TSTP Solution File: LAT233-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT233-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:27:04 EDT 2023
% Result : Unsatisfiable 280.54s 54.23s
% Output : Refutation 280.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 184 ( 92 unt; 7 typ; 0 def)
% Number of atoms : 286 ( 285 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1053 ( 162 ~; 109 |; 0 &; 782 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 269 ( 0 ^; 269 !; 0 ?; 269 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(zero_type,type,
zero: $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(10,axiom,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
thf(34,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= one ),
inference(lifteq,[status(thm)],[34]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ B @ one )
= B )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,23]) ).
thf(86,plain,
! [A: $i] :
( ( meet @ A @ one )
= A ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(95,plain,
! [A: $i] :
( ( meet @ A @ one )
= A ),
inference(simp,[status(thm)],[86]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ B @ A )
= C )
| ( ( meet @ A @ B )
!= ( meet @ C @ one ) ) ),
inference(paramod_ordered,[status(thm)],[27,95]) ).
thf(249,plain,
! [A: $i] :
( ( meet @ one @ A )
= A ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( A ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
thf(36,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ A ) )
= zero ),
inference(lifteq,[status(thm)],[36]) ).
thf(14,axiom,
( ( meet @ b @ a )
= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
thf(43,plain,
( ( meet @ b @ a )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(44,plain,
( ( meet @ b @ a )
= a ),
inference(lifteq,[status(thm)],[43]) ).
thf(48,plain,
! [A: $i] :
( ( zero = a )
| ( ( meet @ A @ ( complement @ A ) )
!= ( meet @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[37,44]) ).
thf(50,plain,
! [A: $i] :
( ( zero = a )
| ( A != b )
| ( ( complement @ A )
!= a ) ),
inference(simp,[status(thm)],[48]) ).
thf(52,plain,
( ( zero = a )
| ( ( complement @ b )
!= a ) ),
inference(simp,[status(thm)],[50]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ zero )
= B )
| ( ( meet @ A @ ( complement @ A ) )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[37,25]) ).
thf(162,plain,
! [A: $i] :
( ( join @ A @ zero )
= A ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(178,plain,
! [A: $i] :
( ( join @ A @ zero )
= A ),
inference(simp,[status(thm)],[162]) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ A )
= C )
| ( ( join @ A @ B )
!= ( join @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[29,178]) ).
thf(334,plain,
! [A: $i] :
( ( join @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( A = one )
| ( ( join @ zero @ A )
!= ( join @ B @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[334,35]) ).
thf(1099,plain,
( ( complement @ zero )
= one ),
inference(pattern_uni,[status(thm)],[1098:[bind(A,$thf( complement @ zero )),bind(B,$thf( zero ))]]) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ A )
= B )
| ( ( meet @ one @ A )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[249,25]) ).
thf(528,plain,
! [A: $i] :
( ( join @ one @ A )
= one ),
inference(pattern_uni,[status(thm)],[527:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( A ))]]) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= one )
| ( ( join @ one @ A )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[528,29]) ).
thf(696,plain,
! [A: $i] :
( ( join @ A @ one )
= one ),
inference(pattern_uni,[status(thm)],[695:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( A ))]]) ).
thf(1,negated_conjecture,
( ( join @ ( complement @ b ) @ ( complement @ a ) )
!= ( complement @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
thf(15,plain,
( ( join @ ( complement @ b ) @ ( complement @ a ) )
!= ( complement @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(16,plain,
( ( join @ ( complement @ b ) @ ( complement @ a ) )
!= ( complement @ a ) ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(17,plain,
( ( join @ ( complement @ b ) @ ( complement @ a ) )
!= ( complement @ a ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(783,plain,
! [A: $i] :
( ( ( complement @ a )
!= one )
| ( ( join @ A @ one )
!= ( join @ ( complement @ b ) @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[696,17]) ).
thf(798,plain,
! [A: $i] :
( ( ( complement @ a )
!= one )
| ( A
!= ( complement @ b ) )
| ( ( complement @ a )
!= one ) ),
inference(simp,[status(thm)],[783]) ).
thf(816,plain,
( ( complement @ a )
!= one ),
inference(simp,[status(thm)],[798]) ).
thf(1169,plain,
( ( complement @ zero )
!= ( complement @ a ) ),
inference(paramod_ordered,[status(thm)],[1099,816]) ).
thf(1188,plain,
zero != a,
inference(simp,[status(thm)],[1169]) ).
thf(1200,plain,
( ( complement @ b )
!= a ),
inference(simplifyReflect,[status(thm)],[52,1188]) ).
thf(3,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(20,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(67,plain,
! [A: $i] :
( ( A
!= ( complement @ a ) )
| ( ( join @ A @ A )
!= ( join @ ( complement @ b ) @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,17]) ).
thf(71,plain,
( ( ( complement @ a )
!= ( complement @ b ) )
| ( ( complement @ a )
!= ( complement @ a ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(74,plain,
( ( complement @ a )
!= ( complement @ b ) ),
inference(simp,[status(thm)],[71]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ C @ B )
= zero )
| ( ( meet @ A @ ( complement @ A ) )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[37,27]) ).
thf(267,plain,
! [A: $i] :
( ( meet @ ( complement @ A ) @ A )
= zero ),
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(292,plain,
! [A: $i] :
( ( meet @ ( complement @ A ) @ A )
= zero ),
inference(simp,[status(thm)],[267]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(451,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ a @ C )
= ( meet @ A @ ( meet @ B @ C ) ) )
| ( ( meet @ b @ a )
!= ( meet @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44,31]) ).
thf(452,plain,
! [A: $i] :
( ( meet @ b @ ( meet @ a @ A ) )
= ( meet @ a @ A ) ),
inference(pattern_uni,[status(thm)],[451:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(489,plain,
! [A: $i] :
( ( meet @ b @ ( meet @ a @ A ) )
= ( meet @ a @ A ) ),
inference(simp,[status(thm)],[452]) ).
thf(2018,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ ( meet @ a @ A ) )
= B )
| ( ( meet @ b @ ( meet @ a @ A ) )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[489,25]) ).
thf(2019,plain,
! [A: $i] :
( ( join @ b @ ( meet @ a @ A ) )
= b ),
inference(pattern_uni,[status(thm)],[2018:[bind(A,$thf( E )),bind(B,$thf( b )),bind(C,$thf( meet @ a @ E ))]]) ).
thf(2115,plain,
! [A: $i] :
( ( join @ b @ ( meet @ a @ A ) )
= b ),
inference(simp,[status(thm)],[2019]) ).
thf(2326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ b @ ( meet @ A @ B ) )
= b )
| ( ( meet @ B @ A )
!= ( meet @ a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,2115]) ).
thf(2327,plain,
! [A: $i] :
( ( join @ b @ ( meet @ A @ a ) )
= b ),
inference(pattern_uni,[status(thm)],[2326:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( A ))]]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( a = A )
| ( ( meet @ b @ a )
!= ( meet @ A @ ( join @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,23]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( a = A )
| ( b != A )
| ( ( join @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[84]) ).
thf(97,plain,
! [A: $i] :
( ( a = b )
| ( ( join @ b @ A )
!= a ) ),
inference(simp,[status(thm)],[90]) ).
thf(77,plain,
a != b,
inference(simp,[status(thm)],[74]) ).
thf(1466,plain,
! [A: $i] :
( ( join @ b @ A )
!= a ),
inference(simplifyReflect,[status(thm)],[97,77]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( zero = B )
| ( ( meet @ A @ ( complement @ A ) )
!= ( meet @ B @ ( join @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,23]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( zero = B )
| ( A != B )
| ( ( complement @ A )
!= ( join @ B @ C ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( zero = A )
| ( ( join @ A @ B )
!= ( complement @ A ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(2534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= b )
| ( ( join @ b @ ( meet @ A @ a ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2327,29]) ).
thf(2535,plain,
! [A: $i] :
( ( join @ ( meet @ A @ a ) @ b )
= b ),
inference(pattern_uni,[status(thm)],[2534:[bind(A,$thf( D )),bind(B,$thf( b )),bind(C,$thf( meet @ D @ a ))]]) ).
thf(2686,plain,
! [A: $i] :
( ( join @ ( meet @ A @ a ) @ b )
= b ),
inference(simp,[status(thm)],[2535]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( ( join @ A @ a )
= A )
| ( ( meet @ b @ a )
!= ( meet @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44,25]) ).
thf(153,plain,
( ( join @ b @ a )
= b ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ B @ A )
= B )
| ( ( join @ zero @ A )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[334,23]) ).
thf(1127,plain,
! [A: $i] :
( ( meet @ zero @ A )
= zero ),
inference(pattern_uni,[status(thm)],[1126:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ ( meet @ B @ C ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ ( join @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H24) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ ( meet @ B @ C ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ ( join @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ ( meet @ B @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ ( join @ A @ B ) ) ) ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ B @ C ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(1471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ A @ B )
!= a )
| ( ( join @ B @ A )
!= ( join @ b @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,1466]) ).
thf(1472,plain,
! [A: $i] :
( ( join @ A @ b )
!= a ),
inference(pattern_uni,[status(thm)],[1471:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( A ))]]) ).
thf(1513,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ b ) ) ),
inference(paramod_ordered,[status(thm)],[25,1472]) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ( a != B )
| ( ( meet @ a @ A )
!= b ) ),
inference(simp,[status(thm)],[1513]) ).
thf(1540,plain,
! [A: $i] :
( ( meet @ a @ A )
!= b ),
inference(simp,[status(thm)],[1530]) ).
thf(1584,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= b )
| ( ( meet @ B @ A )
!= ( meet @ a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,1540]) ).
thf(1585,plain,
! [A: $i] :
( ( meet @ A @ a )
!= b ),
inference(pattern_uni,[status(thm)],[1584:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( A ))]]) ).
thf(1623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ A @ ( meet @ B @ C ) )
!= b )
| ( ( meet @ ( meet @ A @ B ) @ C )
!= ( meet @ D @ a ) ) ),
inference(paramod_ordered,[status(thm)],[31,1585]) ).
thf(1624,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( meet @ B @ a ) )
!= b ),
inference(pattern_uni,[status(thm)],[1623:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( a )),bind(D,$thf( meet @ E @ F ))]]) ).
thf(1641,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( meet @ B @ a ) )
!= b ),
inference(simp,[status(thm)],[1624]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= zero )
| ( ( join @ A @ B )
!= one )
| ( ( complement @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= zero )
| ( ( join @ A @ B )
!= one )
| ( ( complement @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ C @ B )
= zero )
| ( ( meet @ zero @ A )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1127,27]) ).
thf(1234,plain,
! [A: $i] :
( ( meet @ A @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[1233:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( join @ A @ ( join @ B @ C ) )
!= a )
| ( ( join @ ( join @ A @ B ) @ C )
!= ( join @ D @ b ) ) ),
inference(paramod_ordered,[status(thm)],[33,1472]) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( join @ B @ b ) )
!= a ),
inference(pattern_uni,[status(thm)],[1518:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( b )),bind(D,$thf( join @ E @ F ))]]) ).
thf(1534,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( join @ B @ b ) )
!= a ),
inference(simp,[status(thm)],[1519]) ).
thf(2284,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= b )
| ( ( join @ b @ ( meet @ a @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2115,29]) ).
thf(2285,plain,
! [A: $i] :
( ( join @ ( meet @ a @ A ) @ b )
= b ),
inference(pattern_uni,[status(thm)],[2284:[bind(A,$thf( E )),bind(B,$thf( b )),bind(C,$thf( meet @ a @ E ))]]) ).
thf(2430,plain,
! [A: $i] :
( ( join @ ( meet @ a @ A ) @ b )
= b ),
inference(simp,[status(thm)],[2285]) ).
thf(2750,plain,
! [A: $i] :
( ( ( complement @ a )
!= b )
| ( ( join @ ( meet @ a @ A ) @ b )
!= ( join @ ( complement @ b ) @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[2430,17]) ).
thf(2800,plain,
! [A: $i] :
( ( ( complement @ a )
!= b )
| ( ( meet @ a @ A )
!= ( complement @ b ) )
| ( ( complement @ a )
!= b ) ),
inference(simp,[status(thm)],[2750]) ).
thf(2858,plain,
! [A: $i] :
( ( ( complement @ a )
!= b )
| ( ( meet @ a @ A )
!= ( complement @ b ) ) ),
inference(simp,[status(thm)],[2800]) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= one )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,29]) ).
thf(314,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= one ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(345,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= one ),
inference(simp,[status(thm)],[314]) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( join @ A @ zero )
!= ( join @ B @ ( join @ C @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,1534]) ).
thf(1882,plain,
! [B: $i,A: $i] :
( ( a != A )
| ( ( join @ B @ b )
!= zero ) ),
inference(simp,[status(thm)],[1871]) ).
thf(1901,plain,
! [A: $i] :
( ( join @ A @ b )
!= zero ),
inference(simp,[status(thm)],[1882]) ).
thf(1931,plain,
! [B: $i,A: $i] :
( ( zero != one )
| ( ( join @ ( complement @ A ) @ A )
!= ( join @ B @ b ) ) ),
inference(paramod_ordered,[status(thm)],[345,1901]) ).
thf(1932,plain,
zero != one,
inference(pattern_uni,[status(thm)],[1931:[bind(A,$thf( b )),bind(B,$thf( complement @ b ))]]) ).
thf(125,plain,
! [A: $i] :
( ( A = a )
| ( ( meet @ A @ one )
!= ( meet @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[95,44]) ).
thf(135,plain,
! [A: $i] :
( ( A = a )
| ( A != b )
| ( one != a ) ),
inference(simp,[status(thm)],[125]) ).
thf(142,plain,
( ( a = b )
| ( one != a ) ),
inference(simp,[status(thm)],[135]) ).
thf(148,plain,
one != a,
inference(simplifyReflect,[status(thm)],[142,77]) ).
thf(197,plain,
( ( ( complement @ a )
!= b )
| ( ( join @ ( complement @ b ) @ ( complement @ a ) )
!= ( join @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[153,17]) ).
thf(204,plain,
( ( ( complement @ a )
!= b )
| ( ( complement @ b )
!= b )
| ( ( complement @ a )
!= a ) ),
inference(simp,[status(thm)],[197]) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ A @ ( join @ B @ C ) )
!= ( complement @ a ) )
| ( ( join @ ( join @ A @ B ) @ C )
!= ( join @ ( complement @ b ) @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,17]) ).
thf(661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ A @ ( join @ B @ C ) )
!= ( complement @ a ) )
| ( ( join @ A @ B )
!= ( complement @ b ) )
| ( C
!= ( complement @ a ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(675,plain,
! [B: $i,A: $i] :
( ( ( join @ A @ ( join @ B @ ( complement @ a ) ) )
!= ( complement @ a ) )
| ( ( join @ A @ B )
!= ( complement @ b ) ) ),
inference(simp,[status(thm)],[661]) ).
thf(2172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ ( join @ C @ ( complement @ a ) ) )
!= ( complement @ a ) )
| ( A
!= ( complement @ b ) )
| ( ( join @ A @ A )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,675]) ).
thf(2173,plain,
! [A: $i] :
( ( ( join @ A @ ( join @ A @ ( complement @ a ) ) )
!= ( complement @ a ) )
| ( A
!= ( complement @ b ) ) ),
inference(pattern_uni,[status(thm)],[2172:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(2261,plain,
( ( join @ ( complement @ b ) @ ( join @ ( complement @ b ) @ ( complement @ a ) ) )
!= ( complement @ a ) ),
inference(simp,[status(thm)],[2173]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(18,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( meet @ A @ A )
!= ( meet @ B @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,37]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( A != B )
| ( A
!= ( complement @ B ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(63,plain,
! [A: $i] :
( ( A = zero )
| ( ( complement @ A )
!= A ) ),
inference(simp,[status(thm)],[59]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= zero )
| ( ( join @ A @ B )
!= one )
| ( ( complement @ A )
= B ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= zero )
| ( ( join @ A @ B )
!= one )
| ( ( complement @ A )
= B ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != zero )
| ( ( join @ C @ D )
!= one )
| ( ( complement @ C )
= D )
| ( ( meet @ A @ ( join @ A @ B ) )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,40]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A != zero )
| ( ( join @ A @ ( join @ A @ B ) )
!= one )
| ( ( join @ A @ B )
= ( complement @ A ) ) ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( join @ E @ F ))]]) ).
thf(114,plain,
! [A: $i] :
( ( ( join @ zero @ ( join @ zero @ A ) )
!= one )
| ( ( join @ zero @ A )
= ( complement @ zero ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(1790,plain,
! [A: $i] :
( ( ( join @ zero @ A )
!= one )
| ( A = one ) ),
inference(rewrite,[status(thm)],[114,1099,334]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( meet @ A @ ( complement @ A ) )
!= ( meet @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[37,95]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( A != B )
| ( ( complement @ A )
!= one ) ),
inference(simp,[status(thm)],[124]) ).
thf(143,plain,
! [A: $i] :
( ( zero = A )
| ( ( complement @ A )
!= one ) ),
inference(simp,[status(thm)],[136]) ).
thf(1917,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ A )
!= zero )
| ( ( join @ A @ B )
!= ( join @ C @ b ) ) ),
inference(paramod_ordered,[status(thm)],[29,1901]) ).
thf(1918,plain,
! [A: $i] :
( ( join @ b @ A )
!= zero ),
inference(pattern_uni,[status(thm)],[1917:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( A ))]]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( meet @ one @ A )
!= ( meet @ B @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,37]) ).
thf(524,plain,
( ( complement @ one )
= zero ),
inference(pattern_uni,[status(thm)],[523:[bind(A,$thf( complement @ one )),bind(B,$thf( one ))]]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( A = one )
| ( ( join @ A @ A )
!= ( join @ B @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,35]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( A = one )
| ( A != B )
| ( A
!= ( complement @ B ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(75,plain,
! [A: $i] :
( ( A = one )
| ( ( complement @ A )
!= A ) ),
inference(simp,[status(thm)],[72]) ).
thf(1123,plain,
! [A: $i] :
( ( A
!= ( complement @ a ) )
| ( ( join @ zero @ A )
!= ( join @ ( complement @ b ) @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[334,17]) ).
thf(1143,plain,
( ( ( complement @ b )
!= zero )
| ( ( complement @ a )
!= ( complement @ a ) ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1161,plain,
( ( complement @ b )
!= zero ),
inference(simp,[status(thm)],[1143]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= b )
| ( ( join @ b @ a )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[153,29]) ).
thf(300,plain,
( ( join @ a @ b )
= b ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(408,plain,
! [A: $i] :
( ( b = A )
| ( ( join @ a @ b )
!= ( join @ A @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[300,178]) ).
thf(410,plain,
! [A: $i] :
( ( b = A )
| ( a != A )
| ( zero != b ) ),
inference(simp,[status(thm)],[408]) ).
thf(422,plain,
( ( a = b )
| ( zero != b ) ),
inference(simp,[status(thm)],[410]) ).
thf(432,plain,
zero != b,
inference(simplifyReflect,[status(thm)],[422,77]) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ C @ D )
!= zero )
| ( A != one )
| ( ( complement @ C )
= D )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25,40]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( ( meet @ A @ ( meet @ A @ B ) )
!= zero )
| ( A != one )
| ( ( meet @ A @ B )
= ( complement @ A ) ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( meet @ E @ F ))]]) ).
thf(179,plain,
! [A: $i] :
( ( ( meet @ one @ ( meet @ one @ A ) )
!= zero )
| ( ( meet @ one @ A )
= ( complement @ one ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(3100,plain,
! [A: $i] :
( ( ( meet @ one @ A )
!= zero )
| ( A = zero ) ),
inference(rewrite,[status(thm)],[179,249,524]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( ( meet @ B @ A )
= a )
| ( ( meet @ b @ a )
!= ( meet @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[44,27]) ).
thf(277,plain,
( ( meet @ a @ b )
= a ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(1202,plain,
( ( complement @ one )
!= ( complement @ b ) ),
inference(paramod_ordered,[status(thm)],[524,1161]) ).
thf(1204,plain,
one != b,
inference(simp,[status(thm)],[1202]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( A = zero )
| ( ( meet @ A @ ( join @ A @ B ) )
!= ( meet @ C @ ( complement @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,37]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( A = zero )
| ( A != C )
| ( ( join @ A @ B )
!= ( complement @ C ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( B = zero )
| ( ( join @ B @ A )
!= ( complement @ B ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(164118,plain,
$false,
inference(e,[status(thm)],[249,1200,74,292,2327,1466,98,35,696,2686,153,1127,42,24,37,25,20,1641,29,334,21,33,28,38,1234,2115,1534,1540,2858,77,489,1099,1932,41,148,17,32,34,22,44,204,27,345,816,2261,675,1472,63,18,95,1790,1188,1901,31,1585,143,43,1918,524,40,26,23,75,1161,300,432,36,30,3100,19,2430,528,15,178,277,1204,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT233-1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.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 13:37:16 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.97/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.02 % [INFO] Parsing done (126ms).
% 1.17/1.03 % [INFO] Running in sequential loop mode.
% 1.64/1.22 % [INFO] eprover registered as external prover.
% 1.64/1.22 % [INFO] cvc4 registered as external prover.
% 1.64/1.22 % [INFO] Scanning for conjecture ...
% 1.87/1.27 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.87/1.28 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.87/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.30 % [INFO] Type checking passed.
% 1.87/1.30 % [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 ...
% 280.54/54.23 % External prover 'e' found a proof!
% 280.54/54.23 % [INFO] Killing All external provers ...
% 280.54/54.23 % Time passed: 53710ms (effective reasoning time: 53197ms)
% 280.54/54.23 % 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)>
% 280.54/54.23 % Axioms used in derivation (13): commutativity_of_join, absorption1, meet_join_complement, complement_meet, commutativity_of_meet, associativity_of_join, prove_distributivity_hypothesis, associativity_of_meet, complement_join, idempotence_of_join, absorption2, idempotence_of_meet, equation_H24
% 280.54/54.23 % No. of inferences in proof: 177
% 280.54/54.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 53710 ms resp. 53197 ms w/o parsing
% 280.54/54.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 280.54/54.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------