TSTP Solution File: ITP021_3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP021_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 : Mon May 20 22:22:01 EDT 2024
% Result : Theorem 9.95s 3.85s
% Output : Refutation 9.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 82
% Syntax : Number of formulae : 137 ( 30 unt; 29 typ; 0 def)
% Number of atoms : 593 ( 59 equ; 0 cnn)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 1742 ( 130 ~; 104 |; 118 &;1177 @)
% ( 44 <=>; 169 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 11 con; 0-4 aty)
% Number of variables : 237 ( 0 ^ 218 !; 3 ?; 237 :)
% ( 16 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Eextreal_2Eextreal_type,type,
tyop_2Eextreal_2Eextreal: $tType ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(app_2E2_type,type,
app_2E2:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ TA ) > TB > TA ) ).
thf(p_type,type,
p: tyop_2Emin_2Ebool > $o ).
thf(combin_i_2E0_type,type,
combin_i_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ TA @ TA ) ).
thf(combin_k_2E0_type,type,
combin_k_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Emin_2Efun @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) ) ).
thf(combin_s_2E0_type,type,
combin_s_2E0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) ) ).
thf(c_2Ebool_2E_21_2E0_type,type,
c_2Ebool_2E_21_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_21_2E1_type,type,
c_2Ebool_2E_21_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_2F_5C_2E0_type,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_2F_5C_2E2_type,type,
c_2Ebool_2E_2F_5C_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Emin_2E_3D_2E0_type,type,
c_2Emin_2E_3D_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) ).
thf(c_2Emin_2E_3D_2E2_type,type,
c_2Emin_2E_3D_2E2:
!>[TA: $tType] : ( TA > TA > tyop_2Emin_2Ebool ) ).
thf(c_2Emin_2E_3D_3D_3E_2E0_type,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).
thf(c_2Emin_2E_3D_3D_3E_2E2_type,type,
c_2Emin_2E_3D_3D_3E_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_3F_2E0_type,type,
c_2Ebool_2E_3F_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_3F_2E1_type,type,
c_2Ebool_2E_3F_2E1:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2ECOND_2E0_type,type,
c_2Ebool_2ECOND_2E0:
!>[TA: $tType] : ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) ) ) ).
thf(c_2Ebool_2ECOND_2E3_type,type,
c_2Ebool_2ECOND_2E3:
!>[TA: $tType] : ( tyop_2Emin_2Ebool > TA > TA > TA ) ).
thf(c_2Ebool_2EF_2E0_type,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
thf(c_2Ebool_2ET_2E0_type,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_5C_2F_2E0_type,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ).
thf(c_2Ebool_2E_5C_2F_2E2_type,type,
c_2Ebool_2E_5C_2F_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Eextreal_2Eextreal__le_2E0_type,type,
c_2Eextreal_2Eextreal__le_2E0: tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) ).
thf(c_2Eextreal_2Eextreal__le_2E2_type,type,
c_2Eextreal_2Eextreal__le_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Emin_2Ebool ).
thf(c_2Eextreal_2Eextreal__max_2E0_type,type,
c_2Eextreal_2Eextreal__max_2E0: tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ).
thf(c_2Eextreal_2Eextreal__max_2E2_type,type,
c_2Eextreal_2Eextreal__max_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(c_2Ebool_2E_7E_2E0_type,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ).
thf(c_2Ebool_2E_7E_2E1_type,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(47,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ~ ( p @ B )
| ( p @ A ) )
=> ( p @ c_2Ebool_2EF_2E0 ) )
<=> ( ( p @ B )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL3) ).
thf(385,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( ~ ( p @ B )
| ( p @ A ) )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( ( p @ B )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ) )
& ( ( ( p @ B )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) )
=> ( ~ ( ~ ( p @ B )
| ( p @ A ) )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(29,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( p @ c_2Ebool_2EF_2E0 )
=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(185,plain,
! [A: tyop_2Emin_2Ebool] :
( ( p @ c_2Ebool_2EF_2E0 )
=> ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(106,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2ET_2E0 @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2EF_2E0 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
thf(65,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2ET_2E0 @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND_2E3 @ TA @ c_2Ebool_2EF_2E0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__SYM) ).
thf(188,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(54,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B )
| ( p @ C ) )
<=> ( ( p @ A )
| ( p @ B )
| ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__ASSOC) ).
thf(471,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(35,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EF__IMP) ).
thf(264,plain,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(40,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( ( p @ B )
=> ( p @ A ) ) )
<=> ( ( ( p @ C )
| ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ~ ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).
thf(313,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ( ( p @ B )
=> ( p @ A ) )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ~ ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ~ ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ( ( p @ B )
=> ( p @ A ) )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ A @ B @ C )
= ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( c_2Ebool_2ECOND_2E0 @ tyop_2Eextreal_2Eextreal ) @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal) ).
thf(76,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ A @ B @ C )
= ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) ) @ ( c_2Ebool_2ECOND_2E0 @ tyop_2Eextreal_2Eextreal ) @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( p @ A )
& ( p @ B ) )
<=> ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ~ ( ( p @ A )
| ( p @ B ) )
<=> ( ~ ( p @ A )
& ~ ( p @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDE__MORGAN__THM) ).
thf(112,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( p @ A )
& ( p @ B ) )
=> ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ( ~ ( p @ A )
| ~ ( p @ B ) )
=> ~ ( ( p @ A )
& ( p @ B ) ) )
& ( ~ ( ( p @ A )
| ( p @ B ) )
=> ( ~ ( p @ A )
& ~ ( p @ B ) ) )
& ( ( ~ ( p @ A )
& ~ ( p @ B ) )
=> ~ ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(146,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ( p @ A )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(138,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ c_2Ebool_2E_7E_2E0 @ A ) )
=> ~ ( p @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
= ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).
thf(101,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
= ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_21_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E0 @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(88,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_21_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E0 @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
<=> ( ( p @ A )
& ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(372,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) )
& ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( c_2Ebool_2E_2F_5C_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(31,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ( p @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
thf(196,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B )
= ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ c_2Eextreal_2Eextreal__le_2E0 @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eextreal_2Eextreal__le_2E2) ).
thf(157,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B )
= ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Emin_2Ebool ) @ c_2Eextreal_2Eextreal__le_2E0 @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(53,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( ( p @ c_2Ebool_2ET_2E0 )
=> ( p @ A ) )
<=> ( p @ A ) )
& ( ( ( p @ A )
=> ( p @ c_2Ebool_2ET_2E0 ) )
<=> ( p @ c_2Ebool_2ET_2E0 ) )
& ( ( ( p @ c_2Ebool_2EF_2E0 )
=> ( p @ A ) )
<=> ( p @ c_2Ebool_2ET_2E0 ) )
& ( ( ( p @ A )
=> ( p @ A ) )
<=> ( p @ c_2Ebool_2ET_2E0 ) )
& ( ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
<=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(448,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( ( p @ c_2Ebool_2ET_2E0 )
=> ( p @ A ) )
=> ( p @ A ) )
& ( ( p @ A )
=> ( ( p @ c_2Ebool_2ET_2E0 )
=> ( p @ A ) ) )
& ( ( ( p @ A )
=> ( p @ c_2Ebool_2ET_2E0 ) )
=> ( p @ c_2Ebool_2ET_2E0 ) )
& ( ( p @ c_2Ebool_2ET_2E0 )
=> ( ( p @ A )
=> ( p @ c_2Ebool_2ET_2E0 ) ) )
& ( ( ( p @ c_2Ebool_2EF_2E0 )
=> ( p @ A ) )
=> ( p @ c_2Ebool_2ET_2E0 ) )
& ( ( p @ c_2Ebool_2ET_2E0 )
=> ( ( p @ c_2Ebool_2EF_2E0 )
=> ( p @ A ) ) )
& ( p @ c_2Ebool_2ET_2E0 )
& ( ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(34,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) )
<=> ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(261,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) )
=> ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) )
& ( ? [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) )
=> ( p @ ( c_2Ebool_2E_3F_2E1 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(49,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2ENOT__NOT) ).
thf(397,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(132,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( p @ ( c_2Emin_2E_3D_2E2 @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(48,axiom,
p @ c_2Ebool_2ET_2E0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
thf(396,plain,
p @ c_2Ebool_2ET_2E0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ TA,B: tyop_2Emin_2Efun @ TB @ TA] :
( ! [C: TB] :
( ( app_2E2 @ TB @ TA @ A @ C )
= ( app_2E2 @ TB @ TA @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).
thf(85,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ TA,B: tyop_2Emin_2Efun @ TB @ TA] :
( ! [C: TB] :
( ( app_2E2 @ TB @ TA @ A @ C )
= ( app_2E2 @ TB @ TA @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A = B )
<=> ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(366,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( A = B )
=> ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E0 @ TA ) @ A ) @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( p @ B )
| ( p @ A ) )
=> ( p @ c_2Ebool_2EF_2E0 ) )
<=> ( ( ( p @ B )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).
thf(160,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( ( p @ B )
| ( p @ A ) )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( ( ( p @ B )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ) )
& ( ( ( ( p @ B )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) )
=> ( ~ ( ( p @ B )
| ( p @ A ) )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
thf(70,plain,
! [A: tyop_2Emin_2Ebool] :
( ( A = c_2Ebool_2ET_2E0 )
| ( A = c_2Ebool_2EF_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [TA: $tType,A: TA] :
( ( app_2E2 @ TA @ TA @ ( combin_i_2E0 @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).
thf(73,plain,
! [TA: $tType,A: TA] :
( ( app_2E2 @ TA @ TA @ ( combin_i_2E0 @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV2) ).
thf(266,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(32,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = A )
<=> ( p @ A ) )
& ( ( A = c_2Ebool_2ET_2E0 )
<=> ( p @ A ) )
& ( ( c_2Ebool_2EF_2E0 = A )
<=> ~ ( p @ A ) )
& ( ( A = c_2Ebool_2EF_2E0 )
<=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(205,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = A )
=> ( p @ A ) )
& ( ( p @ A )
=> ( c_2Ebool_2ET_2E0 = A ) )
& ( ( A = c_2Ebool_2ET_2E0 )
=> ( p @ A ) )
& ( ( p @ A )
=> ( A = c_2Ebool_2ET_2E0 ) )
& ( ( c_2Ebool_2EF_2E0 = A )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( c_2Ebool_2EF_2E0 = A ) )
& ( ( A = c_2Ebool_2EF_2E0 )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( A = c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(50,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) )
<=> ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(398,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) )
=> ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) ) )
& ( ! [B: TA] : ( p @ ( app_2E2 @ TA @ tyop_2Emin_2Ebool @ A @ B ) )
=> ( p @ ( c_2Ebool_2E_21_2E1 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(18,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F) ).
thf(128,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) )
=> ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(41,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV__IMP) ).
thf(343,plain,
! [A: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ~ ( p @ A )
=> ( p @ c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(42,axiom,
p @ c_2Ebool_2ET_2E0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(345,plain,
p @ c_2Ebool_2ET_2E0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(12,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_3F_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E0 @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(91,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool] :
( ( c_2Ebool_2E_3F_2E1 @ TA @ A )
= ( app_2E2 @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E0 @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).
thf(155,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
= ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ c_2Eextreal_2Eextreal__max_2E0 @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eextreal_2Eextreal__max_2E2) ).
thf(175,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
= ( app_2E2 @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal @ ( app_2E2 @ tyop_2Eextreal_2Eextreal @ ( tyop_2Emin_2Efun @ tyop_2Eextreal_2Eextreal @ tyop_2Eextreal_2Eextreal ) @ c_2Eextreal_2Eextreal__max_2E0 @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(52,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
thf(446,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(22,axiom,
( ! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) )
& ( ~ ( p @ c_2Ebool_2ET_2E0 )
<=> ( p @ c_2Ebool_2EF_2E0 ) )
& ( ~ ( p @ c_2Ebool_2EF_2E0 )
<=> ( p @ c_2Ebool_2ET_2E0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(143,plain,
( ( ~ ( p @ c_2Ebool_2ET_2E0 )
=> ( p @ c_2Ebool_2EF_2E0 ) )
& ( ( p @ c_2Ebool_2EF_2E0 )
=> ~ ( p @ c_2Ebool_2ET_2E0 ) )
& ( ~ ( p @ c_2Ebool_2EF_2E0 )
=> ( p @ c_2Ebool_2ET_2E0 ) )
& ( ( p @ c_2Ebool_2ET_2E0 )
=> ~ ( p @ c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( ( p @ B )
| ( p @ A ) ) )
<=> ( ( ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).
thf(231,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
~ ( p @ c_2Ebool_2EF_2E0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
thf(104,plain,
~ ( p @ c_2Ebool_2EF_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(55,plain,
~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(51,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( B = A ) )
<=> ( ( ( p @ C )
| ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).
thf(401,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( B = A ) )
& ( ( B = A )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( B = A ) )
& ( ( B = A )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(46,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
<=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(378,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) )
& ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ ( c_2Ebool_2E_5C_2F_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(37,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
<=> ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(272,plain,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ ( c_2Ebool_2E_7E_2E1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(43,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
<=> ~ ( p @ A ) )
<=> ( ( ( p @ B )
| ( p @ A ) )
& ( ~ ( p @ A )
| ~ ( p @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__neg) ).
thf(346,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) )
=> ( ( ( p @ B )
| ( p @ A ) )
& ( ~ ( p @ A )
| ~ ( p @ B ) ) ) )
& ( ( ( ( p @ B )
| ( p @ A ) )
& ( ~ ( p @ A )
| ~ ( p @ B ) ) )
=> ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( app_2E2 @ TA @ TB @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) @ ( combin_k_2E0 @ TB @ TA ) @ A ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).
thf(82,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( app_2E2 @ TA @ TB @ ( app_2E2 @ TB @ ( tyop_2Emin_2Efun @ TA @ TB ) @ ( combin_k_2E0 @ TB @ TA ) @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ),B: tyop_2Emin_2Efun @ TC @ TB,C: TC] :
( ( app_2E2 @ TC @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) @ ( combin_s_2E0 @ TC @ TB @ TA ) @ A ) @ B ) @ C )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ C ) @ ( app_2E2 @ TC @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).
thf(79,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ),B: tyop_2Emin_2Efun @ TC @ TB,C: TC] :
( ( app_2E2 @ TC @ TA @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) @ ( app_2E2 @ ( tyop_2Emin_2Efun @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ TC @ TB ) @ ( tyop_2Emin_2Efun @ TC @ TA ) ) @ ( combin_s_2E0 @ TC @ TB @ TA ) @ A ) @ B ) @ C )
= ( app_2E2 @ TB @ TA @ ( app_2E2 @ TC @ ( tyop_2Emin_2Efun @ TB @ TA ) @ A @ C ) @ ( app_2E2 @ TC @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(94,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(39,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( ( p @ B )
& ( p @ A ) ) )
<=> ( ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__conj) ).
thf(283,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ A ) )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ A ) )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( p @ A )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXCLUDED__MIDDLE) ).
thf(131,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ C )
= ( app_2E2 @ TA @ TA @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) ) @ ( c_2Ebool_2ECOND_2E0 @ TA ) @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
thf(62,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA,C: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ C )
= ( app_2E2 @ TA @ TA @ ( app_2E2 @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ TA ) ) @ ( c_2Ebool_2ECOND_2E0 @ TA ) @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
<=> ( ( p @ A )
=> ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(178,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( c_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(38,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
<=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(277,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) )
& ( ( p @ ( app_2E2 @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool @ ( app_2E2 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(699,plain,
$false,
inference(cvc4,[status(thm)],[385,185,106,65,188,471,264,313,76,112,146,138,101,88,372,196,157,448,261,397,132,396,85,366,160,70,73,266,205,398,128,343,345,91,155,175,446,143,231,104,55,401,378,272,346,82,79,94,283,131,62,178,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP021_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n009.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 16:20:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.86/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.00 % [INFO] Parsing done (149ms).
% 1.18/1.01 % [INFO] Running in sequential loop mode.
% 1.88/1.20 % [INFO] eprover registered as external prover.
% 1.88/1.21 % [INFO] cvc4 registered as external prover.
% 1.88/1.21 % [INFO] Scanning for conjecture ...
% 1.98/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ...
% 2.17/1.33 % [INFO] Axiom selection finished. Selected 52 axioms (removed 1 axioms).
% 2.43/1.40 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.43/1.42 % [INFO] Type checking passed.
% 2.43/1.42 % [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 ...
% 2.91/1.58 % [INFO] [Domain constraints] Detected constraint on tyop_2Emin_2Ebool
% 2.91/1.58 % [INFO] [Domain constraints] dom(tyop_2Emin_2Ebool) ⊆ {c_2Ebool_2ET_2E0,c_2Ebool_2EF_2E0}
% 9.95/3.85 % External prover 'cvc4' found a proof!
% 9.95/3.85 % [INFO] Killing All external provers ...
% 9.95/3.85 % Time passed: 3332ms (effective reasoning time: 2836ms)
% 9.95/3.85 % 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)>
% 9.95/3.85 % Axioms used in derivation (52): thm_2Ebool_2EDISJ__SYM, thm_2Eextra_2Dho_2Eboolext, thm_2Esat_2Edc__conj, arityeq2_2Ec_2Eextreal_2Eextreal__max_2E2, thm_2Ebool_2EFALSITY, thm_2Eextra_2Dho_2Ek__thm, thm_2Ebool_2ECOND__CLAUSES, thm_2Ebool_2EF__IMP, logicdef_2E_3D_3D_3E, thm_2Esat_2ENOT__NOT, thm_2Eextra_2Dho_2Etruth, thm_2Eextreal_2Ele__total, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, thm_2Eextreal_2Eextreal__max__def, logicdef_2E_7E, quantdef_2E_3F, thm_2Eextra_2Dho_2Eeq__ext, thm_2Ebool_2ENOT__CLAUSES, thm_2Esat_2EAND__INV__IMP, thm_2Esat_2EOR__DUAL3, logicdef_2E_3D, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EIMP__ANTISYM__AX, thm_2Eextra_2Dho_2Ei__thm, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, thm_2Eextra_2Dho_2Ebool__cases__ax, thm_2Esat_2Edc__eq, thm_2Ebool_2EIMP__F, thm_2Esat_2Edc__imp, logicdef_2E_5C_2F, thm_2Eextreal_2Ele__trans, thm_2Eextra_2Dho_2Enotfalse, thm_2Esat_2Edc__neg, quantdef_2E_21, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal, arityeq2_2Ec_2Eextreal_2Eextreal__le_2E2, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, thm_2Ebool_2EEXCLUDED__MIDDLE, thm_2Ebool_2EDE__MORGAN__THM, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, thm_2Esat_2EAND__INV2, thm_2Ebool_2EDISJ__ASSOC, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Esat_2EOR__DUAL2, logicdef_2E_2F_5C, thm_2Eextra_2Dho_2Es__thm, thm_2Esat_2Edc__disj
% 9.95/3.85 % No. of inferences in proof: 108
% 9.95/3.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3332 ms resp. 2836 ms w/o parsing
% 9.95/3.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.95/3.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------