%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT199-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:55:55 PM UTC 2026
% Result : Unsatisfiable 51.42s 7.06s
% Output : Proof 51.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 154
% Number of leaves : 14
% Syntax : Number of formulae : 627 ( 623 unt; 0 def)
% Number of atoms : 635 ( 634 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 1492 ( 366 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
( complement(X) = Y
| join(X,Y) != one
| meet(X,Y) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).
fof(f10_nnf,plain,
! [X,Y] :
( complement(X) = Y
| join(X,Y) != one
| meet(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] :
( complement(X) = Y
| join(X,Y) != one
| meet(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( complement(X0) = X1
| join(X0,X1) != one
| meet(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t11,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t18,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(f4,axiom,
meet(X,Y) = meet(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
fof(f4_nnf,plain,
! [X,Y] : meet(X,Y) = meet(Y,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : meet(X,Y) = meet(Y,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
meet(X0,X1) = meet(X1,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t7,plain,
meet(X1,X2) = meet(X2,X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t23,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t25,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1),
inference(cp,[status(thm)],[t18,t23]) ).
cnf(f5,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
fof(f5_nnf,plain,
! [X,Y] : join(X,Y) = join(Y,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : join(X,Y) = join(Y,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t67,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t66539,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1),
inference(step,[status(thm)],[t25,t67]) ).
cnf(t875,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t66539]) ).
cnf(f9,axiom,
meet(X,complement(X)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
fof(f9_nnf,plain,
! [X] : meet(X,complement(X)) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : meet(X,complement(X)) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
meet(X0,complement(X0)) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t3,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t61,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t896,plain,
X1 = ifeq(zero,zero,ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t875,t61]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t66540,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t896,t17]) ).
cnf(f8,axiom,
join(X,complement(X)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
fof(f8_nnf,plain,
! [X] : join(X,complement(X)) = one,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : join(X,complement(X)) = one,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
join(X0,complement(X0)) = one,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t2,plain,
join(X1,complement(X1)) = one,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t95,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t66541,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t66540,t95]) ).
cnf(t66542,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t66541,t17]) ).
cnf(t919,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t66542]) ).
cnf(f11,axiom,
meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,join(Y,U))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H49) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,join(Y,U))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,join(Y,U))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(X1,join(meet(X0,X2),meet(X2,join(X1,X3))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t46,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t12]) ).
cnf(f2,axiom,
meet(X,join(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
fof(f2_nnf,plain,
! [X,Y] : meet(X,join(X,Y)) = X,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : meet(X,join(X,Y)) = X,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
meet(X0,join(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t8,plain,
meet(X1,join(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t14,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t47,plain,
meet(X1,join(X2,meet(join(X1,X3),join(X1,X4)))) = meet(X1,join(X2,join(X1,meet(join(X1,X3),join(X2,X4))))),
inference(cp,[status(thm)],[t46,t14]) ).
cnf(f7,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
fof(f7_nnf,plain,
! [X,Y,Z] : join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z] : join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t9,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t66389,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t9,t67]) ).
cnf(t72,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t66389]) ).
cnf(t66876,plain,
meet(X1,join(X2,meet(join(X1,X3),join(X1,X4)))) = meet(X1,join(X1,join(meet(join(X1,X3),join(X2,X4)),X2))),
inference(step,[status(thm)],[t47,t72]) ).
cnf(t66877,plain,
meet(X1,join(X2,meet(join(X1,X3),join(X1,X4)))) = X1,
inference(step,[status(thm)],[t66876,t14]) ).
cnf(t5997,plain,
meet(X1,join(X2,meet(join(X1,X3),join(X1,X4)))) = X1,
inference(orient,[status(thm)],[t66877]) ).
cnf(f1,axiom,
join(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
fof(f1_nnf,plain,
! [X] : join(X,X) = X,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : join(X,X) = X,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
join(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t0,plain,
join(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t15,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t54,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,X2)))),
inference(cp,[status(thm)],[t46,t15]) ).
cnf(t66598,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X2,X3)))),
inference(step,[status(thm)],[t54,t23]) ).
cnf(f3,axiom,
join(X,meet(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
fof(f3_nnf,plain,
! [X,Y] : join(X,meet(X,Y)) = X,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : join(X,meet(X,Y)) = X,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
join(X0,meet(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
join(X1,meet(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t16,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t76,plain,
join(meet(X1,X2),join(X3,X1)) = join(X3,X1),
inference(cp,[status(thm)],[t72,t16]) ).
cnf(t66407,plain,
join(X1,join(meet(X1,X2),X3)) = join(X3,X1),
inference(step,[status(thm)],[t76,t72]) ).
cnf(t66408,plain,
join(X1,join(X3,meet(X1,X2))) = join(X3,X1),
inference(step,[status(thm)],[t66407,t67]) ).
cnf(t66409,plain,
join(X1,join(X3,meet(X1,X2))) = join(X1,X3),
inference(step,[status(thm)],[t66408,t67]) ).
cnf(t188,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(orient,[status(thm)],[t66409]) ).
cnf(t66599,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(step,[status(thm)],[t66598,t188]) ).
cnf(t1339,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(orient,[status(thm)],[t66599]) ).
cnf(t1368,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),meet(X2,one))),
inference(cp,[status(thm)],[t1339,t95]) ).
cnf(t96,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t14,t95]) ).
cnf(t106,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t96]) ).
cnf(t66609,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t1368,t106]) ).
cnf(t66610,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t66609,t67]) ).
cnf(t1454,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t66610]) ).
cnf(f6,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
fof(f6_nnf,plain,
! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t10,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t66388,plain,
meet(X3,meet(X1,X2)) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t10,t23]) ).
cnf(t26,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(orient,[status(thm)],[t66388]) ).
cnf(t30,plain,
meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t66404,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X3,X1),
inference(step,[status(thm)],[t30,t26]) ).
cnf(t66405,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X3,X1),
inference(step,[status(thm)],[t66404,t23]) ).
cnf(t66406,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X1,X3),
inference(step,[status(thm)],[t66405,t23]) ).
cnf(t175,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t66406]) ).
cnf(t1490,plain,
meet(X1,join(meet(X2,join(X1,X3)),complement(X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(cp,[status(thm)],[t1454,t175]) ).
cnf(t66657,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(step,[status(thm)],[t1490,t67]) ).
cnf(t66658,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t66657,t1454]) ).
cnf(t1823,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t66658]) ).
cnf(t1456,plain,
meet(complement(X1),join(X2,complement(complement(X1)))) = meet(complement(X1),join(X1,meet(complement(X1),X2))),
inference(cp,[status(thm)],[t1454,t919]) ).
cnf(t66635,plain,
meet(complement(X1),join(X2,X1)) = meet(complement(X1),join(X1,meet(complement(X1),X2))),
inference(step,[status(thm)],[t1456,t919]) ).
cnf(t66636,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),join(X1,meet(complement(X1),X2))),
inference(step,[status(thm)],[t66635,t67]) ).
cnf(t66637,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),join(X1,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t66636,t23]) ).
cnf(t1677,plain,
meet(complement(X1),join(X1,meet(X2,complement(X1)))) = meet(complement(X1),join(X1,X2)),
inference(orient,[status(thm)],[t66637]) ).
cnf(t1688,plain,
meet(X1,join(meet(X2,complement(X1)),meet(X1,complement(X1)))) = meet(X1,join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2)))),
inference(cp,[status(thm)],[t1339,t1677]) ).
cnf(t66748,plain,
meet(X1,join(meet(X1,complement(X1)),meet(X2,complement(X1)))) = meet(X1,join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2)))),
inference(step,[status(thm)],[t1688,t67]) ).
cnf(t66749,plain,
meet(X1,join(zero,meet(X2,complement(X1)))) = meet(X1,join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2)))),
inference(step,[status(thm)],[t66748,t61]) ).
cnf(t198,plain,
meet(X1,join(X2,meet(X2,join(X1,X3)))) = meet(X1,join(X2,meet(X1,X2))),
inference(cp,[status(thm)],[t46,t188]) ).
cnf(t66410,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,X2))),
inference(step,[status(thm)],[t198,t16]) ).
cnf(t202,plain,
meet(X1,join(X2,meet(X1,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t66410]) ).
cnf(t203,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,join(meet(X2,join(X1,X3)),meet(X1,X2))),
inference(cp,[status(thm)],[t202,t175]) ).
cnf(t66451,plain,
meet(X1,X2) = meet(X1,join(meet(X2,join(X1,X3)),meet(X1,X2))),
inference(step,[status(thm)],[t203,t175]) ).
cnf(t66452,plain,
meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(X2,join(X1,X3)))),
inference(step,[status(thm)],[t66451,t67]) ).
cnf(t373,plain,
meet(X1,join(meet(X1,X2),meet(X2,join(X1,X3)))) = meet(X1,X2),
inference(orient,[status(thm)],[t66452]) ).
cnf(t65,plain,
meet(X1,meet(complement(X1),X2)) = meet(X2,zero),
inference(cp,[status(thm)],[t26,t61]) ).
cnf(t66400,plain,
meet(X1,meet(X2,complement(X1))) = meet(X2,zero),
inference(step,[status(thm)],[t65,t23]) ).
cnf(f0,axiom,
meet(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
fof(f0_nnf,plain,
! [X] : meet(X,X) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : meet(X,X) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
meet(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
meet(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t29,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(cp,[status(thm)],[t26,t13]) ).
cnf(t66390,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t29,t26]) ).
cnf(t66391,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t66390,t23]) ).
cnf(t112,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t66391]) ).
cnf(t115,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t112,t61]) ).
cnf(t66392,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t115,t61]) ).
cnf(t123,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t66392]) ).
cnf(t66401,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t66400,t123]) ).
cnf(t159,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t66401]) ).
cnf(t377,plain,
meet(X1,meet(X2,complement(X1))) = meet(X1,join(zero,meet(meet(X2,complement(X1)),join(X1,X3)))),
inference(cp,[status(thm)],[t373,t159]) ).
cnf(t66477,plain,
zero = meet(X1,join(zero,meet(meet(X2,complement(X1)),join(X1,X3)))),
inference(step,[status(thm)],[t377,t159]) ).
cnf(t66478,plain,
zero = meet(X1,join(zero,meet(join(X1,X3),meet(X2,complement(X1))))),
inference(step,[status(thm)],[t66477,t23]) ).
cnf(t66479,plain,
zero = meet(X1,join(zero,meet(complement(X1),meet(join(X1,X3),X2)))),
inference(step,[status(thm)],[t66478,t26]) ).
cnf(t66480,plain,
zero = meet(X1,join(zero,meet(X2,meet(complement(X1),join(X1,X3))))),
inference(step,[status(thm)],[t66479,t26]) ).
cnf(t501,plain,
meet(X1,join(zero,meet(X2,meet(complement(X1),join(X1,X3))))) = zero,
inference(orient,[status(thm)],[t66480]) ).
cnf(t98,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t72,t95]) ).
cnf(t66402,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t98,t67]) ).
cnf(t75,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t72,t15]) ).
cnf(t66393,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t75,t72]) ).
cnf(t66394,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t66393,t67]) ).
cnf(t129,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t66394]) ).
cnf(t132,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t129,t95]) ).
cnf(t66395,plain,
one = join(X1,one),
inference(step,[status(thm)],[t132,t95]) ).
cnf(t141,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t66395]) ).
cnf(t66403,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t66402,t141]) ).
cnf(t167,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t66403]) ).
cnf(t173,plain,
join(X1,join(join(X2,complement(X1)),X3)) = join(X3,one),
inference(cp,[status(thm)],[t72,t167]) ).
cnf(t66415,plain,
join(X1,join(X3,join(X2,complement(X1)))) = join(X3,one),
inference(step,[status(thm)],[t173,t67]) ).
cnf(t66416,plain,
join(X1,join(X2,join(complement(X1),X3))) = join(X3,one),
inference(step,[status(thm)],[t66415,t72]) ).
cnf(t66417,plain,
join(X1,join(X2,join(X3,complement(X1)))) = join(X3,one),
inference(step,[status(thm)],[t66416,t67]) ).
cnf(t66418,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(step,[status(thm)],[t66417,t141]) ).
cnf(t227,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(orient,[status(thm)],[t66418]) ).
cnf(t509,plain,
zero = meet(X1,join(zero,meet(X2,meet(complement(X1),one)))),
inference(cp,[status(thm)],[t501,t227]) ).
cnf(t66481,plain,
zero = meet(X1,join(zero,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t509,t106]) ).
cnf(t529,plain,
meet(X1,join(zero,meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t66481]) ).
cnf(t66750,plain,
zero = meet(X1,join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2)))),
inference(step,[status(thm)],[t66749,t529]) ).
cnf(t3288,plain,
meet(X1,join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t66750]) ).
cnf(t3328,plain,
meet(meet(X1,complement(X2)),join(X2,complement(meet(X1,complement(X2))))) = meet(meet(X1,complement(X2)),join(complement(meet(X1,complement(X2))),zero)),
inference(cp,[status(thm)],[t1823,t3288]) ).
cnf(t62,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t16,t61]) ).
cnf(t100,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t62]) ).
cnf(t66751,plain,
meet(meet(X1,complement(X2)),join(X2,complement(meet(X1,complement(X2))))) = meet(meet(X1,complement(X2)),complement(meet(X1,complement(X2)))),
inference(step,[status(thm)],[t3328,t100]) ).
cnf(t66752,plain,
meet(meet(X1,complement(X2)),join(X2,complement(meet(X1,complement(X2))))) = zero,
inference(step,[status(thm)],[t66751,t61]) ).
cnf(t3343,plain,
meet(meet(X1,complement(X2)),join(X2,complement(meet(X1,complement(X2))))) = zero,
inference(orient,[status(thm)],[t66752]) ).
cnf(t3350,plain,
join(X1,complement(meet(X2,complement(X1)))) = ifeq(zero,zero,ifeq(join(meet(X2,complement(X1)),join(X1,complement(meet(X2,complement(X1))))),one,complement(meet(X2,complement(X1))),join(X1,complement(meet(X2,complement(X1))))),join(X1,complement(meet(X2,complement(X1))))),
inference(cp,[status(thm)],[t18,t3343]) ).
cnf(t66753,plain,
join(X1,complement(meet(X2,complement(X1)))) = ifeq(join(meet(X2,complement(X1)),join(X1,complement(meet(X2,complement(X1))))),one,complement(meet(X2,complement(X1))),join(X1,complement(meet(X2,complement(X1))))),
inference(step,[status(thm)],[t3350,t17]) ).
cnf(t66754,plain,
join(X1,complement(meet(X2,complement(X1)))) = ifeq(one,one,complement(meet(X2,complement(X1))),join(X1,complement(meet(X2,complement(X1))))),
inference(step,[status(thm)],[t66753,t167]) ).
cnf(t66755,plain,
join(X1,complement(meet(X2,complement(X1)))) = complement(meet(X2,complement(X1))),
inference(step,[status(thm)],[t66754,t17]) ).
cnf(t3371,plain,
join(X1,complement(meet(X2,complement(X1)))) = complement(meet(X2,complement(X1))),
inference(orient,[status(thm)],[t66755]) ).
cnf(t3373,plain,
complement(meet(X1,complement(complement(X2)))) = join(complement(X2),complement(meet(X1,X2))),
inference(cp,[status(thm)],[t3371,t919]) ).
cnf(t66761,plain,
complement(meet(X1,X2)) = join(complement(X2),complement(meet(X1,X2))),
inference(step,[status(thm)],[t3373,t919]) ).
cnf(t3564,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(orient,[status(thm)],[t66761]) ).
cnf(t3402,plain,
join(X1,join(complement(meet(X2,complement(X1))),X3)) = join(X3,complement(meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t72,t3371]) ).
cnf(t66850,plain,
join(X1,join(X3,complement(meet(X2,complement(X1))))) = join(X3,complement(meet(X2,complement(X1)))),
inference(step,[status(thm)],[t3402,t67]) ).
cnf(t4999,plain,
join(X1,join(X2,complement(meet(X3,complement(X1))))) = join(X2,complement(meet(X3,complement(X1)))),
inference(orient,[status(thm)],[t66850]) ).
cnf(t5008,plain,
X1 = meet(X1,join(X2,complement(meet(X3,complement(X1))))),
inference(cp,[status(thm)],[t14,t4999]) ).
cnf(t5043,plain,
meet(X1,join(X2,complement(meet(X3,complement(X1))))) = X1,
inference(orient,[status(thm)],[t5008]) ).
cnf(t3374,plain,
X1 = meet(X1,complement(meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t14,t3371]) ).
cnf(t3404,plain,
meet(X1,complement(meet(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t3374]) ).
cnf(t5045,plain,
meet(X1,complement(X2)) = meet(meet(X1,complement(X2)),join(X3,complement(X2))),
inference(cp,[status(thm)],[t5043,t3404]) ).
cnf(t7398,plain,
meet(meet(X1,complement(X2)),join(X3,complement(X2))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t5045]) ).
cnf(t7402,plain,
meet(X1,complement(complement(X2))) = meet(meet(X1,X2),join(X3,complement(complement(X2)))),
inference(cp,[status(thm)],[t7398,t919]) ).
cnf(t66916,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,complement(complement(X2)))),
inference(step,[status(thm)],[t7402,t919]) ).
cnf(t66917,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,X2)),
inference(step,[status(thm)],[t66916,t919]) ).
cnf(t66918,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X2,X3)),
inference(step,[status(thm)],[t66917,t67]) ).
cnf(t7454,plain,
meet(meet(X1,X2),join(X2,X3)) = meet(X1,X2),
inference(orient,[status(thm)],[t66918]) ).
cnf(t7500,plain,
meet(X1,X2) = meet(meet(X1,X2),complement(meet(X3,complement(X2)))),
inference(cp,[status(thm)],[t7454,t3371]) ).
cnf(t7554,plain,
meet(meet(X1,X2),complement(meet(X3,complement(X2)))) = meet(X1,X2),
inference(orient,[status(thm)],[t7500]) ).
cnf(t7576,plain,
meet(X1,join(X1,X2)) = meet(X1,complement(meet(X3,complement(join(X1,X2))))),
inference(cp,[status(thm)],[t7554,t14]) ).
cnf(t66923,plain,
X1 = meet(X1,complement(meet(X3,complement(join(X1,X2))))),
inference(step,[status(thm)],[t7576,t14]) ).
cnf(t7769,plain,
meet(X1,complement(meet(X2,complement(join(X1,X3))))) = X1,
inference(orient,[status(thm)],[t66923]) ).
cnf(t7793,plain,
complement(meet(X1,complement(meet(X2,complement(join(X1,X3)))))) = join(complement(complement(meet(X2,complement(join(X1,X3))))),complement(X1)),
inference(cp,[status(thm)],[t3564,t7769]) ).
cnf(t66927,plain,
complement(X1) = join(complement(complement(meet(X2,complement(join(X1,X3))))),complement(X1)),
inference(step,[status(thm)],[t7793,t7769]) ).
cnf(t66928,plain,
complement(X1) = join(complement(X1),complement(complement(meet(X2,complement(join(X1,X3)))))),
inference(step,[status(thm)],[t66927,t67]) ).
cnf(t66929,plain,
complement(X1) = join(complement(X1),meet(X2,complement(join(X1,X3)))),
inference(step,[status(thm)],[t66928,t919]) ).
cnf(t7903,plain,
join(complement(X1),meet(X2,complement(join(X1,X3)))) = complement(X1),
inference(orient,[status(thm)],[t66929]) ).
cnf(t7904,plain,
complement(complement(X1)) = join(X1,meet(X2,complement(join(complement(X1),X3)))),
inference(cp,[status(thm)],[t7903,t919]) ).
cnf(t66930,plain,
X1 = join(X1,meet(X2,complement(join(complement(X1),X3)))),
inference(step,[status(thm)],[t7904,t919]) ).
cnf(t66931,plain,
X1 = join(X1,meet(X2,complement(join(X3,complement(X1))))),
inference(step,[status(thm)],[t66930,t67]) ).
cnf(t7944,plain,
join(X1,meet(X2,complement(join(X3,complement(X1))))) = X1,
inference(orient,[status(thm)],[t66931]) ).
cnf(t7952,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X3,complement(complement(meet(X1,X2))))),
inference(cp,[status(thm)],[t7944,t3564]) ).
cnf(t66932,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X3,meet(X1,X2))),
inference(step,[status(thm)],[t7952,t919]) ).
cnf(t66933,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,meet(X3,X1))),
inference(step,[status(thm)],[t66932,t26]) ).
cnf(t66934,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,meet(X2,X3))),
inference(step,[status(thm)],[t66933,t26]) ).
cnf(t8001,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t66934]) ).
cnf(t8123,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,meet(meet(X1,X2),join(meet(X1,X2),X4)))),
inference(cp,[status(thm)],[t5997,t8001]) ).
cnf(t66935,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,meet(X1,X2))),
inference(step,[status(thm)],[t8123,t14]) ).
cnf(t8144,plain,
meet(meet(X1,X2),join(X3,meet(X1,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t66935]) ).
cnf(t143,plain,
one = ifeq(meet(X1,one),zero,ifeq(one,one,complement(X1),one),one),
inference(cp,[status(thm)],[t18,t141]) ).
cnf(t66398,plain,
one = ifeq(X1,zero,ifeq(one,one,complement(X1),one),one),
inference(step,[status(thm)],[t143,t106]) ).
cnf(t66399,plain,
one = ifeq(X1,zero,complement(X1),one),
inference(step,[status(thm)],[t66398,t17]) ).
cnf(t151,plain,
ifeq(X1,zero,complement(X1),one) = one,
inference(orient,[status(thm)],[t66399]) ).
cnf(t922,plain,
one = ifeq(complement(X1),zero,X1,one),
inference(cp,[status(thm)],[t151,t919]) ).
cnf(t944,plain,
ifeq(complement(X1),zero,X1,one) = one,
inference(orient,[status(thm)],[t922]) ).
cnf(t165,plain,
meet(X1,meet(meet(X2,complement(X1)),X3)) = meet(X3,zero),
inference(cp,[status(thm)],[t26,t159]) ).
cnf(t66411,plain,
meet(X1,meet(X3,meet(X2,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t165,t23]) ).
cnf(t66412,plain,
meet(X1,meet(X2,meet(complement(X1),X3))) = meet(X3,zero),
inference(step,[status(thm)],[t66411,t26]) ).
cnf(t66413,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t66412,t23]) ).
cnf(t66414,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(step,[status(thm)],[t66413,t123]) ).
cnf(t216,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(orient,[status(thm)],[t66414]) ).
cnf(t375,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = meet(X1,join(zero,meet(meet(X2,meet(X3,complement(X1))),join(X1,X4)))),
inference(cp,[status(thm)],[t373,t216]) ).
cnf(t66544,plain,
zero = meet(X1,join(zero,meet(meet(X2,meet(X3,complement(X1))),join(X1,X4)))),
inference(step,[status(thm)],[t375,t216]) ).
cnf(t66545,plain,
zero = meet(X1,join(zero,meet(join(X1,X4),meet(X2,meet(X3,complement(X1)))))),
inference(step,[status(thm)],[t66544,t23]) ).
cnf(t66546,plain,
zero = meet(X1,join(zero,meet(X2,meet(meet(X3,complement(X1)),join(X1,X4))))),
inference(step,[status(thm)],[t66545,t26]) ).
cnf(t66547,plain,
zero = meet(X1,join(zero,meet(X2,meet(join(X1,X4),meet(X3,complement(X1)))))),
inference(step,[status(thm)],[t66546,t23]) ).
cnf(t66548,plain,
zero = meet(X1,join(zero,meet(X2,meet(complement(X1),meet(join(X1,X4),X3))))),
inference(step,[status(thm)],[t66547,t26]) ).
cnf(t66549,plain,
zero = meet(X1,join(zero,meet(X2,meet(X3,meet(complement(X1),join(X1,X4)))))),
inference(step,[status(thm)],[t66548,t26]) ).
cnf(t967,plain,
meet(X1,join(zero,meet(X2,meet(X3,meet(complement(X1),join(X1,X4)))))) = zero,
inference(orient,[status(thm)],[t66549]) ).
cnf(t980,plain,
zero = meet(X1,join(zero,meet(X2,meet(X3,meet(complement(X1),one))))),
inference(cp,[status(thm)],[t967,t227]) ).
cnf(t66550,plain,
zero = meet(X1,join(zero,meet(X2,meet(X3,complement(X1))))),
inference(step,[status(thm)],[t980,t106]) ).
cnf(t1006,plain,
meet(X1,join(zero,meet(X2,meet(X3,complement(X1))))) = zero,
inference(orient,[status(thm)],[t66550]) ).
cnf(t3445,plain,
zero = meet(meet(X1,complement(X2)),join(zero,meet(X3,X2))),
inference(cp,[status(thm)],[t1006,t3404]) ).
cnf(t66816,plain,
zero = meet(meet(X1,complement(X2)),join(zero,meet(X2,X3))),
inference(step,[status(thm)],[t3445,t23]) ).
cnf(t4407,plain,
meet(meet(X1,complement(X2)),join(zero,meet(X2,X3))) = zero,
inference(orient,[status(thm)],[t66816]) ).
cnf(t5049,plain,
complement(X1) = meet(complement(X1),join(X2,complement(meet(X3,X1)))),
inference(cp,[status(thm)],[t5043,t919]) ).
cnf(t66856,plain,
complement(X1) = meet(complement(X1),join(X2,complement(meet(X1,X3)))),
inference(step,[status(thm)],[t5049,t23]) ).
cnf(t5195,plain,
meet(complement(X1),join(X2,complement(meet(X1,X3)))) = complement(X1),
inference(orient,[status(thm)],[t66856]) ).
cnf(t5199,plain,
complement(X1) = meet(complement(X1),join(X2,complement(X1))),
inference(cp,[status(thm)],[t5195,t13]) ).
cnf(t5243,plain,
meet(complement(X1),join(X2,complement(X1))) = complement(X1),
inference(orient,[status(thm)],[t5199]) ).
cnf(t3598,plain,
complement(meet(X1,join(X1,X2))) = join(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t3564,t14]) ).
cnf(t66766,plain,
complement(X1) = join(complement(join(X1,X2)),complement(X1)),
inference(step,[status(thm)],[t3598,t14]) ).
cnf(t66767,plain,
complement(X1) = join(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t66766,t67]) ).
cnf(t3675,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t66767]) ).
cnf(t5246,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t5243,t3675]) ).
cnf(t66857,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t5246,t23]) ).
cnf(t5276,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t66857]) ).
cnf(t5289,plain,
zero = meet(meet(X1,complement(complement(X2))),join(zero,complement(join(X2,X3)))),
inference(cp,[status(thm)],[t4407,t5276]) ).
cnf(t66862,plain,
zero = meet(meet(X1,X2),join(zero,complement(join(X2,X3)))),
inference(step,[status(thm)],[t5289,t919]) ).
cnf(t380,plain,
meet(X1,complement(X1)) = meet(X1,join(zero,meet(complement(X1),join(X1,X2)))),
inference(cp,[status(thm)],[t373,t61]) ).
cnf(t66453,plain,
zero = meet(X1,join(zero,meet(complement(X1),join(X1,X2)))),
inference(step,[status(thm)],[t380,t61]) ).
cnf(t415,plain,
meet(X1,join(zero,meet(complement(X1),join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t66453]) ).
cnf(t419,plain,
zero = meet(X1,join(zero,meet(complement(X1),one))),
inference(cp,[status(thm)],[t415,t227]) ).
cnf(t66454,plain,
zero = meet(X1,join(zero,complement(X1))),
inference(step,[status(thm)],[t419,t106]) ).
cnf(t438,plain,
meet(X1,join(zero,complement(X1))) = zero,
inference(orient,[status(thm)],[t66454]) ).
cnf(t439,plain,
join(zero,complement(X1)) = ifeq(zero,zero,ifeq(join(X1,join(zero,complement(X1))),one,complement(X1),join(zero,complement(X1))),join(zero,complement(X1))),
inference(cp,[status(thm)],[t18,t438]) ).
cnf(t66455,plain,
join(zero,complement(X1)) = ifeq(join(X1,join(zero,complement(X1))),one,complement(X1),join(zero,complement(X1))),
inference(step,[status(thm)],[t439,t17]) ).
cnf(t66456,plain,
join(zero,complement(X1)) = ifeq(one,one,complement(X1),join(zero,complement(X1))),
inference(step,[status(thm)],[t66455,t167]) ).
cnf(t66457,plain,
join(zero,complement(X1)) = complement(X1),
inference(step,[status(thm)],[t66456,t17]) ).
cnf(t448,plain,
join(zero,complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t66457]) ).
cnf(t66863,plain,
zero = meet(meet(X1,X2),complement(join(X2,X3))),
inference(step,[status(thm)],[t66862,t448]) ).
cnf(t5347,plain,
meet(meet(X1,X2),complement(join(X2,X3))) = zero,
inference(orient,[status(thm)],[t66863]) ).
cnf(t5377,plain,
zero = meet(meet(X1,X2),complement(join(X1,X3))),
inference(cp,[status(thm)],[t5347,t23]) ).
cnf(t5415,plain,
meet(meet(X1,X2),complement(join(X1,X3))) = zero,
inference(orient,[status(thm)],[t5377]) ).
cnf(t5418,plain,
zero = meet(complement(join(X1,X2)),complement(join(complement(X1),X3))),
inference(cp,[status(thm)],[t5415,t5276]) ).
cnf(t66884,plain,
zero = meet(complement(join(X1,X2)),complement(join(X3,complement(X1)))),
inference(step,[status(thm)],[t5418,t67]) ).
cnf(t6286,plain,
meet(complement(join(X1,X2)),complement(join(X3,complement(X1)))) = zero,
inference(orient,[status(thm)],[t66884]) ).
cnf(t6302,plain,
zero = meet(complement(join(meet(X1,X2),X3)),complement(complement(meet(X1,X2)))),
inference(cp,[status(thm)],[t6286,t3564]) ).
cnf(t66896,plain,
zero = meet(complement(join(meet(X1,X2),X3)),meet(X1,X2)),
inference(step,[status(thm)],[t6302,t919]) ).
cnf(t66897,plain,
zero = meet(X2,meet(complement(join(meet(X1,X2),X3)),X1)),
inference(step,[status(thm)],[t66896,t26]) ).
cnf(t66898,plain,
zero = meet(X1,meet(X2,complement(join(meet(X1,X2),X3)))),
inference(step,[status(thm)],[t66897,t26]) ).
cnf(t66899,plain,
zero = meet(X1,meet(X2,complement(join(X3,meet(X1,X2))))),
inference(step,[status(thm)],[t66898,t67]) ).
cnf(t6598,plain,
meet(X1,meet(X2,complement(join(X3,meet(X1,X2))))) = zero,
inference(orient,[status(thm)],[t66899]) ).
cnf(t3406,plain,
complement(X1) = meet(complement(X1),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t3404,t919]) ).
cnf(t66756,plain,
complement(X1) = meet(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t3406,t23]) ).
cnf(t3474,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t66756]) ).
cnf(t5047,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,complement(complement(X1)))),
inference(cp,[status(thm)],[t5043,t3474]) ).
cnf(t66854,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)),
inference(step,[status(thm)],[t5047,t919]) ).
cnf(t66855,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X1,X3)),
inference(step,[status(thm)],[t66854,t67]) ).
cnf(t5120,plain,
meet(meet(X1,X2),join(X1,X3)) = meet(X1,X2),
inference(orient,[status(thm)],[t66855]) ).
cnf(t5287,plain,
meet(complement(X1),complement(join(X1,X2))) = meet(complement(join(X1,X2)),join(complement(X1),X3)),
inference(cp,[status(thm)],[t5120,t5276]) ).
cnf(t67044,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),join(complement(X1),X3)),
inference(step,[status(thm)],[t5287,t5276]) ).
cnf(t67045,plain,
complement(join(X1,X2)) = meet(join(complement(X1),X3),complement(join(X1,X2))),
inference(step,[status(thm)],[t67044,t23]) ).
cnf(t67046,plain,
complement(join(X1,X2)) = meet(join(X3,complement(X1)),complement(join(X1,X2))),
inference(step,[status(thm)],[t67045,t67]) ).
cnf(t12399,plain,
meet(join(X1,complement(X2)),complement(join(X2,X3))) = complement(join(X2,X3)),
inference(orient,[status(thm)],[t67046]) ).
cnf(t12500,plain,
zero = meet(X1,complement(join(X2,meet(X1,join(X3,complement(X2)))))),
inference(cp,[status(thm)],[t6598,t12399]) ).
cnf(t15754,plain,
meet(X1,complement(join(X2,meet(X1,join(X3,complement(X2)))))) = zero,
inference(orient,[status(thm)],[t12500]) ).
cnf(t3676,plain,
complement(complement(X1)) = join(X1,complement(join(complement(X1),X2))),
inference(cp,[status(thm)],[t3675,t919]) ).
cnf(t66774,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(step,[status(thm)],[t3676,t919]) ).
cnf(t66775,plain,
X1 = join(X1,complement(join(X2,complement(X1)))),
inference(step,[status(thm)],[t66774,t67]) ).
cnf(t4049,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t66775]) ).
cnf(t15760,plain,
zero = meet(X1,complement(join(join(X2,complement(X3)),meet(X1,X3)))),
inference(cp,[status(thm)],[t15754,t4049]) ).
cnf(t67157,plain,
zero = meet(X1,complement(join(meet(X1,X3),join(X2,complement(X3))))),
inference(step,[status(thm)],[t15760,t67]) ).
cnf(t67158,plain,
zero = meet(X1,complement(join(complement(X3),join(meet(X1,X3),X2)))),
inference(step,[status(thm)],[t67157,t72]) ).
cnf(t67159,plain,
zero = meet(X1,complement(join(X2,join(complement(X3),meet(X1,X3))))),
inference(step,[status(thm)],[t67158,t72]) ).
cnf(t16046,plain,
meet(X1,complement(join(X2,join(complement(X3),meet(X1,X3))))) = zero,
inference(orient,[status(thm)],[t67159]) ).
cnf(t16050,plain,
zero = complement(join(X1,join(complement(X2),meet(complement(X1),X2)))),
inference(cp,[status(thm)],[t16046,t5276]) ).
cnf(t67160,plain,
zero = complement(join(X1,join(complement(X2),meet(X2,complement(X1))))),
inference(step,[status(thm)],[t16050,t23]) ).
cnf(t16181,plain,
complement(join(X1,join(complement(X2),meet(X2,complement(X1))))) = zero,
inference(orient,[status(thm)],[t67160]) ).
cnf(t16216,plain,
one = ifeq(zero,zero,join(X1,join(complement(X2),meet(X2,complement(X1)))),one),
inference(cp,[status(thm)],[t944,t16181]) ).
cnf(t67161,plain,
one = join(X1,join(complement(X2),meet(X2,complement(X1)))),
inference(step,[status(thm)],[t16216,t17]) ).
cnf(t16281,plain,
join(X1,join(complement(X2),meet(X2,complement(X1)))) = one,
inference(orient,[status(thm)],[t67161]) ).
cnf(t6600,plain,
zero = meet(X1,complement(join(X2,meet(X1,complement(X2))))),
inference(cp,[status(thm)],[t6598,t5276]) ).
cnf(t6723,plain,
meet(X1,complement(join(X2,meet(X1,complement(X2))))) = zero,
inference(orient,[status(thm)],[t6600]) ).
cnf(t6725,plain,
zero = meet(X1,complement(join(complement(X2),meet(X1,X2)))),
inference(cp,[status(thm)],[t6723,t919]) ).
cnf(t6777,plain,
meet(X1,complement(join(complement(X2),meet(X1,X2)))) = zero,
inference(orient,[status(thm)],[t6725]) ).
cnf(t16289,plain,
one = join(join(complement(X1),meet(X2,X1)),join(complement(X2),zero)),
inference(cp,[status(thm)],[t16281,t6777]) ).
cnf(t67163,plain,
one = join(join(complement(X1),meet(X2,X1)),complement(X2)),
inference(step,[status(thm)],[t16289,t100]) ).
cnf(t67164,plain,
one = join(complement(X2),join(complement(X1),meet(X2,X1))),
inference(step,[status(thm)],[t67163,t67]) ).
cnf(t67165,plain,
one = join(complement(X1),join(meet(X2,X1),complement(X2))),
inference(step,[status(thm)],[t67164,t72]) ).
cnf(t67166,plain,
one = join(complement(X1),join(complement(X2),meet(X2,X1))),
inference(step,[status(thm)],[t67165,t67]) ).
cnf(t67167,plain,
one = join(complement(X1),join(complement(X2),meet(X1,X2))),
inference(step,[status(thm)],[t67166,t23]) ).
cnf(t16383,plain,
join(complement(X1),join(complement(X2),meet(X1,X2))) = one,
inference(orient,[status(thm)],[t67167]) ).
cnf(t538,plain,
meet(X1,meet(join(zero,meet(X2,complement(X1))),X3)) = meet(X3,zero),
inference(cp,[status(thm)],[t26,t529]) ).
cnf(t66482,plain,
meet(X1,meet(X3,join(zero,meet(X2,complement(X1))))) = meet(X3,zero),
inference(step,[status(thm)],[t538,t23]) ).
cnf(t66483,plain,
meet(X1,meet(X3,join(zero,meet(X2,complement(X1))))) = zero,
inference(step,[status(thm)],[t66482,t123]) ).
cnf(t540,plain,
meet(X1,meet(X2,join(zero,meet(X3,complement(X1))))) = zero,
inference(orient,[status(thm)],[t66483]) ).
cnf(t1470,plain,
meet(X1,join(meet(X2,join(zero,meet(X3,complement(X1)))),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t1454,t540]) ).
cnf(t66727,plain,
meet(X1,join(complement(X1),meet(X2,join(zero,meet(X3,complement(X1)))))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t1470,t67]) ).
cnf(t66728,plain,
meet(X1,join(complement(X1),meet(X2,join(zero,meet(X3,complement(X1)))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t66727,t100]) ).
cnf(t66729,plain,
meet(X1,join(complement(X1),meet(X2,join(zero,meet(X3,complement(X1)))))) = zero,
inference(step,[status(thm)],[t66728,t61]) ).
cnf(t3030,plain,
meet(X1,join(complement(X1),meet(X2,join(zero,meet(X3,complement(X1)))))) = zero,
inference(orient,[status(thm)],[t66729]) ).
cnf(t3032,plain,
zero = meet(complement(X1),join(X1,meet(X2,join(zero,meet(X3,complement(complement(X1))))))),
inference(cp,[status(thm)],[t3030,t919]) ).
cnf(t66730,plain,
zero = meet(complement(X1),join(X1,meet(X2,join(zero,meet(X3,X1))))),
inference(step,[status(thm)],[t3032,t919]) ).
cnf(t66731,plain,
zero = meet(complement(X1),join(X1,meet(X2,join(zero,meet(X1,X3))))),
inference(step,[status(thm)],[t66730,t23]) ).
cnf(t3059,plain,
meet(complement(X1),join(X1,meet(X2,join(zero,meet(X1,X3))))) = zero,
inference(orient,[status(thm)],[t66731]) ).
cnf(t3511,plain,
zero = meet(meet(X1,X2),join(zero,meet(X3,complement(X1)))),
inference(cp,[status(thm)],[t1006,t3474]) ).
cnf(t4446,plain,
meet(meet(X1,X2),join(zero,meet(X3,complement(X1)))) = zero,
inference(orient,[status(thm)],[t3511]) ).
cnf(t4475,plain,
zero = meet(complement(meet(X1,X2)),join(meet(X1,X2),meet(X3,join(zero,zero)))),
inference(cp,[status(thm)],[t3059,t4446]) ).
cnf(t66817,plain,
zero = meet(complement(meet(X1,X2)),join(meet(X1,X2),meet(X3,zero))),
inference(step,[status(thm)],[t4475,t100]) ).
cnf(t66818,plain,
zero = meet(complement(meet(X1,X2)),join(meet(X1,X2),zero)),
inference(step,[status(thm)],[t66817,t123]) ).
cnf(t66819,plain,
zero = meet(complement(meet(X1,X2)),meet(X1,X2)),
inference(step,[status(thm)],[t66818,t100]) ).
cnf(t66820,plain,
zero = meet(X2,meet(complement(meet(X1,X2)),X1)),
inference(step,[status(thm)],[t66819,t26]) ).
cnf(t66821,plain,
zero = meet(X1,meet(X2,complement(meet(X1,X2)))),
inference(step,[status(thm)],[t66820,t26]) ).
cnf(t4480,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(orient,[status(thm)],[t66821]) ).
cnf(t4508,plain,
meet(X1,join(meet(X2,complement(meet(X1,X2))),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t1454,t4480]) ).
cnf(t66844,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t4508,t67]) ).
cnf(t66845,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t66844,t100]) ).
cnf(t66846,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(step,[status(thm)],[t66845,t61]) ).
cnf(t4881,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(orient,[status(thm)],[t66846]) ).
cnf(t125,plain,
zero = ifeq(zero,zero,ifeq(join(X1,zero),one,complement(X1),zero),zero),
inference(cp,[status(thm)],[t18,t123]) ).
cnf(t66396,plain,
zero = ifeq(join(X1,zero),one,complement(X1),zero),
inference(step,[status(thm)],[t125,t17]) ).
cnf(t66397,plain,
zero = ifeq(X1,one,complement(X1),zero),
inference(step,[status(thm)],[t66396,t100]) ).
cnf(t147,plain,
ifeq(X1,one,complement(X1),zero) = zero,
inference(orient,[status(thm)],[t66397]) ).
cnf(t923,plain,
zero = ifeq(complement(X1),one,X1,zero),
inference(cp,[status(thm)],[t147,t919]) ).
cnf(t945,plain,
ifeq(complement(X1),one,X1,zero) = zero,
inference(orient,[status(thm)],[t923]) ).
cnf(t5154,plain,
complement(meet(meet(X1,X2),join(X1,X3))) = join(complement(join(X1,X3)),complement(meet(X1,X2))),
inference(cp,[status(thm)],[t3564,t5120]) ).
cnf(t66948,plain,
complement(meet(X1,X2)) = join(complement(join(X1,X3)),complement(meet(X1,X2))),
inference(step,[status(thm)],[t5154,t5120]) ).
cnf(t66949,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(join(X1,X3))),
inference(step,[status(thm)],[t66948,t67]) ).
cnf(t8871,plain,
join(complement(meet(X1,X2)),complement(join(X1,X3))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t66949]) ).
cnf(t8916,plain,
one = join(join(X1,X2),complement(meet(X1,X3))),
inference(cp,[status(thm)],[t167,t8871]) ).
cnf(t8951,plain,
join(join(X1,X2),complement(meet(X1,X3))) = one,
inference(orient,[status(thm)],[t8916]) ).
cnf(t8954,plain,
one = join(complement(meet(X1,complement(X2))),complement(meet(X2,X3))),
inference(cp,[status(thm)],[t8951,t3371]) ).
cnf(t66962,plain,
one = join(complement(meet(X2,X3)),complement(meet(X1,complement(X2)))),
inference(step,[status(thm)],[t8954,t67]) ).
cnf(t9702,plain,
join(complement(meet(X1,X2)),complement(meet(X3,complement(X1)))) = one,
inference(orient,[status(thm)],[t66962]) ).
cnf(t9744,plain,
one = join(complement(meet(join(X1,X2),X3)),complement(complement(join(X1,X2)))),
inference(cp,[status(thm)],[t9702,t5276]) ).
cnf(t66984,plain,
one = join(complement(meet(join(X1,X2),X3)),join(X1,X2)),
inference(step,[status(thm)],[t9744,t919]) ).
cnf(t66985,plain,
one = join(X2,join(complement(meet(join(X1,X2),X3)),X1)),
inference(step,[status(thm)],[t66984,t72]) ).
cnf(t66986,plain,
one = join(X1,join(X2,complement(meet(join(X1,X2),X3)))),
inference(step,[status(thm)],[t66985,t72]) ).
cnf(t66987,plain,
one = join(X1,join(X2,complement(meet(X3,join(X1,X2))))),
inference(step,[status(thm)],[t66986,t23]) ).
cnf(t10476,plain,
join(X1,join(X2,complement(meet(X3,join(X1,X2))))) = one,
inference(orient,[status(thm)],[t66987]) ).
cnf(t5141,plain,
meet(X1,X2) = meet(meet(X1,X2),complement(meet(X3,complement(X1)))),
inference(cp,[status(thm)],[t5120,t3371]) ).
cnf(t5715,plain,
meet(meet(X1,X2),complement(meet(X3,complement(X1)))) = meet(X1,X2),
inference(orient,[status(thm)],[t5141]) ).
cnf(t5738,plain,
complement(meet(meet(X1,X2),complement(meet(X3,complement(X1))))) = join(complement(complement(meet(X3,complement(X1)))),complement(meet(X1,X2))),
inference(cp,[status(thm)],[t3564,t5715]) ).
cnf(t67060,plain,
complement(meet(X1,X2)) = join(complement(complement(meet(X3,complement(X1)))),complement(meet(X1,X2))),
inference(step,[status(thm)],[t5738,t5715]) ).
cnf(t67061,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(complement(meet(X3,complement(X1))))),
inference(step,[status(thm)],[t67060,t67]) ).
cnf(t67062,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),meet(X3,complement(X1))),
inference(step,[status(thm)],[t67061,t919]) ).
cnf(t67063,plain,
complement(meet(X1,X2)) = join(meet(X3,complement(X1)),complement(meet(X1,X2))),
inference(step,[status(thm)],[t67062,t67]) ).
cnf(t13309,plain,
join(meet(X1,complement(X2)),complement(meet(X2,X3))) = complement(meet(X2,X3)),
inference(orient,[status(thm)],[t67063]) ).
cnf(t13414,plain,
one = join(X1,complement(meet(X2,join(X1,meet(X3,complement(X2)))))),
inference(cp,[status(thm)],[t10476,t13309]) ).
cnf(t15848,plain,
join(X1,complement(meet(X2,join(X1,meet(X3,complement(X2)))))) = one,
inference(orient,[status(thm)],[t13414]) ).
cnf(t15850,plain,
one = join(X1,complement(meet(meet(X2,complement(X3)),join(X1,X3)))),
inference(cp,[status(thm)],[t15848,t3404]) ).
cnf(t67200,plain,
one = join(X1,complement(meet(join(X1,X3),meet(X2,complement(X3))))),
inference(step,[status(thm)],[t15850,t23]) ).
cnf(t67201,plain,
one = join(X1,complement(meet(complement(X3),meet(join(X1,X3),X2)))),
inference(step,[status(thm)],[t67200,t26]) ).
cnf(t67202,plain,
one = join(X1,complement(meet(X2,meet(complement(X3),join(X1,X3))))),
inference(step,[status(thm)],[t67201,t26]) ).
cnf(t18872,plain,
join(X1,complement(meet(X2,meet(complement(X3),join(X1,X3))))) = one,
inference(orient,[status(thm)],[t67202]) ).
cnf(t3419,plain,
complement(meet(X1,complement(meet(X2,complement(X1))))) = join(meet(X2,complement(X1)),complement(X1)),
inference(cp,[status(thm)],[t3371,t3404]) ).
cnf(t66757,plain,
complement(X1) = join(meet(X2,complement(X1)),complement(X1)),
inference(step,[status(thm)],[t3419,t3404]) ).
cnf(t66758,plain,
complement(X1) = join(complement(X1),meet(X2,complement(X1))),
inference(step,[status(thm)],[t66757,t67]) ).
cnf(t3540,plain,
join(complement(X1),meet(X2,complement(X1))) = complement(X1),
inference(orient,[status(thm)],[t66758]) ).
cnf(t3544,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t3540,t3474]) ).
cnf(t66778,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t3544,t67]) ).
cnf(t4087,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t66778]) ).
cnf(t18874,plain,
one = complement(meet(X1,meet(complement(X2),join(complement(X1),X2)))),
inference(cp,[status(thm)],[t18872,t4087]) ).
cnf(t67203,plain,
one = complement(meet(X1,meet(complement(X2),join(X2,complement(X1))))),
inference(step,[status(thm)],[t18874,t67]) ).
cnf(t18992,plain,
complement(meet(X1,meet(complement(X2),join(X2,complement(X1))))) = one,
inference(orient,[status(thm)],[t67203]) ).
cnf(t19031,plain,
zero = ifeq(one,one,meet(X1,meet(complement(X2),join(X2,complement(X1)))),zero),
inference(cp,[status(thm)],[t945,t18992]) ).
cnf(t67204,plain,
zero = meet(X1,meet(complement(X2),join(X2,complement(X1)))),
inference(step,[status(thm)],[t19031,t17]) ).
cnf(t19111,plain,
meet(X1,meet(complement(X2),join(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t67204]) ).
cnf(t10478,plain,
one = join(X1,complement(meet(X2,join(X1,complement(X2))))),
inference(cp,[status(thm)],[t10476,t4087]) ).
cnf(t10557,plain,
join(X1,complement(meet(X2,join(X1,complement(X2))))) = one,
inference(orient,[status(thm)],[t10478]) ).
cnf(t10559,plain,
one = join(X1,complement(meet(complement(X2),join(X1,X2)))),
inference(cp,[status(thm)],[t10557,t919]) ).
cnf(t10599,plain,
join(X1,complement(meet(complement(X2),join(X1,X2)))) = one,
inference(orient,[status(thm)],[t10559]) ).
cnf(t19122,plain,
zero = meet(meet(complement(X1),join(X2,X1)),meet(complement(X2),one)),
inference(cp,[status(thm)],[t19111,t10599]) ).
cnf(t67206,plain,
zero = meet(meet(complement(X1),join(X2,X1)),complement(X2)),
inference(step,[status(thm)],[t19122,t106]) ).
cnf(t67207,plain,
zero = meet(complement(X2),meet(complement(X1),join(X2,X1))),
inference(step,[status(thm)],[t67206,t23]) ).
cnf(t67208,plain,
zero = meet(complement(X1),meet(join(X2,X1),complement(X2))),
inference(step,[status(thm)],[t67207,t26]) ).
cnf(t67209,plain,
zero = meet(complement(X1),meet(complement(X2),join(X2,X1))),
inference(step,[status(thm)],[t67208,t23]) ).
cnf(t67210,plain,
zero = meet(complement(X1),meet(complement(X2),join(X1,X2))),
inference(step,[status(thm)],[t67209,t67]) ).
cnf(t19242,plain,
meet(complement(X1),meet(complement(X2),join(X1,X2))) = zero,
inference(orient,[status(thm)],[t67210]) ).
cnf(t19346,plain,
zero = meet(complement(X1),join(complement(complement(X1)),meet(meet(complement(X2),join(X1,X2)),complement(zero)))),
inference(cp,[status(thm)],[t4881,t19242]) ).
cnf(t67314,plain,
zero = meet(complement(X1),join(X1,meet(meet(complement(X2),join(X1,X2)),complement(zero)))),
inference(step,[status(thm)],[t19346,t919]) ).
cnf(t67315,plain,
zero = meet(complement(X1),join(X1,meet(complement(zero),meet(complement(X2),join(X1,X2))))),
inference(step,[status(thm)],[t67314,t23]) ).
cnf(t67316,plain,
zero = meet(complement(X1),join(X1,meet(complement(X2),meet(join(X1,X2),complement(zero))))),
inference(step,[status(thm)],[t67315,t26]) ).
cnf(t67317,plain,
zero = meet(complement(X1),join(X1,meet(complement(X2),meet(complement(zero),join(X1,X2))))),
inference(step,[status(thm)],[t67316,t23]) ).
cnf(t152,plain,
one = complement(zero),
inference(cp,[status(thm)],[t151,t17]) ).
cnf(t154,plain,
complement(zero) = one,
inference(orient,[status(thm)],[t152]) ).
cnf(t67318,plain,
zero = meet(complement(X1),join(X1,meet(complement(X2),meet(one,join(X1,X2))))),
inference(step,[status(thm)],[t67317,t154]) ).
cnf(t33,plain,
meet(X1,X2) = ifeq(meet(X2,meet(X3,X1)),zero,ifeq(join(X3,meet(X1,X2)),one,complement(X3),meet(X1,X2)),meet(X1,X2)),
inference(cp,[status(thm)],[t18,t26]) ).
cnf(t66773,plain,
meet(X1,X2) = ifeq(meet(X1,meet(X2,X3)),zero,ifeq(join(X3,meet(X1,X2)),one,complement(X3),meet(X1,X2)),meet(X1,X2)),
inference(step,[status(thm)],[t33,t26]) ).
cnf(t3719,plain,
ifeq(meet(X1,meet(X2,X3)),zero,ifeq(join(X3,meet(X1,X2)),one,complement(X3),meet(X1,X2)),meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t66773]) ).
cnf(t8955,plain,
one = join(complement(meet(X1,X2)),complement(meet(complement(X2),X3))),
inference(cp,[status(thm)],[t8951,t3564]) ).
cnf(t66963,plain,
one = join(complement(meet(X1,X2)),complement(meet(X3,complement(X2)))),
inference(step,[status(thm)],[t8955,t23]) ).
cnf(t9797,plain,
join(complement(meet(X1,X2)),complement(meet(X3,complement(X2)))) = one,
inference(orient,[status(thm)],[t66963]) ).
cnf(t9846,plain,
one = join(complement(meet(X1,X2)),complement(complement(X2))),
inference(cp,[status(thm)],[t9797,t13]) ).
cnf(t66964,plain,
one = join(complement(complement(X2)),complement(meet(X1,X2))),
inference(step,[status(thm)],[t9846,t67]) ).
cnf(t66965,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t66964,t919]) ).
cnf(t9875,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t66965]) ).
cnf(t6011,plain,
X1 = meet(X1,join(X2,meet(one,join(X1,X3)))),
inference(cp,[status(thm)],[t5997,t227]) ).
cnf(t6103,plain,
meet(X1,join(X2,meet(one,join(X1,X3)))) = X1,
inference(orient,[status(thm)],[t6011]) ).
cnf(t9877,plain,
one = join(join(X1,meet(one,join(X2,X3))),complement(X2)),
inference(cp,[status(thm)],[t9875,t6103]) ).
cnf(t66994,plain,
one = join(complement(X2),join(X1,meet(one,join(X2,X3)))),
inference(step,[status(thm)],[t9877,t67]) ).
cnf(t66995,plain,
one = join(X1,join(meet(one,join(X2,X3)),complement(X2))),
inference(step,[status(thm)],[t66994,t72]) ).
cnf(t66996,plain,
one = join(X1,join(complement(X2),meet(one,join(X2,X3)))),
inference(step,[status(thm)],[t66995,t67]) ).
cnf(t10660,plain,
join(X1,join(complement(X2),meet(one,join(X2,X3)))) = one,
inference(orient,[status(thm)],[t66996]) ).
cnf(t10661,plain,
one = join(complement(X1),meet(one,join(X1,X2))),
inference(cp,[status(thm)],[t10660,t129]) ).
cnf(t10706,plain,
join(complement(X1),meet(one,join(X1,X2))) = one,
inference(orient,[status(thm)],[t10661]) ).
cnf(t8940,plain,
join(X1,X2) = join(join(X1,X2),meet(X3,complement(complement(meet(X1,X4))))),
inference(cp,[status(thm)],[t7944,t8871]) ).
cnf(t66950,plain,
join(X1,X2) = join(join(X1,X2),meet(X3,meet(X1,X4))),
inference(step,[status(thm)],[t8940,t919]) ).
cnf(t66951,plain,
join(X1,X2) = join(join(X1,X2),meet(X1,meet(X4,X3))),
inference(step,[status(thm)],[t66950,t26]) ).
cnf(t66952,plain,
join(X1,X2) = join(join(X1,X2),meet(X1,meet(X3,X4))),
inference(step,[status(thm)],[t66951,t23]) ).
cnf(t9156,plain,
join(join(X1,X2),meet(X1,meet(X3,X4))) = join(X1,X2),
inference(orient,[status(thm)],[t66952]) ).
cnf(t5315,plain,
join(X1,X2) = meet(join(X1,X2),join(X3,complement(complement(join(X1,X2))))),
inference(cp,[status(thm)],[t5043,t5276]) ).
cnf(t66873,plain,
join(X1,X2) = meet(join(X1,X2),join(X3,join(X1,X2))),
inference(step,[status(thm)],[t5315,t919]) ).
cnf(t66874,plain,
join(X1,X2) = meet(join(X1,X2),join(X2,join(X3,X1))),
inference(step,[status(thm)],[t66873,t72]) ).
cnf(t66875,plain,
join(X1,X2) = meet(join(X1,X2),join(X1,join(X2,X3))),
inference(step,[status(thm)],[t66874,t72]) ).
cnf(t5797,plain,
meet(join(X1,X2),join(X1,join(X2,X3))) = join(X1,X2),
inference(orient,[status(thm)],[t66875]) ).
cnf(t9186,plain,
join(X1,X2) = join(join(X1,X2),meet(X1,join(X3,X4))),
inference(cp,[status(thm)],[t9156,t5797]) ).
cnf(t9296,plain,
join(join(X1,X2),meet(X1,join(X3,X4))) = join(X1,X2),
inference(orient,[status(thm)],[t9186]) ).
cnf(t10720,plain,
one = join(complement(join(X1,X2)),meet(one,join(X1,X2))),
inference(cp,[status(thm)],[t10706,t9296]) ).
cnf(t11507,plain,
join(complement(join(X1,X2)),meet(one,join(X1,X2))) = one,
inference(orient,[status(thm)],[t10720]) ).
cnf(t11542,plain,
meet(one,join(X1,X2)) = ifeq(meet(one,meet(join(X1,X2),complement(join(X1,X2)))),zero,ifeq(one,one,complement(complement(join(X1,X2))),meet(one,join(X1,X2))),meet(one,join(X1,X2))),
inference(cp,[status(thm)],[t3719,t11507]) ).
cnf(t67022,plain,
meet(one,join(X1,X2)) = ifeq(meet(one,zero),zero,ifeq(one,one,complement(complement(join(X1,X2))),meet(one,join(X1,X2))),meet(one,join(X1,X2))),
inference(step,[status(thm)],[t11542,t61]) ).
cnf(t67023,plain,
meet(one,join(X1,X2)) = ifeq(zero,zero,ifeq(one,one,complement(complement(join(X1,X2))),meet(one,join(X1,X2))),meet(one,join(X1,X2))),
inference(step,[status(thm)],[t67022,t123]) ).
cnf(t67024,plain,
meet(one,join(X1,X2)) = ifeq(one,one,complement(complement(join(X1,X2))),meet(one,join(X1,X2))),
inference(step,[status(thm)],[t67023,t17]) ).
cnf(t67025,plain,
meet(one,join(X1,X2)) = complement(complement(join(X1,X2))),
inference(step,[status(thm)],[t67024,t17]) ).
cnf(t67026,plain,
meet(one,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t67025,t919]) ).
cnf(t11562,plain,
meet(one,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t67026]) ).
cnf(t67319,plain,
zero = meet(complement(X1),join(X1,meet(complement(X2),join(X1,X2)))),
inference(step,[status(thm)],[t67318,t11562]) ).
cnf(t23943,plain,
meet(complement(X1),join(X1,meet(complement(X2),join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t67319]) ).
cnf(t24055,plain,
one = join(complement(complement(X1)),join(complement(join(X1,meet(complement(X2),join(X1,X2)))),zero)),
inference(cp,[status(thm)],[t16383,t23943]) ).
cnf(t67363,plain,
one = join(zero,join(complement(complement(X1)),complement(join(X1,meet(complement(X2),join(X1,X2)))))),
inference(step,[status(thm)],[t24055,t72]) ).
cnf(t67364,plain,
one = join(zero,join(X1,complement(join(X1,meet(complement(X2),join(X1,X2)))))),
inference(step,[status(thm)],[t67363,t919]) ).
cnf(t67365,plain,
one = join(X1,join(complement(join(X1,meet(complement(X2),join(X1,X2)))),zero)),
inference(step,[status(thm)],[t67364,t72]) ).
cnf(t67366,plain,
one = join(X1,complement(join(X1,meet(complement(X2),join(X1,X2))))),
inference(step,[status(thm)],[t67365,t100]) ).
cnf(t27361,plain,
join(X1,complement(join(X1,meet(complement(X2),join(X1,X2))))) = one,
inference(orient,[status(thm)],[t67366]) ).
cnf(t27487,plain,
X1 = ifeq(meet(X1,complement(join(X1,meet(complement(X2),join(X1,X2))))),zero,ifeq(one,one,complement(complement(join(X1,meet(complement(X2),join(X1,X2))))),X1),X1),
inference(cp,[status(thm)],[t875,t27361]) ).
cnf(t4413,plain,
zero = meet(meet(X1,X2),join(zero,meet(complement(X2),X3))),
inference(cp,[status(thm)],[t4407,t919]) ).
cnf(t66826,plain,
zero = meet(meet(X1,X2),join(zero,meet(X3,complement(X2)))),
inference(step,[status(thm)],[t4413,t23]) ).
cnf(t4543,plain,
meet(meet(X1,X2),join(zero,meet(X3,complement(X2)))) = zero,
inference(orient,[status(thm)],[t66826]) ).
cnf(t4563,plain,
zero = meet(X1,join(zero,meet(X2,complement(join(X1,X3))))),
inference(cp,[status(thm)],[t4543,t14]) ).
cnf(t4687,plain,
meet(X1,join(zero,meet(X2,complement(join(X1,X3))))) = zero,
inference(orient,[status(thm)],[t4563]) ).
cnf(t4688,plain,
zero = meet(X1,join(zero,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t4687,t13]) ).
cnf(t66831,plain,
zero = meet(X1,complement(join(X1,X2))),
inference(step,[status(thm)],[t4688,t448]) ).
cnf(t4723,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t66831]) ).
cnf(t67367,plain,
X1 = ifeq(zero,zero,ifeq(one,one,complement(complement(join(X1,meet(complement(X2),join(X1,X2))))),X1),X1),
inference(step,[status(thm)],[t27487,t4723]) ).
cnf(t67368,plain,
X1 = ifeq(one,one,complement(complement(join(X1,meet(complement(X2),join(X1,X2))))),X1),
inference(step,[status(thm)],[t67367,t17]) ).
cnf(t67369,plain,
X1 = complement(complement(join(X1,meet(complement(X2),join(X1,X2))))),
inference(step,[status(thm)],[t67368,t17]) ).
cnf(t67370,plain,
X1 = join(X1,meet(complement(X2),join(X1,X2))),
inference(step,[status(thm)],[t67369,t919]) ).
cnf(t27536,plain,
join(X1,meet(complement(X2),join(X1,X2))) = X1,
inference(orient,[status(thm)],[t67370]) ).
cnf(t27666,plain,
meet(complement(X1),join(X2,X1)) = meet(meet(complement(X1),join(X2,X1)),X2),
inference(cp,[status(thm)],[t8144,t27536]) ).
cnf(t67520,plain,
meet(complement(X1),join(X1,X2)) = meet(meet(complement(X1),join(X2,X1)),X2),
inference(step,[status(thm)],[t27666,t67]) ).
cnf(t67521,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,meet(complement(X1),join(X2,X1))),
inference(step,[status(thm)],[t67520,t23]) ).
cnf(t67522,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(step,[status(thm)],[t67521,t175]) ).
cnf(t39728,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t67522]) ).
cnf(t39754,plain,
meet(X1,complement(complement(X2))) = meet(X2,join(complement(X2),X1)),
inference(cp,[status(thm)],[t39728,t919]) ).
cnf(t67528,plain,
meet(X1,X2) = meet(X2,join(complement(X2),X1)),
inference(step,[status(thm)],[t39754,t919]) ).
cnf(t67529,plain,
meet(X1,X2) = meet(X2,join(X1,complement(X2))),
inference(step,[status(thm)],[t67528,t67]) ).
cnf(t40072,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,X1),
inference(orient,[status(thm)],[t67529]) ).
cnf(t16438,plain,
one = join(complement(X1),join(complement(meet(X2,complement(meet(X1,X2)))),zero)),
inference(cp,[status(thm)],[t16383,t4480]) ).
cnf(t67168,plain,
one = join(complement(X1),complement(meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t16438,t100]) ).
cnf(t16505,plain,
join(complement(X1),complement(meet(X2,complement(meet(X1,X2))))) = one,
inference(orient,[status(thm)],[t67168]) ).
cnf(t16506,plain,
one = join(X1,complement(meet(X2,complement(meet(complement(X1),X2))))),
inference(cp,[status(thm)],[t16505,t919]) ).
cnf(t67182,plain,
one = join(X1,complement(meet(X2,complement(meet(X2,complement(X1)))))),
inference(step,[status(thm)],[t16506,t23]) ).
cnf(t17041,plain,
join(X1,complement(meet(X2,complement(meet(X2,complement(X1)))))) = one,
inference(orient,[status(thm)],[t67182]) ).
cnf(t40093,plain,
meet(X1,meet(X2,complement(meet(X2,complement(X1))))) = meet(meet(X2,complement(meet(X2,complement(X1)))),one),
inference(cp,[status(thm)],[t40072,t17041]) ).
cnf(t3380,plain,
meet(X1,X2) = meet(X1,meet(X2,complement(meet(X3,complement(X1))))),
inference(cp,[status(thm)],[t175,t3371]) ).
cnf(t4340,plain,
meet(X1,meet(X2,complement(meet(X3,complement(X1))))) = meet(X1,X2),
inference(orient,[status(thm)],[t3380]) ).
cnf(t67547,plain,
meet(X1,X2) = meet(meet(X2,complement(meet(X2,complement(X1)))),one),
inference(step,[status(thm)],[t40093,t4340]) ).
cnf(t67548,plain,
meet(X1,X2) = meet(X2,complement(meet(X2,complement(X1)))),
inference(step,[status(thm)],[t67547,t106]) ).
cnf(t40787,plain,
meet(X1,complement(meet(X1,complement(X2)))) = meet(X2,X1),
inference(orient,[status(thm)],[t67548]) ).
cnf(t40842,plain,
meet(complement(X1),X2) = meet(X2,complement(meet(X2,X1))),
inference(cp,[status(thm)],[t40787,t919]) ).
cnf(t67558,plain,
meet(X2,complement(X1)) = meet(X2,complement(meet(X2,X1))),
inference(step,[status(thm)],[t40842,t23]) ).
cnf(t67559,plain,
meet(X2,complement(X1)) = meet(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t67558,t23]) ).
cnf(t41563,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t67559]) ).
cnf(t41669,plain,
meet(X1,complement(X2)) = meet(X1,complement(meet(X1,X2))),
inference(cp,[status(thm)],[t41563,t23]) ).
cnf(t42301,plain,
meet(X1,complement(meet(X1,X2))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t41669]) ).
cnf(t42306,plain,
meet(X1,complement(join(X2,complement(X1)))) = meet(X1,complement(meet(X2,X1))),
inference(cp,[status(thm)],[t42301,t40072]) ).
cnf(t5245,plain,
complement(join(X1,complement(X2))) = meet(complement(join(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t5243,t4049]) ).
cnf(t66864,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(join(X1,complement(X2)))),
inference(step,[status(thm)],[t5245,t23]) ).
cnf(t5457,plain,
meet(X1,complement(join(X2,complement(X1)))) = complement(join(X2,complement(X1))),
inference(orient,[status(thm)],[t66864]) ).
cnf(t67565,plain,
complement(join(X2,complement(X1))) = meet(X1,complement(meet(X2,X1))),
inference(step,[status(thm)],[t42306,t5457]) ).
cnf(t67566,plain,
complement(join(X2,complement(X1))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t67565,t41563]) ).
cnf(t42530,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t67566]) ).
cnf(t42574,plain,
join(X1,complement(X2)) = complement(meet(X2,complement(X1))),
inference(cp,[status(thm)],[t919,t42530]) ).
cnf(t43041,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t42574]) ).
cnf(t43042,plain,
join(meet(X1,X2),complement(X1)) = complement(meet(X1,complement(X2))),
inference(cp,[status(thm)],[t43041,t42301]) ).
cnf(t67610,plain,
join(complement(X1),meet(X1,X2)) = complement(meet(X1,complement(X2))),
inference(step,[status(thm)],[t43042,t67]) ).
cnf(t67611,plain,
join(complement(X1),meet(X1,X2)) = join(X2,complement(X1)),
inference(step,[status(thm)],[t67610,t43041]) ).
cnf(t43437,plain,
join(complement(X1),meet(X1,X2)) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t67611]) ).
cnf(t43446,plain,
join(X1,complement(complement(X2))) = join(X2,meet(complement(X2),X1)),
inference(cp,[status(thm)],[t43437,t919]) ).
cnf(t67619,plain,
join(X1,X2) = join(X2,meet(complement(X2),X1)),
inference(step,[status(thm)],[t43446,t919]) ).
cnf(t67620,plain,
join(X1,X2) = join(X2,meet(X1,complement(X2))),
inference(step,[status(thm)],[t67619,t23]) ).
cnf(t43686,plain,
join(X1,meet(X2,complement(X1))) = join(X2,X1),
inference(orient,[status(thm)],[t67620]) ).
cnf(t39908,plain,
meet(X1,complement(X2)) = meet(complement(X2),join(X1,X2)),
inference(cp,[status(thm)],[t39728,t67]) ).
cnf(t40305,plain,
meet(complement(X1),join(X2,X1)) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t39908]) ).
cnf(t42372,plain,
meet(complement(X1),complement(join(X2,X1))) = meet(complement(X1),complement(meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t42301,t40305]) ).
cnf(t5462,plain,
complement(join(X1,complement(complement(X2)))) = meet(complement(X2),complement(join(X1,X2))),
inference(cp,[status(thm)],[t5457,t919]) ).
cnf(t66866,plain,
complement(join(X1,X2)) = meet(complement(X2),complement(join(X1,X2))),
inference(step,[status(thm)],[t5462,t919]) ).
cnf(t5527,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(orient,[status(thm)],[t66866]) ).
cnf(t67585,plain,
complement(join(X2,X1)) = meet(complement(X1),complement(meet(X2,complement(X1)))),
inference(step,[status(thm)],[t42372,t5527]) ).
cnf(t67586,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(meet(X2,complement(X1)))),
inference(step,[status(thm)],[t67585,t67]) ).
cnf(t67587,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(X2)),
inference(step,[status(thm)],[t67586,t41563]) ).
cnf(t42843,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t67587]) ).
cnf(t43721,plain,
join(complement(X1),X2) = join(X2,complement(join(X1,X2))),
inference(cp,[status(thm)],[t43686,t42843]) ).
cnf(t67624,plain,
join(X2,complement(X1)) = join(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t43721,t67]) ).
cnf(t44048,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t67624]) ).
cnf(t9893,plain,
one = join(meet(X1,join(X2,X3)),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t9875,t175]) ).
cnf(t66998,plain,
one = join(complement(meet(X2,X1)),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t9893,t67]) ).
cnf(t66999,plain,
one = join(complement(meet(X1,X2)),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t66998,t23]) ).
cnf(t10786,plain,
join(complement(meet(X1,X2)),meet(X1,join(X2,X3))) = one,
inference(orient,[status(thm)],[t66999]) ).
cnf(t44099,plain,
join(meet(X1,join(X2,X3)),complement(complement(meet(X1,X2)))) = join(meet(X1,join(X2,X3)),complement(one)),
inference(cp,[status(thm)],[t44048,t10786]) ).
cnf(t67890,plain,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = join(meet(X1,join(X2,X3)),complement(one)),
inference(step,[status(thm)],[t44099,t919]) ).
cnf(t67891,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = join(meet(X1,join(X2,X3)),complement(one)),
inference(step,[status(thm)],[t67890,t67]) ).
cnf(t67892,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = join(complement(one),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t67891,t67]) ).
cnf(t148,plain,
zero = complement(one),
inference(cp,[status(thm)],[t147,t17]) ).
cnf(t149,plain,
complement(one) = zero,
inference(orient,[status(thm)],[t148]) ).
cnf(t67893,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = join(zero,meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t67892,t149]) ).
cnf(t9903,plain,
one = join(join(X1,join(X2,X3)),complement(join(X1,X2))),
inference(cp,[status(thm)],[t9875,t5797]) ).
cnf(t67000,plain,
one = join(complement(join(X1,X2)),join(X1,join(X2,X3))),
inference(step,[status(thm)],[t9903,t67]) ).
cnf(t67001,plain,
one = join(join(X2,X3),join(complement(join(X1,X2)),X1)),
inference(step,[status(thm)],[t67000,t72]) ).
cnf(t67002,plain,
one = join(X1,join(join(X2,X3),complement(join(X1,X2)))),
inference(step,[status(thm)],[t67001,t72]) ).
cnf(t10944,plain,
join(X1,join(join(X2,X3),complement(join(X1,X2)))) = one,
inference(orient,[status(thm)],[t67002]) ).
cnf(t10954,plain,
one = join(X1,join(join(X2,X3),complement(join(X1,X3)))),
inference(cp,[status(thm)],[t10944,t67]) ).
cnf(t11829,plain,
join(X1,join(join(X2,X3),complement(join(X1,X3)))) = one,
inference(orient,[status(thm)],[t10954]) ).
cnf(t11840,plain,
one = join(X1,join(X2,complement(join(X1,meet(X2,X3))))),
inference(cp,[status(thm)],[t11829,t16]) ).
cnf(t12140,plain,
join(X1,join(X2,complement(join(X1,meet(X2,X3))))) = one,
inference(orient,[status(thm)],[t11840]) ).
cnf(t12141,plain,
one = join(X1,join(complement(join(X2,meet(X1,X3))),X2)),
inference(cp,[status(thm)],[t12140,t72]) ).
cnf(t67031,plain,
one = join(X1,join(X2,complement(join(X2,meet(X1,X3))))),
inference(step,[status(thm)],[t12141,t67]) ).
cnf(t12177,plain,
join(X1,join(X2,complement(join(X2,meet(X1,X3))))) = one,
inference(orient,[status(thm)],[t67031]) ).
cnf(t12179,plain,
one = join(X1,complement(join(zero,meet(X1,X2)))),
inference(cp,[status(thm)],[t12177,t448]) ).
cnf(t12234,plain,
join(X1,complement(join(zero,meet(X1,X2)))) = one,
inference(orient,[status(thm)],[t12179]) ).
cnf(t12247,plain,
one = join(meet(X1,X2),complement(join(zero,meet(X1,X2)))),
inference(cp,[status(thm)],[t12234,t8144]) ).
cnf(t12285,plain,
join(meet(X1,X2),complement(join(zero,meet(X1,X2)))) = one,
inference(orient,[status(thm)],[t12247]) ).
cnf(t12322,plain,
meet(X1,X2) = ifeq(meet(meet(X1,X2),complement(join(zero,meet(X1,X2)))),zero,ifeq(one,one,complement(complement(join(zero,meet(X1,X2)))),meet(X1,X2)),meet(X1,X2)),
inference(cp,[status(thm)],[t875,t12285]) ).
cnf(t5543,plain,
zero = meet(complement(join(X1,X2)),complement(join(complement(X2),X3))),
inference(cp,[status(thm)],[t5415,t5527]) ).
cnf(t66886,plain,
zero = meet(complement(join(X1,X2)),complement(join(X3,complement(X2)))),
inference(step,[status(thm)],[t5543,t67]) ).
cnf(t6386,plain,
meet(complement(join(X1,X2)),complement(join(X3,complement(X2)))) = zero,
inference(orient,[status(thm)],[t66886]) ).
cnf(t6403,plain,
zero = meet(complement(join(X1,X2)),complement(complement(X2))),
inference(cp,[status(thm)],[t6386,t15]) ).
cnf(t66887,plain,
zero = meet(complement(complement(X2)),complement(join(X1,X2))),
inference(step,[status(thm)],[t6403,t23]) ).
cnf(t66888,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t66887,t919]) ).
cnf(t6433,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t66888]) ).
cnf(t67032,plain,
meet(X1,X2) = ifeq(zero,zero,ifeq(one,one,complement(complement(join(zero,meet(X1,X2)))),meet(X1,X2)),meet(X1,X2)),
inference(step,[status(thm)],[t12322,t6433]) ).
cnf(t67033,plain,
meet(X1,X2) = ifeq(one,one,complement(complement(join(zero,meet(X1,X2)))),meet(X1,X2)),
inference(step,[status(thm)],[t67032,t17]) ).
cnf(t67034,plain,
meet(X1,X2) = complement(complement(join(zero,meet(X1,X2)))),
inference(step,[status(thm)],[t67033,t17]) ).
cnf(t67035,plain,
meet(X1,X2) = join(zero,meet(X1,X2)),
inference(step,[status(thm)],[t67034,t919]) ).
cnf(t12339,plain,
join(zero,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t67035]) ).
cnf(t67894,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t67893,t12339]) ).
cnf(t65735,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t67894]) ).
cnf(t65769,plain,
meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t65735,t112]) ).
cnf(t67895,plain,
meet(X1,join(X3,meet(X1,X2))) = join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))),
inference(step,[status(thm)],[t65769,t67]) ).
cnf(t43070,plain,
join(join(X1,complement(X2)),complement(X3)) = complement(meet(X3,meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t43041,t42530]) ).
cnf(t67689,plain,
join(complement(X3),join(X1,complement(X2))) = complement(meet(X3,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t43070,t67]) ).
cnf(t67690,plain,
join(complement(X2),join(complement(X3),X1)) = complement(meet(X3,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t67689,t72]) ).
cnf(t67691,plain,
join(X1,join(complement(X2),complement(X3))) = complement(meet(X3,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t67690,t72]) ).
cnf(t43071,plain,
join(complement(X1),complement(X2)) = complement(meet(X2,X1)),
inference(cp,[status(thm)],[t43041,t919]) ).
cnf(t67606,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(step,[status(thm)],[t43071,t23]) ).
cnf(t43289,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t67606]) ).
cnf(t67692,plain,
join(X1,complement(meet(X2,X3))) = complement(meet(X3,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t67691,t43289]) ).
cnf(t67693,plain,
join(X1,complement(meet(X2,X3))) = complement(meet(X2,meet(complement(X1),X3))),
inference(step,[status(thm)],[t67692,t26]) ).
cnf(t67694,plain,
join(X1,complement(meet(X2,X3))) = complement(meet(X2,meet(X3,complement(X1)))),
inference(step,[status(thm)],[t67693,t23]) ).
cnf(t47933,plain,
complement(meet(X1,meet(X2,complement(X3)))) = join(X3,complement(meet(X1,X2))),
inference(orient,[status(thm)],[t67694]) ).
cnf(t48000,plain,
meet(X1,complement(meet(X2,complement(X3)))) = meet(X1,join(X3,complement(meet(X1,X2)))),
inference(cp,[status(thm)],[t42301,t47933]) ).
cnf(t67846,plain,
meet(X1,join(X3,complement(X2))) = meet(X1,join(X3,complement(meet(X1,X2)))),
inference(step,[status(thm)],[t48000,t43041]) ).
cnf(t60874,plain,
meet(X1,join(X2,complement(meet(X1,X3)))) = meet(X1,join(X2,complement(X3))),
inference(orient,[status(thm)],[t67846]) ).
cnf(t60904,plain,
meet(X1,join(X2,complement(complement(meet(X1,X3))))) = meet(X1,join(X2,complement(meet(X1,complement(X3))))),
inference(cp,[status(thm)],[t60874,t42301]) ).
cnf(t67849,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,complement(meet(X1,complement(X3))))),
inference(step,[status(thm)],[t60904,t919]) ).
cnf(t67850,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,complement(complement(X3)))),
inference(step,[status(thm)],[t67849,t60874]) ).
cnf(t67851,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t67850,t919]) ).
cnf(t61065,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t67851]) ).
cnf(t67896,plain,
meet(X1,join(X3,X2)) = join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))),
inference(step,[status(thm)],[t67895,t61065]) ).
cnf(t67897,plain,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))),
inference(step,[status(thm)],[t67896,t67]) ).
cnf(t44114,plain,
join(X1,complement(X2)) = join(X1,complement(join(X1,X2))),
inference(cp,[status(thm)],[t44048,t67]) ).
cnf(t44201,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t44114]) ).
cnf(t42857,plain,
complement(join(join(X1,complement(X2)),X3)) = meet(meet(X2,complement(X1)),complement(X3)),
inference(cp,[status(thm)],[t42843,t42530]) ).
cnf(t67681,plain,
complement(join(X3,join(X1,complement(X2)))) = meet(meet(X2,complement(X1)),complement(X3)),
inference(step,[status(thm)],[t42857,t67]) ).
cnf(t67682,plain,
complement(join(X1,join(complement(X2),X3))) = meet(meet(X2,complement(X1)),complement(X3)),
inference(step,[status(thm)],[t67681,t72]) ).
cnf(t67683,plain,
complement(join(X1,join(X3,complement(X2)))) = meet(meet(X2,complement(X1)),complement(X3)),
inference(step,[status(thm)],[t67682,t67]) ).
cnf(t67684,plain,
complement(join(X1,join(X3,complement(X2)))) = meet(complement(X3),meet(X2,complement(X1))),
inference(step,[status(thm)],[t67683,t23]) ).
cnf(t67685,plain,
complement(join(X1,join(X3,complement(X2)))) = meet(complement(X1),meet(complement(X3),X2)),
inference(step,[status(thm)],[t67684,t26]) ).
cnf(t67686,plain,
complement(join(X1,join(X3,complement(X2)))) = meet(X2,meet(complement(X1),complement(X3))),
inference(step,[status(thm)],[t67685,t26]) ).
cnf(t67687,plain,
complement(join(X1,join(X3,complement(X2)))) = meet(X2,complement(join(X1,X3))),
inference(step,[status(thm)],[t67686,t42843]) ).
cnf(t47743,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(X3,complement(join(X1,X2))),
inference(orient,[status(thm)],[t67687]) ).
cnf(t47810,plain,
join(X1,complement(join(X2,complement(X3)))) = join(X1,meet(X3,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t44201,t47743]) ).
cnf(t67838,plain,
join(X1,meet(X3,complement(X2))) = join(X1,meet(X3,complement(join(X1,X2)))),
inference(step,[status(thm)],[t47810,t42530]) ).
cnf(t60203,plain,
join(X1,meet(X2,complement(join(X1,X3)))) = join(X1,meet(X2,complement(X3))),
inference(orient,[status(thm)],[t67838]) ).
cnf(t60231,plain,
join(X1,meet(X2,complement(complement(join(X1,X3))))) = join(X1,meet(X2,complement(join(X1,complement(X3))))),
inference(cp,[status(thm)],[t60203,t44201]) ).
cnf(t67839,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,complement(join(X1,complement(X3))))),
inference(step,[status(thm)],[t60231,t919]) ).
cnf(t67840,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,complement(complement(X3)))),
inference(step,[status(thm)],[t67839,t60203]) ).
cnf(t67841,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t67840,t919]) ).
cnf(t60381,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t67841]) ).
cnf(t67898,plain,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
inference(step,[status(thm)],[t67897,t60381]) ).
cnf(t66016,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t67898]) ).
cnf(f12,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f12_nnf,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
join(meet(a,b),meet(a,c)) != meet(a,join(b,c)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
meet(a,join(b,c)) != meet(a,join(b,c)),
inference(rw,[status(thm)],[goal_0,t66016]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT199-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 20:31:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 51.42/7.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.42/7.06 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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