TSTP Solution File: ITP004+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP004+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 07:46:30 EDT 2024
% Result : Theorem 5.51s 2.31s
% Output : Refutation 5.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 65
% Syntax : Number of formulae : 98 ( 30 unt; 34 typ; 0 def)
% Number of atoms : 154 ( 41 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1837 ( 13 ~; 8 |; 24 &;1734 @)
% ( 15 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 19 con; 0-2 aty)
% Number of variables : 155 ( 0 ^ 152 !; 3 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(p_type,type,
p: $i > $o ).
thf(s_type,type,
s: $i > $i > $i ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $i ).
thf(c_2Epred__set_2ESUBSET_2E2_type,type,
c_2Epred__set_2ESUBSET_2E2: $i > $i > $i ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: $i > $i > $i ).
thf(c_2Epred__set_2EREST_2E1_type,type,
c_2Epred__set_2EREST_2E1: $i > $i ).
thf(c_2Ebool_2E_3F_2E1_type,type,
c_2Ebool_2E_3F_2E1: $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_2Ebool_2E_7E_2E1_type,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
thf(c_2Epred__set_2EREST_2E0_type,type,
c_2Epred__set_2EREST_2E0: $i ).
thf(c_2Ebool_2ET_2E0_type,type,
c_2Ebool_2ET_2E0: $i ).
thf(c_2Ebool_2EF_2E0_type,type,
c_2Ebool_2EF_2E0: $i ).
thf(c_2Ebool_2EIN_2E2_type,type,
c_2Ebool_2EIN_2E2: $i > $i > $i ).
thf(c_2Ebool_2EIN_2E0_type,type,
c_2Ebool_2EIN_2E0: $i ).
thf(c_2Epred__set_2EDELETE_2E2_type,type,
c_2Epred__set_2EDELETE_2E2: $i > $i > $i ).
thf(combin_k_2E0_type,type,
combin_k_2E0: $i ).
thf(c_2Ebool_2E_21_2E1_type,type,
c_2Ebool_2E_21_2E1: $i > $i ).
thf(c_2Ebool_2E_21_2E0_type,type,
c_2Ebool_2E_21_2E0: $i ).
thf(c_2Ebool_2E_3F_2E0_type,type,
c_2Ebool_2E_3F_2E0: $i ).
thf(c_2Emin_2E_3D_3D_3E_2E0_type,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(c_2Epred__set_2ECHOICE_2E1_type,type,
c_2Epred__set_2ECHOICE_2E1: $i > $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(combin_s_2E0_type,type,
combin_s_2E0: $i ).
thf(c_2Ebool_2E_2F_5C_2E0_type,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
thf(c_2Epred__set_2ECHOICE_2E0_type,type,
c_2Epred__set_2ECHOICE_2E0: $i ).
thf(c_2Epred__set_2ESUBSET_2E0_type,type,
c_2Epred__set_2ESUBSET_2E0: $i ).
thf(combin_i_2E0_type,type,
combin_i_2E0: $i ).
thf(c_2Epred__set_2EDELETE_2E0_type,type,
c_2Epred__set_2EDELETE_2E0: $i ).
thf(c_2Emin_2E_3D_2E2_type,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(c_2Emin_2E_3D_2E0_type,type,
c_2Emin_2E_3D_2E0: $i ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) ).
thf(60,plain,
! [A: $i,B: $i,C: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(118,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)],[22]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
& ( ( s @ A @ C )
!= ( s @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).
thf(63,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
& ( ( s @ A @ C )
!= ( s @ A @ D ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
& ( ( s @ A @ C )
!= ( s @ A @ D ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EREST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EREST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(154,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)],[29]) ).
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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(40,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(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(131,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)],[24]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(83,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)],[14]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(138,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)],[25]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(101,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)],[18]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(110,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)],[20]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(93,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)],[16]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(57,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)],[9]) ).
thf(21,axiom,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(116,plain,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(74,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)],[13]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(160,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)],[31]) ).
thf(1,conjecture,
! [A: $i,B: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(33,plain,
~ ! [A: $i,B: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(53,plain,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(141,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)],[26]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(124,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)],[23]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(96,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)],[17]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( s @ A @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) @ c_2Epred__set_2ECHOICE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( s @ A @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) @ c_2Epred__set_2ECHOICE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(45,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)],[5]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(71,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)],[12]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(54,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)],[8]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
<=> ! [D: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
thf(86,plain,
! [A: $i,B: $i,C: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
=> ! [D: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
& ( ! [D: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(167,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(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/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(35,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(187,plain,
$false,
inference(cvc4,[status(thm)],[60,118,63,50,154,40,151,107,131,83,138,101,110,157,93,57,116,74,160,33,53,141,124,96,148,45,71,54,86,167,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP004+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n014.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 6 14:31:09 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.89/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (151ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.81/1.21 % [INFO] eprover registered as external prover.
% 1.81/1.22 % [INFO] cvc4 registered as external prover.
% 1.81/1.22 % [INFO] Scanning for conjecture ...
% 2.08/1.31 % [INFO] Found a conjecture and 30 axioms. Running axiom selection ...
% 2.08/1.36 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.31/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.31/1.44 % [INFO] Type checking passed.
% 2.31/1.44 % [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 ...
% 5.51/2.31 % External prover 'cvc4' found a proof!
% 5.51/2.31 % [INFO] Killing All external provers ...
% 5.51/2.31 % Time passed: 1782ms (effective reasoning time: 1323ms)
% 5.51/2.31 % 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)>
% 5.51/2.31 % Axioms used in derivation (30): arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a, thm_2Epred__set_2EREST__DEF, reserved_2Eho_2Enotfalse, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, reserved_2Equant_2E_3F, arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, reserved_2Eho_2Ebool__cases__ax, thm_2Epred__set_2EIN__DELETE, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, reserved_2Equant_2E_21, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, reserved_2Elogic_2E_3D, arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a, reserved_2Elogic_2E_7E, reserved_2Eho_2Eboolext, reserved_2Eho_2Eeq__ext, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, reserved_2Elogic_2E_5C_2F, thm_2Epred__set_2ESUBSET__DEF
% 5.51/2.31 % No. of inferences in proof: 64
% 5.51/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1782 ms resp. 1323 ms w/o parsing
% 5.51/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.51/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------