TSTP Solution File: ITP019+2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP019+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 07:47:02 EDT 2024
% Result : Theorem 3.35s 1.86s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 55
% Syntax : Number of formulae : 90 ( 32 unt; 22 typ; 0 def)
% Number of atoms : 193 ( 25 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 582 ( 14 ~; 0 |; 15 &; 443 @)
% ( 13 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 14 con; 0-2 aty)
% Number of variables : 80 ( 0 ^ 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(mem_type,type,
mem: $i > $i > $o ).
thf(ty_2Epair_2Eprod_type,type,
ty_2Epair_2Eprod: $i > $i > $i ).
thf(ty_2Erealax_2Ereal_type,type,
ty_2Erealax_2Ereal: $i ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(c_2Ecomplex_2Ecomplex__of__num_type,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
thf(c_2Enum_2E0_type,type,
c_2Enum_2E0: $i ).
thf(c_2Ecomplex_2Ecomplex__inv_type,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
thf(ne_type,type,
ne: $i > $o ).
thf(arr_type,type,
arr: $i > $i > $i ).
thf(ind_type,type,
ind: $i ).
thf(ty_2Enum_2Enum_type,type,
ty_2Enum_2Enum: $i ).
thf(p_type,type,
p: $i > $o ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $i ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $i ).
thf(bool_type,type,
bool: $i ).
thf(c_2Ebool_2E_21_type,type,
c_2Ebool_2E_21: $i > $i ).
thf(c_2Emin_2E_3D_type,type,
c_2Emin_2E_3D: $i > $i ).
thf(k_type,type,
k: $i > $i > $i ).
thf(c_2Emin_2E_3D_3D_3E_type,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(c_2Ebool_2E_7E_type,type,
c_2Ebool_2E_7E: $i ).
thf(i_type,type,
i: $i > $i ).
thf(c_2Ebool_2E_2F_5C_type,type,
c_2Ebool_2E_2F_5C: $i ).
thf(18,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
<=> ( p @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolext) ).
thf(69,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
ne @ ty_2Erealax_2Ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Erealax_2Ereal) ).
thf(84,plain,
ne @ ty_2Erealax_2Ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Enum_2E0) ).
thf(96,plain,
mem @ c_2Enum_2E0 @ ty_2Enum_2Enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(3,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( arr @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arr_ne) ).
thf(41,plain,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( arr @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
ne @ ty_2Enum_2Enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Enum_2Enum) ).
thf(44,plain,
ne @ ty_2Enum_2Enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
ne @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bool_ne) ).
thf(49,plain,
ne @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
thf(113,plain,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( A
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( A
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( A
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
!= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(48,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
ne @ ind,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ind_ne) ).
thf(43,plain,
ne @ ind,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,axiom,
! [A: $i] :
( ( ne @ A )
=> ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(82,plain,
! [A: $i] :
( ( ne @ A )
=> ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
<=> ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
thf(51,plain,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) )
=> ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
=> ( p @ A ) )
<=> ( p @ A ) )
& ( ( ( p @ A )
=> $true )
<=> $true )
& ( ( $false
=> ( p @ A ) )
<=> $true )
& ( ( ( p @ A )
=> ( p @ A ) )
<=> $true )
& ( ( ( p @ A )
=> $false )
<=> ~ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__CLAUSES) ).
thf(68,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(28,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Epair_2Eprod) ).
thf(100,plain,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( ne @ B )
=> ( ne @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
thf(46,plain,
~ ( p @ c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(78,plain,
mem @ c_2Ebool_2EF @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( k @ A @ B ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kbeta) ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( k @ A @ B ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ B ) )
<=> ( p @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EFORALL__SIMP) ).
thf(89,plain,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ B ) )
=> ( p @ B ) )
& ( ( p @ B )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(23,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
<=> ( ( p @ A )
=> ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p) ).
thf(85,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(102,plain,
mem @ c_2Ebool_2ET @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(65,plain,
! [A: $i,B: $i,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( mem @ B @ A )
=> ( ( ap @ ( i @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ibeta) ).
thf(97,plain,
! [A: $i,B: $i] :
( ( mem @ B @ A )
=> ( ( ap @ ( i @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(45,plain,
p @ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__inv) ).
thf(64,plain,
mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
<=> ( ( p @ A )
& ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
thf(103,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) )
& ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(108,plain,
! [A: $i,B: $i,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
mem @ c_2Ecomplex_2Ecomplex__of__num @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ecomplex_2Ecomplex__of__num) ).
thf(50,plain,
mem @ c_2Ecomplex_2Ecomplex__of__num @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
thf(67,plain,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
<=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(55,plain,
! [A: $i] :
( ( ne @ A )
=> ! [B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
<=> ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(114,plain,
! [A: $i] :
( ( mem @ A @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( ( ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
& ( ( A
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( ap @ c_2Ecomplex_2Ecomplex__inv @ A )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(31,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(107,plain,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(20,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
<=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).
thf(79,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ ( ap @ c_2Ebool_2E_7E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
! [A: $i] :
( ( ne @ A )
=> ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(94,plain,
! [A: $i] :
( ( ne @ A )
=> ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(122,plain,
$false,
inference(cvc4,[status(thm)],[69,84,96,41,44,49,113,35,48,43,82,51,68,100,46,78,61,89,85,102,65,97,45,64,103,108,50,67,55,114,107,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ITP019+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon May 6 14:39:39 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.64/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.81 % [INFO] Parsing done (126ms).
% 0.99/0.82 % [INFO] Running in sequential loop mode.
% 1.32/1.06 % [INFO] eprover registered as external prover.
% 1.32/1.06 % [INFO] cvc4 registered as external prover.
% 1.32/1.06 % [INFO] Scanning for conjecture ...
% 1.59/1.13 % [INFO] Found a conjecture and 32 axioms. Running axiom selection ...
% 1.63/1.18 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 1.91/1.23 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.23 % [INFO] Type checking passed.
% 1.91/1.24 % [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 ...
% 3.35/1.85 % External prover 'cvc4' found a proof!
% 3.35/1.85 % [INFO] Killing All external provers ...
% 3.35/1.85 % Time passed: 1459ms (effective reasoning time: 1027ms)
% 3.35/1.85 % 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)>
% 3.35/1.85 % Axioms used in derivation (32): conj_thm_2Ebool_2EIMP__CLAUSES, ibeta, conj_thm_2Ebool_2EFORALL__SIMP, kbeta, mem_c_2Enum_2E0, funcext, ne_ty_2Epair_2Eprod, ax_true_p, mem_c_2Emin_2E_3D, mem_c_2Ebool_2E_7E, mem_c_2Ebool_2EF, ax_all_p, conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0, ap_tp, ax_false_p, ne_ty_2Erealax_2Ereal, mem_c_2Ebool_2ET, ax_neg_p, mem_c_2Ebool_2E_2F_5C, ax_imp_p, ax_eq_p, mem_c_2Ebool_2E_21, mem_c_2Ecomplex_2Ecomplex__of__num, ax_and_p, ne_ty_2Enum_2Enum, arr_ne, conj_thm_2Ebool_2ETRUTH, mem_c_2Ecomplex_2Ecomplex__inv, boolext, ind_ne, mem_c_2Emin_2E_3D_3D_3E, bool_ne
% 3.35/1.85 % No. of inferences in proof: 68
% 3.35/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1459 ms resp. 1027 ms w/o parsing
% 3.54/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.54/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------