TSTP Solution File: ITP015+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP015+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:46:51 EDT 2024
% Result : Theorem 6.36s 2.67s
% Output : Refutation 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 102
% Syntax : Number of formulae : 154 ( 55 unt; 52 typ; 0 def)
% Number of atoms : 238 ( 100 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2760 ( 20 ~; 11 |; 38 &;2604 @)
% ( 18 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 29 con; 0-3 aty)
% Number of variables : 219 ( 0 ^ 216 !; 3 ?; 219 :)
% Comments :
%------------------------------------------------------------------------------
thf(s_type,type,
s: $i > $i > $i ).
thf(tyop_2Efcp_2Ecart_type,type,
tyop_2Efcp_2Ecart: $i > $i > $i ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $i ).
thf(c_2Einteger__word_2Ei2w_2E1_type,type,
c_2Einteger__word_2Ei2w_2E1: $i > $i ).
thf(tyop_2Einteger_2Eint_type,type,
tyop_2Einteger_2Eint: $i ).
thf(c_2Einteger_2Eint__of__num_2E1_type,type,
c_2Einteger_2Eint__of__num_2E1: $i > $i ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $i ).
thf(c_2Enum_2E0_2E0_type,type,
c_2Enum_2E0_2E0: $i ).
thf(c_2Ewords_2En2w_2E1_type,type,
c_2Ewords_2En2w_2E1: $i > $i ).
thf(p_type,type,
p: $i > $o ).
thf(c_2Ebool_2E_3F_2E1_type,type,
c_2Ebool_2E_3F_2E1: $i > $i ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: $i > $i > $i ).
thf(app_2E2_type,type,
app_2E2: $i > $i > $i ).
thf(c_2Ebool_2E_7E_2E0_type,type,
c_2Ebool_2E_7E_2E0: $i ).
thf(c_2Einteger_2Eint__lt_2E2_type,type,
c_2Einteger_2Eint__lt_2E2: $i > $i > $i ).
thf(c_2Eprim__rec_2E_3C_2E2_type,type,
c_2Eprim__rec_2E_3C_2E2: $i > $i > $i ).
thf(c_2Einteger_2Eint__neg_2E1_type,type,
c_2Einteger_2Eint__neg_2E1: $i > $i ).
thf(c_2Ebool_2EF_2E0_type,type,
c_2Ebool_2EF_2E0: $i ).
thf(c_2Ebool_2E_7E_2E1_type,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
thf(c_2Ebool_2ET_2E0_type,type,
c_2Ebool_2ET_2E0: $i ).
thf(c_2Emin_2E_3D_3D_3E_2E0_type,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(c_2Einteger_2ENum_2E1_type,type,
c_2Einteger_2ENum_2E1: $i > $i ).
thf(c_2Ewords_2Edimword_2E1_type,type,
c_2Ewords_2Edimword_2E1: $i > $i ).
thf(tyop_2Ebool_2Eitself_type,type,
tyop_2Ebool_2Eitself: $i > $i ).
thf(c_2Ewords_2Edimword_2E0_type,type,
c_2Ewords_2Edimword_2E0: $i ).
thf(c_2Einteger_2Eint__lt_2E0_type,type,
c_2Einteger_2Eint__lt_2E0: $i ).
thf(c_2Einteger_2ENum_2E0_type,type,
c_2Einteger_2ENum_2E0: $i ).
thf(c_2Einteger_2Eint__of__num_2E0_type,type,
c_2Einteger_2Eint__of__num_2E0: $i ).
thf(c_2Ebool_2ECOND_2E3_type,type,
c_2Ebool_2ECOND_2E3: $i > $i > $i > $i ).
thf(c_2Ewords_2Eword__2comp_2E1_type,type,
c_2Ewords_2Eword__2comp_2E1: $i > $i ).
thf(c_2Earithmetic_2EMOD_2E2_type,type,
c_2Earithmetic_2EMOD_2E2: $i > $i > $i ).
thf(c_2Earithmetic_2EMOD_2E0_type,type,
c_2Earithmetic_2EMOD_2E0: $i ).
thf(combin_k_2E0_type,type,
combin_k_2E0: $i ).
thf(combin_s_2E0_type,type,
combin_s_2E0: $i ).
thf(c_2Ebool_2ECOND_2E0_type,type,
c_2Ebool_2ECOND_2E0: $i ).
thf(c_2Eprim__rec_2E_3C_2E0_type,type,
c_2Eprim__rec_2E_3C_2E0: $i ).
thf(c_2Einteger_2Eint__neg_2E0_type,type,
c_2Einteger_2Eint__neg_2E0: $i ).
thf(c_2Emin_2E_3D_2E0_type,type,
c_2Emin_2E_3D_2E0: $i ).
thf(c_2Ewords_2En2w_2E0_type,type,
c_2Ewords_2En2w_2E0: $i ).
thf(c_2Ebool_2E_3F_2E0_type,type,
c_2Ebool_2E_3F_2E0: $i ).
thf(c_2Ebool_2E_21_2E1_type,type,
c_2Ebool_2E_21_2E1: $i > $i ).
thf(c_2Ewords_2Eword__2comp_2E0_type,type,
c_2Ewords_2Eword__2comp_2E0: $i ).
thf(c_2Ebool_2E_5C_2F_2E0_type,type,
c_2Ebool_2E_5C_2F_2E0: $i ).
thf(c_2Ebool_2E_2F_5C_2E2_type,type,
c_2Ebool_2E_2F_5C_2E2: $i > $i > $i ).
thf(c_2Ebool_2E_5C_2F_2E2_type,type,
c_2Ebool_2E_5C_2F_2E2: $i > $i > $i ).
thf(c_2Emin_2E_3D_3D_3E_2E2_type,type,
c_2Emin_2E_3D_3D_3E_2E2: $i > $i > $i ).
thf(c_2Ebool_2Ethe__value_2E0_type,type,
c_2Ebool_2Ethe__value_2E0: $i ).
thf(c_2Ebool_2E_2F_5C_2E0_type,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
thf(c_2Ebool_2E_21_2E0_type,type,
c_2Ebool_2E_21_2E0: $i ).
thf(combin_i_2E0_type,type,
combin_i_2E0: $i ).
thf(c_2Einteger__word_2Ei2w_2E0_type,type,
c_2Einteger__word_2Ei2w_2E0: $i ).
thf(c_2Emin_2E_3D_2E2_type,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
= ( s @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(142,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
= ( s @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(6,axiom,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
<=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(84,plain,
! [A: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,axiom,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(169,plain,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2En2w_2E0 ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(266,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(24,axiom,
! [A: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).
thf(145,plain,
! [A: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) )
= ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
thf(282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) )
= ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ B ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ B ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Eprim__rec_2E_3C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Eprim__rec_2E_3C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(101,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) )
<=> ( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__11) ).
thf(234,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) )
=> ( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
& ( ( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ C ) @ ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
=> ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
= ( s @ A @ C ) )
<=> ( ( s @ A @ C )
= ( s @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__SYM__EQ) ).
thf(170,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( s @ A @ B )
= ( s @ A @ C ) )
=> ( ( s @ A @ C )
= ( s @ A @ B ) ) )
& ( ( ( s @ A @ C )
= ( s @ A @ B ) )
=> ( ( s @ A @ B )
= ( s @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
= ( s @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(269,plain,
! [A: $i,B: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
= ( s @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
! [A: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(52,plain,
~ ! [A: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ B )
= ( s @ tyop_2Emin_2Ebool @ C ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
=> ( ( s @ A @ D )
= ( s @ A @ E ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
=> ( ( s @ A @ F )
= ( s @ A @ G ) ) ) )
=> ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
= ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ C ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(184,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ B )
= ( s @ tyop_2Emin_2Ebool @ C ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
=> ( ( s @ A @ D )
= ( s @ A @ E ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ C ) )
=> ( ( s @ A @ F )
= ( s @ A @ G ) ) ) )
=> ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
= ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ C ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
! [A: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
thf(110,plain,
! [A: $i] :
~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(125,plain,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
= ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(157,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
= ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ B ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Enum_2Enum ) @ c_2Ewords_2Edimword_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Ewords_2Edimword_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ B ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Enum_2Enum ) @ c_2Ewords_2Edimword_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= ( s @ A @ B ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(89,plain,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i] :
( ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ c_2Einteger_2Eint__of__num_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) ).
thf(133,plain,
! [A: $i] :
( ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ c_2Einteger_2Eint__of__num_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) )
<=> ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(248,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) )
=> ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) )
& ( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(60,plain,
! [A: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(220,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29) ).
thf(160,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ B ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) )
<=> ( ( s @ A @ B )
= ( s @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(275,plain,
! [A: $i,B: $i,C: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) )
=> ( ( s @ A @ B )
= ( s @ A @ C ) ) )
& ( ( ( s @ A @ B )
= ( s @ A @ C ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) ) )
<=> ( ( ( s @ tyop_2Enum_2Enum @ A )
!= ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) )
| ( ( s @ tyop_2Enum_2Enum @ B )
!= ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Eprim__rec_2E_3C_2E2 @ ( s @ tyop_2Enum_2Enum @ B ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) ) )
=> ( ( ( s @ tyop_2Enum_2Enum @ A )
!= ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) )
| ( ( s @ tyop_2Enum_2Enum @ B )
!= ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) )
& ( ( ( ( s @ tyop_2Enum_2Enum @ A )
!= ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) )
| ( ( s @ tyop_2Enum_2Enum @ B )
!= ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) ) ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: $i] :
( ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ A ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ c_2Einteger_2Eint__neg_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__neg_2E1) ).
thf(166,plain,
! [A: $i] :
( ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ A ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ c_2Einteger_2Eint__neg_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).
thf(204,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Ewords_2Eword__2comp_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(46,axiom,
! [A: $i] :
( ! [B: $i,C: $i] :
( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
= ( s @ A @ B ) )
& ! [B: $i,C: $i] :
( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
= ( s @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(259,plain,
! [A: $i] :
( ! [B: $i,C: $i] :
( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
= ( s @ A @ B ) )
& ! [B: $i,C: $i] :
( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
= ( s @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(13,axiom,
! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(113,plain,
! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ) )
= ( s @ tyop_2Enum_2Enum @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
thf(98,plain,
! [A: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ A ) ) ) ) )
= ( s @ tyop_2Enum_2Enum @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(130,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(241,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
<=> ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(199,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
& ( ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
= ( s @ A @ C ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(177,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( s @ A @ B )
= ( s @ A @ C ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) )
=> ( ( s @ A @ B )
= ( s @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
! [A: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ A ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ c_2Einteger_2ENum_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2ENum_2E1) ).
thf(127,plain,
! [A: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Einteger_2ENum_2E1 @ ( s @ tyop_2Einteger_2Eint @ A ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ c_2Einteger_2ENum_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
<=> ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
& ( ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Earithmetic_2EMOD_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2EMOD_2E2) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EMOD_2E2 @ ( s @ tyop_2Enum_2Enum @ A ) @ ( s @ tyop_2Enum_2Enum @ B ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Earithmetic_2EMOD_2E0 ) @ ( s @ tyop_2Enum_2Enum @ A ) ) ) @ ( s @ tyop_2Enum_2Enum @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
= ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
= ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(207,plain,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Einteger__word_2Ei2w_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a) ).
thf(272,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ B ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ c_2Einteger__word_2Ei2w_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(214,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(8,axiom,
( ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
thf(90,plain,
( ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__neg_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__of__num_2E1 @ ( s @ tyop_2Enum_2Enum @ c_2Enum_2E0_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(227,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ A ) @ ( s @ tyop_2Einteger_2Eint @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ c_2Einteger_2Eint__lt_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ A ) ) ) @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Einteger_2Eint__lt_2E2) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Einteger_2Eint__lt_2E2 @ ( s @ tyop_2Einteger_2Eint @ A ) @ ( s @ tyop_2Einteger_2Eint @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ c_2Einteger_2Eint__lt_2E0 ) @ ( s @ tyop_2Einteger_2Eint @ A ) ) ) @ ( s @ tyop_2Einteger_2Eint @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(287,plain,
$false,
inference(cvc4,[status(thm)],[142,84,169,193,266,145,282,136,163,101,234,170,269,52,184,110,125,196,157,116,89,133,248,60,220,160,275,92,65,166,148,204,259,113,98,208,130,241,199,177,127,55,139,119,207,272,214,90,227,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP015+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 15:37:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.92/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.04 % [INFO] Parsing done (166ms).
% 1.53/1.05 % [INFO] Running in sequential loop mode.
% 2.15/1.36 % [INFO] eprover registered as external prover.
% 2.15/1.37 % [INFO] cvc4 registered as external prover.
% 2.15/1.37 % [INFO] Scanning for conjecture ...
% 2.39/1.49 % [INFO] Found a conjecture and 49 axioms. Running axiom selection ...
% 2.67/1.58 % [INFO] Axiom selection finished. Selected 49 axioms (removed 0 axioms).
% 3.05/1.69 % [INFO] Problem is first-order (TPTP FOF).
% 3.05/1.70 % [INFO] Type checking passed.
% 3.05/1.70 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.36/2.66 % External prover 'cvc4' found a proof!
% 6.36/2.66 % [INFO] Killing All external provers ...
% 6.36/2.66 % Time passed: 2124ms (effective reasoning time: 1613ms)
% 6.36/2.66 % 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)>
% 6.36/2.67 % Axioms used in derivation (49): arityeq2_2Ec_2Eprim__rec_2E_3C_2E2, reserved_2Eho_2Enotfalse, thm_2Ebool_2EREFL__CLAUSE, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, reserved_2Equant_2E_3F, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a, thm_2Eprim__rec_2ENOT__LESS__0, reserved_2Eho_2Ebool__cases__ax, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, reserved_2Equant_2E_21, thm_2Ebool_2EIMP__ANTISYM__AX, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, thm_2Ebool_2EFALSITY, reserved_2Elogic_2E_3D, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Earithmetic_2EMOD_2E2, thm_2Einteger_2EINT__NEG__0, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29, thm_2Ebool_2ETRUTH, arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, reserved_2Elogic_2E_7E, thm_2Einteger_2EINT__LT__CALCULATE, reserved_2Eho_2Eboolext, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Einteger_2Eint__of__num_2E1, reserved_2Eho_2Eeq__ext, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq1_2Ec_2Einteger_2ENum_2E1, arityeq2_2Ec_2Einteger_2Eint__lt_2E2, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Einteger__word_2Ei2w__def, thm_2Ebool_2EEQ__SYM__EQ, reserved_2Elogic_2E_5C_2F, arityeq1_2Ec_2Einteger_2Eint__neg_2E1, thm_2Ewords_2EWORD__NEG__0, thm_2Einteger_2ENUM__OF__INT, thm_2Ewords_2En2w__11, thm_2Ebool_2Ebool__case__thm
% 6.36/2.67 % No. of inferences in proof: 102
% 6.36/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2124 ms resp. 1613 ms w/o parsing
% 6.68/2.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.68/2.74 % [INFO] Killing All external provers ...
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