~ ( A @ c_2Ebool_2E_7E_2E1 @ p ) ),
inference(simp,[status(thm)],[330]) ).
thf(332,plain,
~ ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 @ p ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( c_2Ebool_2ET_2E0 ))]]) ).
thf(344,plain,
( ( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,332]) ).
thf(345,plain,
( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) ),
inference(simp,[status(thm)],[344]) ).
thf(348,plain,
( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[345]) ).
thf(384,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 ) )
| ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[64,348]) ).
thf(385,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 ) )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[384]) ).
thf(386,plain,
( ( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( c_2Ebool_2ET_2E0 @ c_2Ebool_2E_7E_2E1 ))]]) ).
thf(113,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(cnf,[status(esa)],[112]) ).
thf(114,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combin_i_2E0 @ ( TA @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(lifteq,[status(thm)],[113]) ).
thf(20,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A @ p )
<=> ( B @ p ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
thf(139,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( B @ p )
=> ( A @ p ) )
& ( ( A @ p )
=> ( B @ p ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(48,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
<=> ( ( TA @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ c_2Ewords_2Edimword_2E1 ) @ ( A @ c_2Earithmetic_2EMOD_2E2 ) )
= ( TA @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ c_2Ewords_2Edimword_2E1 ) @ ( B @ c_2Earithmetic_2EMOD_2E2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__11) ).
thf(262,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( ( TA @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ c_2Ewords_2Edimword_2E1 ) @ ( A @ c_2Earithmetic_2EMOD_2E2 ) )
= ( TA @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ c_2Ewords_2Edimword_2E1 ) @ ( B @ c_2Earithmetic_2EMOD_2E2 ) ) )
=> ( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) )
& ( ( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
=> ( ( TA @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ c_2Ewords_2Edimword_2E1 ) @ ( A @ c_2Earithmetic_2EMOD_2E2 ) )
= ( TA @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ c_2Ewords_2Edimword_2E1 ) @ ( B @ c_2Earithmetic_2EMOD_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(19,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(136,plain,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 @ p )
=> ( A @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(49,axiom,
! [A: tyop_2Enum_2Enum] :
( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2ENum_2E1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
thf(268,plain,
! [A: tyop_2Enum_2Enum] :
( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2ENum_2E1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A = B )
<=> ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(195,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p )
=> ( A = B ) )
& ( ( A = B )
=> ( B @ ( A @ ( TA @ c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( TA @ tyop_2Emin_2Efun ) @ ( TA @ app_2E2 ) ) ) @ ( tyop_2Emin_2Ebool @ ( TA @ app_2E2 ) ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(258,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
= ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(532,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Einteger_2Eint__neg_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ app_2E2 ) ) ) )
= ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
inference(rewrite,[status(thm)],[258,155]) ).
thf(40,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2EMOD_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2EMOD_2E2) ).
thf(239,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) )
= ( B @ ( A @ ( c_2Earithmetic_2EMOD_2E0 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(41,axiom,
! [A: tyop_2Enum_2Enum] :
( ( A @ c_2Einteger_2Eint__of__num_2E1 )
= ( A @ ( c_2Einteger_2Eint__of__num_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) ).
thf(242,plain,
! [A: tyop_2Enum_2Enum] :
( ( A @ c_2Einteger_2Eint__of__num_2E1 )
= ( A @ ( c_2Einteger_2Eint__of__num_2E0 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(66,plain,
( ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p ) )
& ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) ) ),
inference(miniscope,[status(thm)],[65]) ).
thf(67,plain,
! [D: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( ( D @ ( C @ c_2Ebool_2E_2F_5C_2E2 ) @ p )
| ~ ( D @ p )
| ~ ( C @ p ) )
& ( ( B @ p )
| ~ ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p ) )
& ( ( A @ p )
| ~ ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(68,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( A @ p )
| ~ ( B @ ( A @ c_2Ebool_2E_2F_5C_2E2 ) @ p ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(45,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum] :
( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2En2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).
thf(254,plain,
! [TA: $tType,A: tyop_2Enum_2Enum] :
( ( A @ ( TA @ c_2Ewords_2En2w_2E1 ) )
= ( A @ ( TA @ c_2Ewords_2En2w_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(482,plain,
! [TB: $tType,A: TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
( ( ( A @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) )
!= ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E1 ) ) )
| ( ( A @ ( TB @ c_2Ewords_2Eword__2comp_2E0 @ ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) )
= ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[121,261]) ).
thf(483,plain,
! [TB: $tType] :
( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TB @ c_2Ewords_2Eword__2comp_2E0 @ ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) )
= ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ))]]) ).
thf(486,plain,
! [TA: $tType] :
( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E0 @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ app_2E2 ) ) ) )
= ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
inference(simp,[status(thm)],[483]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( B @ ( A @ ( TA @ ( TB @ combin_k_2E0 ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ app_2E2 ) ) ) @ ( TB @ ( TA @ app_2E2 ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( B @ ( A @ ( TA @ ( TB @ combin_k_2E0 ) @ ( TB @ ( TA @ tyop_2Emin_2Efun ) @ ( TB @ app_2E2 ) ) ) @ ( TB @ ( TA @ app_2E2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(272,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= c_2Ebool_2EF_2E0 )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( B != c_2Enum_2E0_2E0 )
| ( A != c_2Enum_2E0_2E0 ) )
=> ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
=> ( ( B != c_2Enum_2E0_2E0 )
| ( A != c_2Enum_2E0_2E0 ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( A @ ( B @ c_2Eprim__rec_2E_3C_2E2 ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( B @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) ) ) ),
inference(miniscope,[status(thm)],[271]) ).
thf(273,plain,
! [J: tyop_2Enum_2Enum,I: tyop_2Enum_2Enum,H: tyop_2Enum_2Enum,G: tyop_2Enum_2Enum,F: tyop_2Enum_2Enum,E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( J @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( I @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= c_2Ebool_2EF_2E0 )
& ( ( H @ c_2Einteger_2Eint__of__num_2E1 @ ( G @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
| ( H = c_2Enum_2E0_2E0 ) )
& ( ( H @ c_2Einteger_2Eint__of__num_2E1 @ ( G @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
| ( G = c_2Enum_2E0_2E0 ) )
& ( ( F != c_2Enum_2E0_2E0 )
| ( E != c_2Enum_2E0_2E0 )
| ~ ( F @ c_2Einteger_2Eint__of__num_2E1 @ ( E @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p ) )
& ( ( D @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( C @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( C @ ( D @ c_2Eprim__rec_2E_3C_2E2 ) ) )
& ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= ( B @ ( A @ c_2Eprim__rec_2E_3C_2E2 ) ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(279,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0_2E0 )
| ( A != c_2Enum_2E0_2E0 )
| ~ ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(284,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
| ( B != c_2Enum_2E0_2E0 )
| ( A != c_2Enum_2E0_2E0 ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(285,plain,
~ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p ),
inference(simp,[status(thm)],[284]) ).
thf(321,plain,
~ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p ),
inference(rewrite,[status(thm)],[285,258]) ).
thf(322,plain,
( ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,321]) ).
thf(323,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) @ p )
!= ( c_2Ebool_2ET_2E0 @ p ) ),
inference(simp,[status(thm)],[322]) ).
thf(326,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
!= c_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[323]) ).
thf(362,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) )
| ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[64,326]) ).
thf(363,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A
!= ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[362]) ).
thf(364,plain,
( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ))]]) ).
thf(817,plain,
$false,
inference(e,[status(thm)],[125,173,54,112,150,370,99,115,440,202,340,153,436,257,189,57,261,211,106,121,84,61,221,293,248,60,380,160,192,92,65,156,188,53,77,124,225,128,105,205,508,166,64,149,176,191,259,76,245,271,208,251,155,72,386,114,139,75,119,262,51,136,268,195,532,239,242,163,68,62,254,486,122,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP015_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 17:21:17 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.50/1.25 % [INFO] Parsing done (273ms).
% 1.50/1.26 % [INFO] Running in sequential loop mode.
% 2.62/1.67 % [INFO] eprover registered as external prover.
% 2.62/1.68 % [INFO] Scanning for conjecture ...
% 3.05/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 49 axioms. Running axiom selection ...
% 3.26/1.91 % [INFO] Axiom selection finished. Selected 48 axioms (removed 1 axioms).
% 3.26/2.03 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.69/2.04 % [INFO] Type checking passed.
% 3.69/2.05 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.37/2.38 % [INFO] [Domain constraints] Detected constraint on tyop_2Emin_2Ebool
% 4.37/2.38 % [INFO] [Domain constraints] dom(tyop_2Emin_2Ebool) ⊆ {c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0}
% 24.09/8.66 % External prover 'e' found a proof!
% 24.09/8.66 % [INFO] Killing All external provers ...
% 24.09/8.66 % Time passed: 8128ms (effective reasoning time: 7392ms)
% 24.09/8.66 % 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)>
% 24.09/8.66 % Axioms used in derivation (48): arityeq2_2Ec_2Eprim__rec_2E_3C_2E2, thm_2Eextra_2Dho_2Eeq__ext, thm_2Eextra_2Dho_2Eboolext, logicdef_2E_5C_2F, thm_2Ebool_2EFALSITY, thm_2Eextra_2Dho_2Ek__thm, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, thm_2Eextra_2Dho_2Etruth, arityeq1_2Ec_2Einteger_2Eint__of__num_2E1, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, quantdef_2E_3F, logicdef_2E_3D, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2EIMP__ANTISYM__AX, thm_2Eextra_2Dho_2Ei__thm, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, thm_2Eextra_2Dho_2Ebool__cases__ax, thm_2Eextra_2Dho_2Enotfalse, arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Earithmetic_2EMOD_2E2, thm_2Einteger_2EINT__NEG__0, quantdef_2E_21, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29, thm_2Ebool_2ETRUTH, thm_2Eprim__rec_2ENOT__LESS__0, logicdef_2E_3D_3D_3E, arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, thm_2Einteger_2EINT__LT__CALCULATE, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq1_2Ec_2Einteger_2ENum_2E1, arityeq2_2Ec_2Einteger_2Eint__lt_2E2, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Einteger__word_2Ei2w__def, logicdef_2E_2F_5C, logicdef_2E_7E, arityeq1_2Ec_2Einteger_2Eint__neg_2E1, thm_2Ewords_2EWORD__NEG__0, thm_2Eextra_2Dho_2Es__thm, thm_2Einteger_2ENUM__OF__INT, thm_2Ewords_2En2w__11, thm_2Ebool_2Ebool__case__thm
% 24.09/8.66 % No. of inferences in proof: 188
% 24.09/8.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8128 ms resp. 7392 ms w/o parsing
% 21.46/8.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.46/8.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------