TSTP Solution File: LAT256-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT256-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:27:07 EDT 2023
% Result : Unsatisfiable 196.24s 38.14s
% Output : Refutation 196.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of formulae : 266 ( 130 unt; 7 typ; 0 def)
% Number of atoms : 426 ( 425 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1644 ( 241 ~; 167 |; 0 &;1236 @)
% ( 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 : 439 ( 0 ^; 439 !; 0 ?; 439 :)
% 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(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(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(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(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(1302,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(1303,plain,
! [A: $i] :
( ( meet @ zero @ A )
= zero ),
inference(pattern_uni,[status(thm)],[1302:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
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(1422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ C @ B )
= zero )
| ( ( meet @ zero @ A )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1303,27]) ).
thf(1423,plain,
! [A: $i] :
( ( meet @ A @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[1422:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
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(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(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(481,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ a @ C )
= ( meet @ A @ ( meet @ B @ C ) ) )
| ( ( meet @ a @ b )
!= ( meet @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[277,31]) ).
thf(482,plain,
! [A: $i] :
( ( meet @ a @ ( meet @ b @ A ) )
= ( meet @ a @ A ) ),
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(503,plain,
! [A: $i] :
( ( meet @ a @ ( meet @ b @ A ) )
= ( meet @ a @ A ) ),
inference(simp,[status(thm)],[482]) ).
thf(3570,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ a @ A )
= ( meet @ a @ C ) )
| ( ( meet @ A @ ( join @ A @ B ) )
!= ( meet @ b @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,503]) ).
thf(3571,plain,
! [A: $i] :
( ( meet @ a @ ( join @ b @ A ) )
= ( meet @ a @ b ) ),
inference(pattern_uni,[status(thm)],[3570:[bind(A,$thf( b )),bind(B,$thf( E )),bind(C,$thf( join @ b @ E ))]]) ).
thf(3678,plain,
! [A: $i] :
( ( meet @ a @ ( join @ b @ A ) )
= ( meet @ a @ b ) ),
inference(simp,[status(thm)],[3571]) ).
thf(4236,plain,
! [A: $i] :
( ( meet @ a @ ( join @ b @ A ) )
= a ),
inference(rewrite,[status(thm)],[3678,277]) ).
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(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(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(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(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(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(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(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(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(77,plain,
a != b,
inference(simp,[status(thm)],[74]) ).
thf(1686,plain,
! [A: $i] :
( ( join @ b @ A )
!= a ),
inference(simplifyReflect,[status(thm)],[97,77]) ).
thf(1691,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ A @ B )
!= a )
| ( ( join @ B @ A )
!= ( join @ b @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,1686]) ).
thf(1692,plain,
! [A: $i] :
( ( join @ A @ b )
!= a ),
inference(pattern_uni,[status(thm)],[1691:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( A ))]]) ).
thf(1733,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)],[33,1692]) ).
thf(1734,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( join @ B @ b ) )
!= a ),
inference(pattern_uni,[status(thm)],[1733:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( b )),bind(D,$thf( join @ E @ F ))]]) ).
thf(1748,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( join @ B @ b ) )
!= a ),
inference(simp,[status(thm)],[1734]) ).
thf(2086,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( join @ A @ zero )
!= ( join @ B @ ( join @ C @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[178,1748]) ).
thf(2099,plain,
! [B: $i,A: $i] :
( ( a != A )
| ( ( join @ B @ b )
!= zero ) ),
inference(simp,[status(thm)],[2086]) ).
thf(2124,plain,
! [A: $i] :
( ( join @ A @ b )
!= zero ),
inference(simp,[status(thm)],[2099]) ).
thf(2138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( join @ A @ ( join @ B @ C ) )
!= zero )
| ( ( join @ ( join @ A @ B ) @ C )
!= ( join @ D @ b ) ) ),
inference(paramod_ordered,[status(thm)],[33,2124]) ).
thf(2139,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( join @ B @ b ) )
!= zero ),
inference(pattern_uni,[status(thm)],[2138:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( b )),bind(D,$thf( join @ E @ F ))]]) ).
thf(2163,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( join @ B @ b ) )
!= zero ),
inference(simp,[status(thm)],[2139]) ).
thf(2130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ B @ A )
!= zero )
| ( ( join @ A @ B )
!= ( join @ C @ b ) ) ),
inference(paramod_ordered,[status(thm)],[29,2124]) ).
thf(2131,plain,
! [A: $i] :
( ( join @ b @ A )
!= zero ),
inference(pattern_uni,[status(thm)],[2130:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( A ))]]) ).
thf(1728,plain,
! [C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ b ) ) ),
inference(paramod_ordered,[status(thm)],[25,1692]) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ( a != B )
| ( ( meet @ a @ A )
!= b ) ),
inference(simp,[status(thm)],[1728]) ).
thf(1750,plain,
! [A: $i] :
( ( meet @ a @ A )
!= b ),
inference(simp,[status(thm)],[1742]) ).
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(611,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ b @ C )
= ( join @ A @ ( join @ B @ C ) ) )
| ( ( join @ b @ a )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[153,33]) ).
thf(612,plain,
! [A: $i] :
( ( join @ b @ ( join @ a @ A ) )
= ( join @ b @ A ) ),
inference(pattern_uni,[status(thm)],[611:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(679,plain,
! [A: $i] :
( ( join @ b @ ( join @ a @ A ) )
= ( join @ b @ A ) ),
inference(simp,[status(thm)],[612]) ).
thf(6183,plain,
! [B: $i,A: $i] :
( ( ( join @ b @ one )
= ( join @ b @ B ) )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35,679]) ).
thf(6184,plain,
( ( join @ b @ ( complement @ a ) )
= ( join @ b @ one ) ),
inference(pattern_uni,[status(thm)],[6183:[bind(A,$thf( a )),bind(B,$thf( complement @ a ))]]) ).
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(6467,plain,
( ( join @ b @ ( complement @ a ) )
= one ),
inference(rewrite,[status(thm)],[6184,696]) ).
thf(6494,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= one )
| ( ( join @ b @ ( complement @ a ) )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6467,29]) ).
thf(6495,plain,
( ( join @ ( complement @ a ) @ b )
= one ),
inference(pattern_uni,[status(thm)],[6494:[bind(A,$thf( b )),bind(B,$thf( complement @ a ))]]) ).
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(2140,plain,
! [B: $i,A: $i] :
( ( zero != one )
| ( ( join @ ( complement @ A ) @ A )
!= ( join @ B @ b ) ) ),
inference(paramod_ordered,[status(thm)],[345,2124]) ).
thf(2141,plain,
zero != one,
inference(pattern_uni,[status(thm)],[2140:[bind(A,$thf( b )),bind(B,$thf( complement @ b ))]]) ).
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(652,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ b @ C )
= ( join @ A @ ( join @ B @ C ) ) )
| ( ( join @ a @ b )
!= ( join @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[300,33]) ).
thf(653,plain,
! [A: $i] :
( ( join @ a @ ( join @ b @ A ) )
= ( join @ b @ A ) ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(670,plain,
! [A: $i] :
( ( join @ a @ ( join @ b @ A ) )
= ( join @ b @ A ) ),
inference(simp,[status(thm)],[653]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ ( join @ A @ ( meet @ B @ ( join @ A @ C ) ) ) ) ) )
= ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H81) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ ( join @ A @ ( meet @ B @ ( join @ A @ C ) ) ) ) ) )
= ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ C @ ( join @ A @ ( meet @ B @ ( join @ A @ C ) ) ) ) ) )
= ( meet @ A @ ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[41]) ).
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(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(1273,plain,
! [B: $i,A: $i] :
( ( A = one )
| ( ( join @ zero @ A )
!= ( join @ B @ ( complement @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[334,35]) ).
thf(1274,plain,
( ( complement @ zero )
= one ),
inference(pattern_uni,[status(thm)],[1273:[bind(A,$thf( complement @ zero )),bind(B,$thf( zero ))]]) ).
thf(2010,plain,
! [A: $i] :
( ( ( join @ zero @ A )
!= one )
| ( A = one ) ),
inference(rewrite,[status(thm)],[114,1274,334]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( A = one )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ ( complement @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,35]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( A = one )
| ( A != C )
| ( ( meet @ A @ B )
!= ( complement @ C ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( B = one )
| ( ( meet @ B @ A )
!= ( complement @ B ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(4274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ a @ ( join @ A @ B ) )
= a )
| ( ( join @ B @ A )
!= ( join @ b @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,4236]) ).
thf(4275,plain,
! [A: $i] :
( ( meet @ a @ ( join @ A @ b ) )
= a ),
inference(pattern_uni,[status(thm)],[4274:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( A ))]]) ).
thf(1799,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= b )
| ( ( meet @ B @ A )
!= ( meet @ a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,1750]) ).
thf(1800,plain,
! [A: $i] :
( ( meet @ A @ a )
!= b ),
inference(pattern_uni,[status(thm)],[1799:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( A ))]]) ).
thf(4301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ C @ B )
= a )
| ( ( meet @ a @ ( join @ b @ A ) )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4236,27]) ).
thf(4302,plain,
! [A: $i] :
( ( meet @ ( join @ b @ A ) @ a )
= a ),
inference(pattern_uni,[status(thm)],[4301:[bind(A,$thf( E )),bind(B,$thf( a )),bind(C,$thf( join @ b @ E ))]]) ).
thf(4432,plain,
! [A: $i] :
( ( meet @ ( join @ b @ A ) @ a )
= a ),
inference(simp,[status(thm)],[4302]) ).
thf(319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( join @ D @ C ) )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[25,29]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[319:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( meet @ E @ F ))]]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( join @ ( meet @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[320]) ).
thf(7923,plain,
! [B: $i,A: $i] :
( ( A
!= ( complement @ a ) )
| ( ( join @ ( meet @ A @ B ) @ A )
!= ( join @ ( complement @ b ) @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,17]) ).
thf(8023,plain,
! [A: $i] :
( ( ( meet @ ( complement @ a ) @ A )
!= ( complement @ b ) )
| ( ( complement @ a )
!= ( complement @ a ) ) ),
inference(simp,[status(thm)],[7923]) ).
thf(8094,plain,
! [A: $i] :
( ( meet @ ( complement @ a ) @ A )
!= ( complement @ b ) ),
inference(simp,[status(thm)],[8023]) ).
thf(8189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= ( complement @ b ) )
| ( ( meet @ B @ A )
!= ( meet @ ( complement @ a ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,8094]) ).
thf(8190,plain,
! [A: $i] :
( ( meet @ A @ ( complement @ a ) )
!= ( complement @ b ) ),
inference(pattern_uni,[status(thm)],[8189:[bind(A,$thf( A )),bind(B,$thf( complement @ a )),bind(C,$thf( A ))]]) ).
thf(1828,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)],[31,1800]) ).
thf(1829,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( meet @ B @ a ) )
!= b ),
inference(pattern_uni,[status(thm)],[1828:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( a )),bind(D,$thf( meet @ E @ F ))]]) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( meet @ B @ a ) )
!= b ),
inference(simp,[status(thm)],[1829]) ).
thf(2051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != a )
| ( ( join @ A @ ( meet @ A @ B ) )
!= ( join @ C @ ( join @ D @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,1748]) ).
thf(2097,plain,
! [C: $i,B: $i,A: $i] :
( ( a != B )
| ( ( meet @ a @ A )
!= ( join @ C @ b ) ) ),
inference(simp,[status(thm)],[2051]) ).
thf(2122,plain,
! [B: $i,A: $i] :
( ( meet @ a @ A )
!= ( join @ B @ b ) ),
inference(simp,[status(thm)],[2097]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( one = B )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[35,178]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( one = B )
| ( A != B )
| ( ( complement @ A )
!= zero ) ),
inference(simp,[status(thm)],[224]) ).
thf(243,plain,
! [A: $i] :
( ( one = A )
| ( ( complement @ A )
!= zero ) ),
inference(simp,[status(thm)],[236]) ).
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(351,plain,
! [A: $i] :
( ( zero = a )
| ( ( meet @ a @ b )
!= ( meet @ A @ ( complement @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,37]) ).
thf(374,plain,
! [A: $i] :
( ( zero = a )
| ( a != A )
| ( ( complement @ A )
!= b ) ),
inference(simp,[status(thm)],[351]) ).
thf(382,plain,
( ( zero = a )
| ( ( complement @ a )
!= b ) ),
inference(simp,[status(thm)],[374]) ).
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(1344,plain,
( ( complement @ zero )
!= ( complement @ a ) ),
inference(paramod_ordered,[status(thm)],[1274,816]) ).
thf(1364,plain,
zero != a,
inference(simp,[status(thm)],[1344]) ).
thf(8397,plain,
( ( complement @ a )
!= b ),
inference(simplifyReflect,[status(thm)],[382,1364]) ).
thf(2052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( join @ C @ ( join @ B @ A ) )
!= a )
| ( ( join @ A @ B )
!= ( join @ D @ b ) ) ),
inference(paramod_ordered,[status(thm)],[29,1748]) ).
thf(2053,plain,
! [B: $i,A: $i] :
( ( join @ B @ ( join @ b @ A ) )
!= a ),
inference(pattern_uni,[status(thm)],[2052:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2100,plain,
! [B: $i,A: $i] :
( ( join @ B @ ( join @ b @ A ) )
!= a ),
inference(simp,[status(thm)],[2053]) ).
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(1375,plain,
( ( complement @ b )
!= a ),
inference(simplifyReflect,[status(thm)],[52,1364]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ C @ D )
!= zero )
| ( ( join @ A @ B )
!= one )
| ( ( complement @ C )
= D )
| ( ( join @ B @ A )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,40]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( ( meet @ B @ A )
!= zero )
| ( ( join @ A @ B )
!= one )
| ( ( complement @ B )
= A ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
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(2239,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(2240,plain,
! [A: $i] :
( ( join @ b @ ( meet @ a @ A ) )
= b ),
inference(pattern_uni,[status(thm)],[2239:[bind(A,$thf( E )),bind(B,$thf( b )),bind(C,$thf( meet @ a @ E ))]]) ).
thf(2323,plain,
! [A: $i] :
( ( join @ b @ ( meet @ a @ A ) )
= b ),
inference(simp,[status(thm)],[2240]) ).
thf(2550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ b @ ( meet @ A @ B ) )
= b )
| ( ( meet @ B @ A )
!= ( meet @ a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,2323]) ).
thf(2551,plain,
! [A: $i] :
( ( join @ b @ ( meet @ A @ a ) )
= b ),
inference(pattern_uni,[status(thm)],[2550:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( A ))]]) ).
thf(3530,plain,
! [B: $i,A: $i] :
( ( ( meet @ a @ zero )
= ( meet @ a @ B ) )
| ( ( meet @ A @ ( complement @ A ) )
!= ( meet @ b @ B ) ) ),
inference(paramod_ordered,[status(thm)],[37,503]) ).
thf(3531,plain,
( ( meet @ a @ ( complement @ b ) )
= ( meet @ a @ zero ) ),
inference(pattern_uni,[status(thm)],[3530:[bind(A,$thf( b )),bind(B,$thf( complement @ b ))]]) ).
thf(3774,plain,
( ( meet @ a @ ( complement @ b ) )
= zero ),
inference(rewrite,[status(thm)],[3531,1423]) ).
thf(3818,plain,
! [B: $i,A: $i] :
( ( ( meet @ B @ A )
= zero )
| ( ( meet @ a @ ( complement @ b ) )
!= ( meet @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3774,27]) ).
thf(3819,plain,
( ( meet @ ( complement @ b ) @ a )
= zero ),
inference(pattern_uni,[status(thm)],[3818:[bind(A,$thf( a )),bind(B,$thf( complement @ b ))]]) ).
thf(4516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ C @ B )
= a )
| ( ( meet @ a @ ( join @ A @ b ) )
!= ( meet @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4275,27]) ).
thf(4517,plain,
! [A: $i] :
( ( meet @ ( join @ A @ b ) @ a )
= a ),
inference(pattern_uni,[status(thm)],[4516:[bind(A,$thf( D )),bind(B,$thf( a )),bind(C,$thf( join @ D @ b ))]]) ).
thf(4613,plain,
! [A: $i] :
( ( meet @ ( join @ A @ b ) @ a )
= a ),
inference(simp,[status(thm)],[4517]) ).
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(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( meet @ C @ D ) )
| ( ( meet @ A @ ( join @ A @ B ) )
!= ( meet @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,27]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( meet @ ( join @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( join @ E @ F )),bind(D,$thf( E ))]]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( meet @ ( join @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[289]) ).
thf(8186,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( complement @ b ) )
| ( ( meet @ ( join @ A @ B ) @ A )
!= ( meet @ ( complement @ a ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[291,8094]) ).
thf(8204,plain,
! [B: $i,A: $i] :
( ( ( join @ ( complement @ b ) @ A )
!= ( complement @ a ) )
| ( ( complement @ b )
!= B ) ),
inference(simp,[status(thm)],[8186]) ).
thf(8222,plain,
! [A: $i] :
( ( join @ ( complement @ b ) @ A )
!= ( complement @ a ) ),
inference(simp,[status(thm)],[8204]) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ B @ A )
!= zero )
| ( ( join @ C @ D )
!= one )
| ( ( complement @ C )
= D )
| ( ( meet @ A @ B )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27,40]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( ( meet @ B @ A )
!= zero )
| ( ( join @ A @ B )
!= one )
| ( ( complement @ A )
= B ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
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(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( join @ C @ ( meet @ B @ A ) )
= C )
| ( ( meet @ A @ B )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27,25]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ C @ ( join @ B @ A ) )
= C )
| ( ( join @ A @ B )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,23]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
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(2531,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= b )
| ( ( join @ b @ ( meet @ a @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2323,29]) ).
thf(2532,plain,
! [A: $i] :
( ( join @ ( meet @ a @ A ) @ b )
= b ),
inference(pattern_uni,[status(thm)],[2531:[bind(A,$thf( E )),bind(B,$thf( b )),bind(C,$thf( meet @ a @ E ))]]) ).
thf(2652,plain,
! [A: $i] :
( ( join @ ( meet @ a @ A ) @ b )
= b ),
inference(simp,[status(thm)],[2532]) ).
thf(1299,plain,
! [A: $i] :
( ( A
!= ( complement @ a ) )
| ( ( join @ zero @ A )
!= ( join @ ( complement @ b ) @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[334,17]) ).
thf(1323,plain,
( ( ( complement @ b )
!= zero )
| ( ( complement @ a )
!= ( complement @ a ) ) ),
inference(simp,[status(thm)],[1299]) ).
thf(1340,plain,
( ( complement @ b )
!= zero ),
inference(simp,[status(thm)],[1323]) ).
thf(3428,plain,
! [C: $i,B: $i,A: $i] :
( ( A != b )
| ( ( meet @ A @ one )
!= ( meet @ B @ ( meet @ C @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[95,1858]) ).
thf(3458,plain,
! [B: $i,A: $i] :
( ( b != A )
| ( ( meet @ B @ a )
!= one ) ),
inference(simp,[status(thm)],[3428]) ).
thf(3462,plain,
! [A: $i] :
( ( meet @ A @ a )
!= one ),
inference(simp,[status(thm)],[3458]) ).
thf(3736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ B @ A )
!= one )
| ( ( meet @ A @ B )
!= ( meet @ C @ a ) ) ),
inference(paramod_ordered,[status(thm)],[27,3462]) ).
thf(3737,plain,
! [A: $i] :
( ( meet @ a @ A )
!= one ),
inference(pattern_uni,[status(thm)],[3736:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( A ))]]) ).
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(155,plain,
! [C: $i,B: $i,A: $i] :
( ( one = B )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ ( meet @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,25]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( one = B )
| ( A != B )
| ( ( complement @ A )
!= ( meet @ B @ C ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( one = A )
| ( ( meet @ A @ B )
!= ( complement @ A ) ) ),
inference(simp,[status(thm)],[170]) ).
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(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(2783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= b )
| ( ( join @ b @ ( meet @ A @ a ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2551,29]) ).
thf(2784,plain,
! [A: $i] :
( ( join @ ( meet @ A @ a ) @ b )
= b ),
inference(pattern_uni,[status(thm)],[2783:[bind(A,$thf( D )),bind(B,$thf( b )),bind(C,$thf( meet @ D @ a ))]]) ).
thf(2912,plain,
! [A: $i] :
( ( join @ ( meet @ A @ a ) @ b )
= b ),
inference(simp,[status(thm)],[2784]) ).
thf(2391,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(2392,plain,
! [A: $i] :
( ( ( join @ A @ ( join @ A @ ( complement @ a ) ) )
!= ( complement @ a ) )
| ( A
!= ( complement @ b ) ) ),
inference(pattern_uni,[status(thm)],[2391:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(2462,plain,
( ( join @ ( complement @ b ) @ ( join @ ( complement @ b ) @ ( complement @ a ) ) )
!= ( complement @ a ) ),
inference(simp,[status(thm)],[2392]) ).
thf(8273,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( complement @ b ) )
| ( ( meet @ A @ ( join @ B @ A ) )
!= ( meet @ C @ ( complement @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[330,8190]) ).
thf(8303,plain,
! [B: $i,A: $i] :
( ( ( complement @ b )
!= B )
| ( ( join @ A @ ( complement @ b ) )
!= ( complement @ a ) ) ),
inference(simp,[status(thm)],[8273]) ).
thf(8324,plain,
! [A: $i] :
( ( join @ A @ ( complement @ b ) )
!= ( complement @ a ) ),
inference(simp,[status(thm)],[8303]) ).
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(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ C @ D )
!= zero )
| ( ( join @ B @ A )
!= one )
| ( ( complement @ C )
= D )
| ( ( join @ A @ B )
!= ( join @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,40]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= zero )
| ( ( join @ B @ A )
!= one )
| ( ( complement @ A )
= B ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
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(3347,plain,
! [A: $i] :
( ( ( meet @ one @ A )
!= zero )
| ( A = zero ) ),
inference(rewrite,[status(thm)],[179,249,524]) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= zero )
| ( ( join @ C @ D )
!= one )
| ( ( complement @ C )
= D )
| ( ( meet @ B @ A )
!= ( meet @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27,40]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( ( meet @ A @ B )
!= zero )
| ( ( join @ B @ A )
!= one )
| ( ( complement @ B )
= A ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1376,plain,
( ( complement @ one )
!= ( complement @ b ) ),
inference(paramod_ordered,[status(thm)],[524,1340]) ).
thf(1378,plain,
one != b,
inference(simp,[status(thm)],[1376]) ).
thf(129426,plain,
$false,
inference(cvc4,[status(thm)],[1423,4236,524,100,2163,2131,249,1686,1750,6495,1692,2141,153,670,42,24,2010,37,25,184,4275,1800,20,29,4432,8190,1858,2122,243,8094,74,292,8397,1274,334,21,33,28,38,2100,1375,328,2323,77,489,2551,679,3819,41,503,4613,148,17,32,34,22,44,8222,291,281,27,98,271,345,816,330,1364,35,675,2652,2124,1340,1748,3737,63,18,95,3462,182,3774,31,6467,143,43,40,26,23,75,2912,2462,300,8324,432,36,30,1303,19,326,341,3347,696,283,1378,528,15,178,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT256-1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 14:18:25 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (119ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.54/1.15 % [INFO] eprover registered as external prover.
% 1.54/1.16 % [INFO] cvc4 registered as external prover.
% 1.54/1.16 % [INFO] Scanning for conjecture ...
% 1.71/1.21 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.71/1.23 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.71/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.71/1.24 % [INFO] Type checking passed.
% 1.71/1.25 % [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 ...
% 196.24/38.13 % External prover 'cvc4' found a proof!
% 196.24/38.13 % [INFO] Killing All external provers ...
% 196.24/38.14 % Time passed: 37623ms (effective reasoning time: 37171ms)
% 196.24/38.14 % 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)>
% 196.24/38.14 % Axioms used in derivation (13): commutativity_of_join, absorption1, meet_join_complement, complement_meet, commutativity_of_meet, equation_H81, associativity_of_join, idempotence_of_meet, prove_distributivity_hypothesis, associativity_of_meet, complement_join, idempotence_of_join, absorption2
% 196.24/38.14 % No. of inferences in proof: 259
% 196.24/38.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 37623 ms resp. 37171 ms w/o parsing
% 196.24/38.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 196.24/38.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------