TSTP Solution File: SEU351+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU351+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 : Fri May 19 11:58:26 EDT 2023
% Result : Theorem 69.93s 13.34s
% Output : Refutation 70.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 75
% Syntax : Number of formulae : 159 ( 37 unt; 42 typ; 0 def)
% Number of atoms : 422 ( 45 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1101 ( 93 ~; 42 |; 133 &; 711 @)
% ( 9 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 15 con; 0-3 aty)
% Number of variables : 170 ( 0 ^; 148 !; 22 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(lattice_type,type,
lattice: $i > $o ).
thf(complete_latt_str_type,type,
complete_latt_str: $i > $o ).
thf(latt_str_type,type,
latt_str: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(meet_of_latt_set_type,type,
meet_of_latt_set: $i > $i > $i ).
thf(latt_set_smaller_type,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(below_refl_type,type,
below_refl: $i > $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(join_semilatt_str_type,type,
join_semilatt_str: $i > $o ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(meet_semilatt_str_type,type,
meet_semilatt_str: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(meet_commutative_type,type,
meet_commutative: $i > $o ).
thf(meet_absorbing_type,type,
meet_absorbing: $i > $o ).
thf(join_absorbing_type,type,
join_absorbing: $i > $o ).
thf(below_type,type,
below: $i > $i > $i > $o ).
thf(join_of_latt_set_type,type,
join_of_latt_set: $i > $i > $i ).
thf(latt_element_smaller_type,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(join_commutative_type,type,
join_commutative: $i > $o ).
thf(join_associative_type,type,
join_associative: $i > $o ).
thf(meet_associative_type,type,
meet_associative: $i > $o ).
thf(a_2_2_lattice3_type,type,
a_2_2_lattice3: $i > $i > $i ).
thf(a_2_3_lattice3_type,type,
a_2_3_lattice3: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(sk10_type,type,
sk10: $i > $i > $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk16_type,type,
sk16: $i > $i ).
thf(sk17_type,type,
sk17: $i ).
thf(sk21_type,type,
sk21: $i ).
thf(15,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(87,plain,
? [A: $i] : ( join_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,plain,
join_semilatt_str @ sk13,
inference(cnf,[status(esa)],[87]) ).
thf(32,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( meet_of_latt_set @ A @ B )
= ( join_of_latt_set @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d22_lattice3) ).
thf(170,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( meet_of_latt_set @ A @ B )
= ( join_of_latt_set @ A @ ( a_2_2_lattice3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(14,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(84,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(60,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( B
= ( meet_of_latt_set @ A @ C ) )
<=> ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( B
= ( meet_of_latt_set @ A @ C ) )
<=> ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( B
= ( meet_of_latt_set @ A @ C ) )
=> ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) ) )
& ( ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) )
=> ( B
= ( meet_of_latt_set @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ! [C: $i] :
( ( B
= ( meet_of_latt_set @ A @ C ) )
=> ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) ) )
& ! [C: $i] :
( ( ( latt_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_set_smaller @ A @ D @ C )
=> ( below_refl @ A @ D @ B ) ) ) )
=> ( B
= ( meet_of_latt_set @ A @ C ) ) ) ) ) ),
inference(miniscope,[status(thm)],[35]) ).
thf(38,plain,
complete_latt_str @ sk1,
inference(cnf,[status(esa)],[36]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(68,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[68]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[69]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(23,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(128,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattices) ).
thf(123,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( lattice @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(63,plain,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(82,plain,
? [A: $i] : ( meet_semilatt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(126,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( latt_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice3) ).
thf(142,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( latt_set_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ B @ D ) ) )
=> ( latt_set_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
? [A: $i] : ( latt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(173,plain,
? [A: $i] : ( latt_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(174,plain,
latt_str @ sk21,
inference(cnf,[status(esa)],[173]) ).
thf(37,plain,
element @ sk2 @ ( the_carrier @ sk1 ),
inference(cnf,[status(esa)],[36]) ).
thf(46,plain,
lattice @ sk1,
inference(cnf,[status(esa)],[36]) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(57,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(61,plain,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( below_refl @ A @ B @ C )
<=> ( below @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
thf(89,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( ( ( below_refl @ A @ B @ C )
=> ( below @ A @ B @ C ) )
& ( ( below @ A @ B @ C )
=> ( below_refl @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( C
= ( join_of_latt_set @ A @ B ) )
<=> ( ( latt_element_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_element_smaller @ A @ D @ B )
=> ( below @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattice3) ).
thf(92,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A )
& ( complete_latt_str @ A )
& ( latt_str @ A ) )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( C
= ( join_of_latt_set @ A @ B ) )
=> ( ( latt_element_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_element_smaller @ A @ D @ B )
=> ( below @ A @ C @ D ) ) ) ) )
& ( ( ( latt_element_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( latt_element_smaller @ A @ D @ B )
=> ( below @ A @ C @ D ) ) ) )
=> ( C
= ( join_of_latt_set @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(62,plain,
! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ),
inference(cnf,[status(esa)],[61]) ).
thf(196,plain,
! [A: $i] :
( ( one_sorted_str @ A )
| ( ( join_semilatt_str @ sk13 )
!= ( join_semilatt_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[88,62]) ).
thf(197,plain,
one_sorted_str @ sk13,
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( sk13 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(65,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(55,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,plain,
empty @ sk7,
inference(cnf,[status(esa)],[55]) ).
thf(85,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[84]) ).
thf(86,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(492,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk7 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[56,86]) ).
thf(493,plain,
sk7 = empty_set,
inference(pattern_uni,[status(thm)],[492:[bind(A,$thf( sk7 ))]]) ).
thf(129,plain,
~ ( empty_carrier @ sk17 ),
inference(cnf,[status(esa)],[128]) ).
thf(41,plain,
( sk3
| ( latt_set_smaller @ sk1 @ sk2 @ sk6 ) ),
inference(cnf,[status(esa)],[36]) ).
thf(45,plain,
! [A: $i] :
( sk3
| ~ ( element @ A @ ( the_carrier @ sk1 ) )
| ~ ( latt_set_smaller @ sk1 @ A @ sk6 )
| ( below_refl @ sk1 @ A @ sk2 ) ),
inference(cnf,[status(esa)],[36]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( complete_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( in @ A @ ( a_2_3_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_lattice3) ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( lattice @ B )
& ( complete_latt_str @ B )
& ( latt_str @ B ) )
=> ( ( ( in @ A @ ( a_2_3_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) )
=> ( in @ A @ ( a_2_3_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,plain,
! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ),
inference(cnf,[status(esa)],[63]) ).
thf(44,plain,
( ~ ( latt_set_smaller @ sk1 @ sk2 @ sk4 )
| ( element @ sk5 @ ( the_carrier @ sk1 ) )
| ~ sk3 ),
inference(cnf,[status(esa)],[36]) ).
thf(58,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
~ ( empty @ sk8 ),
inference(cnf,[status(esa)],[58]) ).
thf(48,plain,
( ( sk2
= ( meet_of_latt_set @ sk1 @ sk4 ) )
| ~ sk3 ),
inference(cnf,[status(esa)],[36]) ).
thf(49,plain,
( ( ( meet_of_latt_set @ sk1 @ sk4 )
= sk2 )
| ~ sk3 ),
inference(lifteq,[status(thm)],[48]) ).
thf(12,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(80,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(81,plain,
one_sorted_str @ sk11,
inference(cnf,[status(esa)],[80]) ).
thf(39,plain,
( ~ ( latt_set_smaller @ sk1 @ sk2 @ sk4 )
| ( latt_set_smaller @ sk1 @ sk5 @ sk4 )
| ~ sk3 ),
inference(cnf,[status(esa)],[36]) ).
thf(25,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(140,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( meet_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_lattice3) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( meet_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(18,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(108,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(40,plain,
~ ( empty_carrier @ sk1 ),
inference(cnf,[status(esa)],[36]) ).
thf(520,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty_carrier @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[86,40]) ).
thf(521,plain,
( ~ ( empty @ sk1 )
| ~ ( empty_carrier @ empty_set ) ),
inference(pattern_uni,[status(thm)],[520:[bind(A,$thf( sk1 ))]]) ).
thf(130,plain,
one_sorted_str @ sk17,
inference(cnf,[status(esa)],[128]) ).
thf(504,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( complete_latt_str @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[86,38]) ).
thf(505,plain,
( ~ ( empty @ sk1 )
| ( complete_latt_str @ empty_set ) ),
inference(pattern_uni,[status(thm)],[504:[bind(A,$thf( sk1 ))]]) ).
thf(42,plain,
( sk3
| ( sk2
!= ( meet_of_latt_set @ sk1 @ sk6 ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(50,plain,
( ( ( meet_of_latt_set @ sk1 @ sk6 )
!= sk2 )
| sk3 ),
inference(lifteq,[status(thm)],[42]) ).
thf(127,plain,
! [A: $i] : ( element @ ( sk16 @ A ) @ A ),
inference(cnf,[status(esa)],[126]) ).
thf(34,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
thf(175,plain,
! [A: $i] :
( ( latt_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( lattice @ A ) )
=> ( ~ ( empty_carrier @ A )
& ( join_commutative @ A )
& ( join_associative @ A )
& ( meet_commutative @ A )
& ( meet_associative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(189,plain,
( ( empty @ sk8 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[60,59]) ).
thf(190,plain,
sk8 != empty_set,
inference(simp,[status(thm)],[189]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( in @ ( sk9 @ B @ A ) @ A )
| ( in @ ( sk10 @ B @ A ) @ B )
| ( B != empty_set )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[77,190]) ).
thf(259,plain,
! [A: $i] :
( ( in @ ( sk9 @ A @ sk8 ) @ sk8 )
| ( in @ ( sk10 @ A @ sk8 ) @ A )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( sk8 ))]]) ).
thf(386,plain,
( ( in @ ( sk9 @ empty_set @ sk8 ) @ sk8 )
| ( in @ ( sk10 @ empty_set @ sk8 ) @ empty_set ) ),
inference(simp,[status(thm)],[259]) ).
thf(496,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( lattice @ empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[86,46]) ).
thf(497,plain,
( ~ ( empty @ sk1 )
| ( lattice @ empty_set ) ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( sk1 ))]]) ).
thf(43,plain,
latt_str @ sk1,
inference(cnf,[status(esa)],[36]) ).
thf(83,plain,
meet_semilatt_str @ sk12,
inference(cnf,[status(esa)],[82]) ).
thf(481,plain,
! [A: $i] :
( ( one_sorted_str @ A )
| ( ( meet_semilatt_str @ sk12 )
!= ( meet_semilatt_str @ A ) ) ),
inference(paramod_ordered,[status(thm)],[83,64]) ).
thf(482,plain,
one_sorted_str @ sk12,
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( sk12 ))]]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( below_refl @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
thf(158,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_commutative @ A )
& ( meet_absorbing @ A )
& ( join_absorbing @ A )
& ( latt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( below_refl @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(20,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( latt_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
thf(114,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( latt_element_smaller @ A @ B @ C )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) ) )
& ( ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ C )
=> ( below @ A @ D @ B ) ) )
=> ( latt_element_smaller @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(51,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( latt_str @ B ) )
=> ( ( in @ A @ ( a_2_2_lattice3 @ B @ C ) )
<=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
thf(131,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ B )
& ( latt_str @ B ) )
=> ( ( ( in @ A @ ( a_2_2_lattice3 @ B @ C ) )
=> ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) ) )
& ( ? [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
& ( A = D )
& ( latt_set_smaller @ B @ D @ C ) )
=> ( in @ A @ ( a_2_2_lattice3 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(47,plain,
( ~ ( latt_set_smaller @ sk1 @ sk2 @ sk4 )
| ~ ( below_refl @ sk1 @ sk5 @ sk2 )
| ~ sk3 ),
inference(cnf,[status(esa)],[36]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( join_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ~ ( empty_carrier @ A )
& ( latt_str @ A ) )
=> ( element @ ( join_of_latt_set @ A @ B ) @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(49205,plain,
$false,
inference(cvc4,[status(thm)],[88,170,84,60,38,77,128,123,63,82,126,142,153,174,37,46,57,78,61,89,92,197,65,493,173,129,41,45,161,64,44,59,49,86,81,39,140,155,108,521,130,505,80,35,50,127,175,386,497,43,87,482,40,158,55,114,151,51,190,68,62,131,47,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU351+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 13:14:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.80/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/0.96 % [INFO] Parsing done (132ms).
% 1.33/0.97 % [INFO] Running in sequential loop mode.
% 1.71/1.17 % [INFO] eprover registered as external prover.
% 1.71/1.17 % [INFO] cvc4 registered as external prover.
% 1.71/1.17 % [INFO] Scanning for conjecture ...
% 1.85/1.24 % [INFO] Found a conjecture and 36 axioms. Running axiom selection ...
% 2.01/1.29 % [INFO] Axiom selection finished. Selected 32 axioms (removed 4 axioms).
% 2.01/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.01/1.35 % [INFO] Type checking passed.
% 2.01/1.35 % [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 ...
% 69.93/13.33 % External prover 'cvc4' found a proof!
% 69.93/13.33 % [INFO] Killing All external provers ...
% 69.93/13.33 % Time passed: 12824ms (effective reasoning time: 12359ms)
% 69.93/13.33 % 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)>
% 69.93/13.33 % Axioms used in derivation (32): d16_lattice3, existence_l3_lattices, d22_lattice3, d21_lattice3, cc1_lattices, redefinition_r3_lattices, fraenkel_a_2_2_lattice3, fc1_struct_0, t2_subset, existence_l1_struct_0, rc2_xboole_0, fc1_xboole_0, existence_l1_lattices, t1_subset, reflexivity_r3_lattices, dt_l1_lattices, t6_boole, existence_l2_lattices, fraenkel_a_2_3_lattice3, dt_l3_lattices, dt_l2_lattices, t2_tarski, t7_boole, d17_lattice3, rc3_struct_0, existence_m1_subset_1, dt_k16_lattice3, dt_k15_lattice3, t8_boole, rc1_xboole_0, antisymmetry_r2_hidden, cc2_lattices
% 69.93/13.34 % No. of inferences in proof: 117
% 69.93/13.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12824 ms resp. 12359 ms w/o parsing
% 70.05/13.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 70.05/13.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------