%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT200-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 42.26s 6.63s
% Output : Proof 42.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 102
% Number of leaves : 14
% Syntax : Number of formulae : 399 ( 395 unt; 0 def)
% Number of atoms : 407 ( 406 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 17 ~; 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 : 878 ( 111 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t52,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
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(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(t25,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1),
inference(cp,[status(thm)],[t18,t23]) ).
cnf(t10294,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t25]) ).
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(t47,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t10346,plain,
X1 = ifeq(zero,zero,ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t10294,t47]) ).
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(t119274,plain,
X1 = ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t10346,t17]) ).
cnf(t119275,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t119274,t52]) ).
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(t69,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t119276,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t119275,t69]) ).
cnf(t119277,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t119276,t17]) ).
cnf(t18820,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t119277]) ).
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(t26,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
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(t53,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t14,t52]) ).
cnf(t122,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t53]) ).
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(t124,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t122,t16]) ).
cnf(t119110,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t124,t26]) ).
cnf(t149,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t119110]) ).
cnf(t155,plain,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3),
inference(cp,[status(thm)],[t26,t149]) ).
cnf(t119160,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3),
inference(step,[status(thm)],[t155,t26]) ).
cnf(t119161,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t119160,t26]) ).
cnf(t1313,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t119161]) ).
cnf(t24,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t16,t23]) ).
cnf(t114,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t24]) ).
cnf(f11,axiom,
meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(X,meet(Z,join(Y,U)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H50) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(X,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,meet(Z,join(X,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,meet(X2,join(X0,meet(X2,join(X1,X3)))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
meet(X1,join(X2,meet(X3,join(X1,meet(X3,join(X2,X4)))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
meet(X1,join(X2,meet(X3,join(X1,meet(X3,join(X2,X4)))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t12]) ).
cnf(t28,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t2207,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t28]) ).
cnf(t32,plain,
meet(X1,meet(X2,X3)) = meet(meet(X2,X1),X3),
inference(cp,[status(thm)],[t26,t23]) ).
cnf(t119163,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t32,t26]) ).
cnf(t1676,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t119163]) ).
cnf(t2209,plain,
meet(X1,X2) = meet(X2,meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t2207,t1676]) ).
cnf(t4099,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t2209]) ).
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(t57,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t62,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t57,t16]) ).
cnf(t320,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t62]) ).
cnf(t332,plain,
join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)),
inference(cp,[status(thm)],[t122,t320]) ).
cnf(t119279,plain,
join(meet(X1,X2),X3) = meet(join(X1,X3),join(meet(X1,X2),X3)),
inference(step,[status(thm)],[t332,t23]) ).
cnf(t19120,plain,
meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2),
inference(orient,[status(thm)],[t119279]) ).
cnf(t19138,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))),
inference(cp,[status(thm)],[t19120,t16]) ).
cnf(t42048,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(orient,[status(thm)],[t19138]) ).
cnf(t42250,plain,
meet(X1,X2) = meet(X2,join(meet(X1,X2),meet(X1,X3))),
inference(cp,[status(thm)],[t4099,t42048]) ).
cnf(t42304,plain,
meet(X1,join(meet(X2,X1),meet(X2,X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t42250]) ).
cnf(t42453,plain,
meet(X1,X2) = meet(X2,join(meet(X2,X1),meet(X1,X3))),
inference(cp,[status(thm)],[t42304,t23]) ).
cnf(t43559,plain,
meet(X1,join(meet(X1,X2),meet(X2,X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t42453]) ).
cnf(t118,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t114,t26]) ).
cnf(t257,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t118]) ).
cnf(t116,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t114,t14]) ).
cnf(t119109,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t116,t57]) ).
cnf(t141,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t119109]) ).
cnf(t145,plain,
join(X1,X2) = meet(join(X1,X2),join(X2,X1)),
inference(cp,[status(thm)],[t122,t141]) ).
cnf(t392,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t145]) ).
cnf(t416,plain,
join(X1,X2) = join(join(X1,X2),meet(X3,join(X2,X1))),
inference(cp,[status(thm)],[t257,t392]) ).
cnf(t119169,plain,
join(X1,X2) = join(X1,join(X2,meet(X3,join(X2,X1)))),
inference(step,[status(thm)],[t416,t57]) ).
cnf(t3087,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t119169]) ).
cnf(t31,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t302,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t31]) ).
cnf(t315,plain,
meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)),
inference(cp,[status(thm)],[t114,t302]) ).
cnf(t119278,plain,
meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)),
inference(step,[status(thm)],[t315,t52]) ).
cnf(t18844,plain,
join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2),
inference(orient,[status(thm)],[t119278]) ).
cnf(t18866,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))),
inference(cp,[status(thm)],[t18844,t14]) ).
cnf(t34858,plain,
join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)),
inference(orient,[status(thm)],[t18866]) ).
cnf(t35040,plain,
join(X1,X2) = join(X1,meet(join(X2,X3),join(X2,X1))),
inference(cp,[status(thm)],[t3087,t34858]) ).
cnf(t35480,plain,
join(X1,meet(join(X2,X3),join(X2,X1))) = join(X1,X2),
inference(orient,[status(thm)],[t35040]) ).
cnf(t59,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(cp,[status(thm)],[t57,t16]) ).
cnf(t2325,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(orient,[status(thm)],[t59]) ).
cnf(t63,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t57,t52]) ).
cnf(t119164,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t63,t57]) ).
cnf(t1933,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t119164]) ).
cnf(t2327,plain,
join(X1,X2) = join(X2,join(X1,meet(join(X1,X2),X3))),
inference(cp,[status(thm)],[t2325,t1933]) ).
cnf(t4250,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(orient,[status(thm)],[t2327]) ).
cnf(t35035,plain,
join(X1,X2) = join(X2,meet(join(X1,X2),join(X1,X3))),
inference(cp,[status(thm)],[t4250,t34858]) ).
cnf(t35087,plain,
join(X1,meet(join(X2,X1),join(X2,X3))) = join(X2,X1),
inference(orient,[status(thm)],[t35035]) ).
cnf(t35493,plain,
join(X1,X2) = join(X1,meet(join(X3,X2),join(X2,X1))),
inference(cp,[status(thm)],[t35480,t35087]) ).
cnf(t36652,plain,
join(X1,meet(join(X2,X3),join(X3,X1))) = join(X1,X3),
inference(orient,[status(thm)],[t35493]) ).
cnf(t36835,plain,
join(X1,X2) = join(X1,meet(join(X3,X2),join(X1,X2))),
inference(cp,[status(thm)],[t36652,t52]) ).
cnf(t37740,plain,
join(X1,meet(join(X2,X3),join(X1,X3))) = join(X1,X3),
inference(orient,[status(thm)],[t36835]) ).
cnf(t43588,plain,
meet(join(X1,X2),X3) = meet(X3,join(meet(X3,join(X1,X2)),X2)),
inference(cp,[status(thm)],[t43559,t37740]) ).
cnf(t119330,plain,
meet(join(X1,X2),X3) = meet(X3,join(X2,meet(X3,join(X1,X2)))),
inference(step,[status(thm)],[t43588,t52]) ).
cnf(t46933,plain,
meet(X1,join(X2,meet(X1,join(X3,X2)))) = meet(join(X3,X2),X1),
inference(orient,[status(thm)],[t119330]) ).
cnf(t47271,plain,
meet(X1,join(X2,meet(X3,join(X1,X1)))) = meet(X1,join(X2,meet(join(X2,X1),X3))),
inference(cp,[status(thm)],[t35,t46933]) ).
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(t119333,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,meet(join(X2,X1),X3))),
inference(step,[status(thm)],[t47271,t15]) ).
cnf(t52961,plain,
meet(X1,join(X2,meet(join(X2,X1),X3))) = meet(X1,join(X2,meet(X3,X1))),
inference(orient,[status(thm)],[t119333]) ).
cnf(t53232,plain,
meet(complement(X1),join(X1,meet(X2,complement(X1)))) = meet(complement(X1),join(X1,meet(one,X2))),
inference(cp,[status(thm)],[t52961,t69]) ).
cnf(t71,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t14,t69]) ).
cnf(t79,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t71]) ).
cnf(t80,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t79,t23]) ).
cnf(t93,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t80]) ).
cnf(t119334,plain,
meet(complement(X1),join(X1,meet(X2,complement(X1)))) = meet(complement(X1),join(X1,X2)),
inference(step,[status(thm)],[t53232,t93]) ).
cnf(t53491,plain,
meet(complement(X1),join(X1,meet(X2,complement(X1)))) = meet(complement(X1),join(X1,X2)),
inference(orient,[status(thm)],[t119334]) ).
cnf(t53508,plain,
join(X1,meet(X2,complement(X1))) = join(join(X1,meet(X2,complement(X1))),meet(complement(X1),join(X1,X2))),
inference(cp,[status(thm)],[t114,t53491]) ).
cnf(t119337,plain,
join(X1,meet(X2,complement(X1))) = join(X1,join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2)))),
inference(step,[status(thm)],[t53508,t57]) ).
cnf(t125,plain,
X1 = meet(X1,join(X2,join(X3,X1))),
inference(cp,[status(thm)],[t122,t57]) ).
cnf(t271,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(orient,[status(thm)],[t125]) ).
cnf(t276,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)),
inference(cp,[status(thm)],[t271,t16]) ).
cnf(t119133,plain,
meet(X1,X2) = meet(X1,meet(X2,join(X3,X1))),
inference(step,[status(thm)],[t276,t26]) ).
cnf(t477,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t119133]) ).
cnf(t495,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X3,X1)),
inference(cp,[status(thm)],[t114,t477]) ).
cnf(t119285,plain,
meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t495,t52]) ).
cnf(t22273,plain,
join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X3,X1)),
inference(orient,[status(thm)],[t119285]) ).
cnf(t119338,plain,
join(X1,meet(X2,complement(X1))) = join(X1,meet(complement(X1),join(X1,X2))),
inference(step,[status(thm)],[t119337,t22273]) ).
cnf(t54002,plain,
join(X1,meet(complement(X1),join(X1,X2))) = join(X1,meet(X2,complement(X1))),
inference(orient,[status(thm)],[t119338]) ).
cnf(t72,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t57,t69]) ).
cnf(t95,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t93,t14]) ).
cnf(t106,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t95]) ).
cnf(t119122,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t72,t106]) ).
cnf(t205,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t119122]) ).
cnf(t208,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t141,t205]) ).
cnf(t119123,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t208,t57]) ).
cnf(t119124,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t119123,t57]) ).
cnf(t107,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t106,t52]) ).
cnf(t111,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t107]) ).
cnf(t119125,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t119124,t111]) ).
cnf(t119126,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t119125,t111]) ).
cnf(t218,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t119126]) ).
cnf(t223,plain,
one = join(complement(meet(X1,X2)),X1),
inference(cp,[status(thm)],[t218,t16]) ).
cnf(t119127,plain,
one = join(X1,complement(meet(X1,X2))),
inference(step,[status(thm)],[t223,t52]) ).
cnf(t231,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(orient,[status(thm)],[t119127]) ).
cnf(t54111,plain,
join(X1,meet(complement(meet(X1,X2)),complement(X1))) = join(X1,meet(complement(X1),one)),
inference(cp,[status(thm)],[t54002,t231]) ).
cnf(t119339,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = join(X1,meet(complement(X1),one)),
inference(step,[status(thm)],[t54111,t23]) ).
cnf(t119340,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = join(X1,complement(X1)),
inference(step,[status(thm)],[t119339,t79]) ).
cnf(t119341,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = one,
inference(step,[status(thm)],[t119340,t69]) ).
cnf(t54347,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = one,
inference(orient,[status(thm)],[t119341]) ).
cnf(t54408,plain,
meet(complement(X1),complement(meet(X1,X2))) = ifeq(meet(X1,meet(complement(X1),complement(meet(X1,X2)))),zero,ifeq(one,one,complement(X1),meet(complement(X1),complement(meet(X1,X2)))),meet(complement(X1),complement(meet(X1,X2)))),
inference(cp,[status(thm)],[t18,t54347]) ).
cnf(t49,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t26,t47]) ).
cnf(t50,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t16,t47]) ).
cnf(t74,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t50]) ).
cnf(t75,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t74,t52]) ).
cnf(t83,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t75]) ).
cnf(t85,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t83,t16]) ).
cnf(t103,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t85]) ).
cnf(t119115,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t49,t103]) ).
cnf(t159,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t119115]) ).
cnf(t119342,plain,
meet(complement(X1),complement(meet(X1,X2))) = ifeq(zero,zero,ifeq(one,one,complement(X1),meet(complement(X1),complement(meet(X1,X2)))),meet(complement(X1),complement(meet(X1,X2)))),
inference(step,[status(thm)],[t54408,t159]) ).
cnf(t119343,plain,
meet(complement(X1),complement(meet(X1,X2))) = ifeq(one,one,complement(X1),meet(complement(X1),complement(meet(X1,X2)))),
inference(step,[status(thm)],[t119342,t17]) ).
cnf(t119344,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(step,[status(thm)],[t119343,t17]) ).
cnf(t54542,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t119344]) ).
cnf(t35214,plain,
join(X1,X2) = join(X2,meet(join(X2,X1),join(X1,X3))),
inference(cp,[status(thm)],[t35087,t52]) ).
cnf(t35792,plain,
join(X1,meet(join(X1,X2),join(X2,X3))) = join(X2,X1),
inference(orient,[status(thm)],[t35214]) ).
cnf(t35947,plain,
join(X1,X2) = join(X2,meet(join(X2,X1),join(X3,X1))),
inference(cp,[status(thm)],[t35792,t35087]) ).
cnf(t37264,plain,
join(X1,meet(join(X1,X2),join(X3,X2))) = join(X2,X1),
inference(orient,[status(thm)],[t35947]) ).
cnf(t37503,plain,
join(meet(X1,X2),X3) = join(X3,meet(join(X3,meet(X1,X2)),X2)),
inference(cp,[status(thm)],[t37264,t114]) ).
cnf(t119326,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t37503,t23]) ).
cnf(t38996,plain,
join(X1,meet(X2,join(X1,meet(X3,X2)))) = join(meet(X3,X2),X1),
inference(orient,[status(thm)],[t119326]) ).
cnf(t42321,plain,
meet(X1,X2) = meet(X2,join(meet(X3,X1),meet(X1,X2))),
inference(cp,[status(thm)],[t42304,t38996]) ).
cnf(t43084,plain,
meet(X1,join(meet(X2,X3),meet(X3,X1))) = meet(X3,X1),
inference(orient,[status(thm)],[t42321]) ).
cnf(t43737,plain,
meet(X1,X2) = meet(X2,join(meet(X2,X1),meet(X3,X1))),
inference(cp,[status(thm)],[t43559,t43084]) ).
cnf(t45330,plain,
meet(X1,join(meet(X1,X2),meet(X3,X2))) = meet(X2,X1),
inference(orient,[status(thm)],[t43737]) ).
cnf(t54549,plain,
complement(X1) = meet(complement(X1),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t54542,t45330]) ).
cnf(t55094,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(orient,[status(thm)],[t54549]) ).
cnf(t55168,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t114,t55094]) ).
cnf(t119350,plain,
complement(meet(X1,X2)) = join(complement(X2),complement(meet(X1,X2))),
inference(step,[status(thm)],[t55168,t52]) ).
cnf(t56663,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(orient,[status(thm)],[t119350]) ).
cnf(t70,plain,
one = join(X1,join(X2,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t69,t57]) ).
cnf(t557,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(orient,[status(thm)],[t70]) ).
cnf(t54105,plain,
join(X1,meet(join(X2,complement(join(X1,X2))),complement(X1))) = join(X1,meet(complement(X1),one)),
inference(cp,[status(thm)],[t54002,t557]) ).
cnf(t119428,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = join(X1,meet(complement(X1),one)),
inference(step,[status(thm)],[t54105,t23]) ).
cnf(t119429,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = join(X1,complement(X1)),
inference(step,[status(thm)],[t119428,t79]) ).
cnf(t119430,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = one,
inference(step,[status(thm)],[t119429,t69]) ).
cnf(t96543,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = one,
inference(orient,[status(thm)],[t119430]) ).
cnf(t96711,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = ifeq(meet(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))),zero,ifeq(one,one,complement(X1),meet(complement(X1),join(X2,complement(join(X1,X2))))),meet(complement(X1),join(X2,complement(join(X1,X2))))),
inference(cp,[status(thm)],[t18,t96543]) ).
cnf(t119431,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = ifeq(zero,zero,ifeq(one,one,complement(X1),meet(complement(X1),join(X2,complement(join(X1,X2))))),meet(complement(X1),join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t96711,t159]) ).
cnf(t119432,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = ifeq(one,one,complement(X1),meet(complement(X1),join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t119431,t17]) ).
cnf(t119433,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = complement(X1),
inference(step,[status(thm)],[t119432,t17]) ).
cnf(t96858,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = complement(X1),
inference(orient,[status(thm)],[t119433]) ).
cnf(t96986,plain,
complement(meet(complement(X1),join(X2,complement(join(X1,X2))))) = join(complement(join(X2,complement(join(X1,X2)))),complement(complement(X1))),
inference(cp,[status(thm)],[t56663,t96858]) ).
cnf(t119435,plain,
complement(complement(X1)) = join(complement(join(X2,complement(join(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t96986,t96858]) ).
cnf(t119436,plain,
X1 = join(complement(join(X2,complement(join(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t119435,t18820]) ).
cnf(t119437,plain,
X1 = join(complement(complement(X1)),complement(join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t119436,t52]) ).
cnf(t119438,plain,
X1 = join(X1,complement(join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t119437,t18820]) ).
cnf(t97523,plain,
join(X1,complement(join(X2,complement(join(X1,X2))))) = X1,
inference(orient,[status(thm)],[t119438]) ).
cnf(t224,plain,
one = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t218,t114]) ).
cnf(t119128,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t224,t52]) ).
cnf(t239,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t119128]) ).
cnf(t243,plain,
one = join(X1,complement(meet(X2,meet(X3,X1)))),
inference(cp,[status(thm)],[t239,t26]) ).
cnf(t825,plain,
join(X1,complement(meet(X2,meet(X3,X1)))) = one,
inference(orient,[status(thm)],[t243]) ).
cnf(t838,plain,
one = join(join(X1,X2),complement(meet(X3,join(X2,X1)))),
inference(cp,[status(thm)],[t825,t392]) ).
cnf(t119233,plain,
one = join(X1,join(X2,complement(meet(X3,join(X2,X1))))),
inference(step,[status(thm)],[t838,t57]) ).
cnf(t9833,plain,
join(X1,join(X2,complement(meet(X3,join(X2,X1))))) = one,
inference(orient,[status(thm)],[t119233]) ).
cnf(t54578,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t114,t54542]) ).
cnf(t119346,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t54578,t52]) ).
cnf(t55314,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t119346]) ).
cnf(t55483,plain,
one = join(X1,complement(meet(X2,join(complement(X2),X1)))),
inference(cp,[status(thm)],[t9833,t55314]) ).
cnf(t59825,plain,
join(X1,complement(meet(X2,join(complement(X2),X1)))) = one,
inference(orient,[status(thm)],[t55483]) ).
cnf(t97532,plain,
X1 = join(X1,complement(join(complement(meet(X2,join(complement(X2),X1))),complement(one)))),
inference(cp,[status(thm)],[t97523,t59825]) ).
cnf(t119439,plain,
X1 = join(X1,complement(join(complement(one),complement(meet(X2,join(complement(X2),X1)))))),
inference(step,[status(thm)],[t97532,t52]) ).
cnf(t94,plain,
complement(one) = zero,
inference(cp,[status(thm)],[t93,t47]) ).
cnf(t101,plain,
complement(one) = zero,
inference(orient,[status(thm)],[t94]) ).
cnf(t119440,plain,
X1 = join(X1,complement(join(zero,complement(meet(X2,join(complement(X2),X1)))))),
inference(step,[status(thm)],[t119439,t101]) ).
cnf(t119441,plain,
X1 = join(X1,complement(complement(meet(X2,join(complement(X2),X1))))),
inference(step,[status(thm)],[t119440,t83]) ).
cnf(t119442,plain,
X1 = join(X1,meet(X2,join(complement(X2),X1))),
inference(step,[status(thm)],[t119441,t18820]) ).
cnf(t97898,plain,
join(X1,meet(X2,join(complement(X2),X1))) = X1,
inference(orient,[status(thm)],[t119442]) ).
cnf(t53496,plain,
meet(complement(complement(X1)),join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(cp,[status(thm)],[t53491,t18820]) ).
cnf(t119335,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t53496,t18820]) ).
cnf(t119336,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X2,X1))),
inference(step,[status(thm)],[t119335,t18820]) ).
cnf(t53675,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),X2)),
inference(orient,[status(thm)],[t119336]) ).
cnf(t97904,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,join(complement(X2),X1))),
inference(cp,[status(thm)],[t97898,t53675]) ).
cnf(t119443,plain,
meet(X1,X2) = meet(X2,join(complement(X2),X1)),
inference(step,[status(thm)],[t97904,t22273]) ).
cnf(t98278,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(orient,[status(thm)],[t119443]) ).
cnf(t98610,plain,
meet(X1,meet(X2,join(complement(X1),X3))) = meet(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t1313,t98278]) ).
cnf(t153,plain,
meet(X1,meet(X2,X3)) = meet(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t149,t26]) ).
cnf(t1261,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t153]) ).
cnf(t119516,plain,
meet(X1,meet(X2,join(complement(X1),X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t98610,t1261]) ).
cnf(t108117,plain,
meet(X1,meet(X2,join(complement(X1),X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t119516]) ).
cnf(t108163,plain,
meet(X1,meet(complement(X2),complement(join(X2,complement(X1))))) = meet(X1,complement(X2)),
inference(cp,[status(thm)],[t108117,t96858]) ).
cnf(t55141,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t55094,t14]) ).
cnf(t119347,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t55141,t23]) ).
cnf(t55497,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t119347]) ).
cnf(t119517,plain,
meet(X1,complement(join(X2,complement(X1)))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t108163,t55497]) ).
cnf(t55533,plain,
complement(X1) = join(complement(X1),complement(join(X1,X2))),
inference(cp,[status(thm)],[t16,t55497]) ).
cnf(t55678,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t55533]) ).
cnf(t55679,plain,
complement(complement(X1)) = join(X1,complement(join(complement(X1),X2))),
inference(cp,[status(thm)],[t55678,t18820]) ).
cnf(t119348,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(step,[status(thm)],[t55679,t18820]) ).
cnf(t55858,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t119348]) ).
cnf(t55865,plain,
X1 = join(X1,complement(join(X2,complement(X1)))),
inference(cp,[status(thm)],[t55858,t37264]) ).
cnf(t56049,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t55865]) ).
cnf(t56054,plain,
complement(join(X1,complement(X2))) = meet(complement(join(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t122,t56049]) ).
cnf(t119353,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(join(X1,complement(X2)))),
inference(step,[status(thm)],[t56054,t23]) ).
cnf(t57437,plain,
meet(X1,complement(join(X2,complement(X1)))) = complement(join(X2,complement(X1))),
inference(orient,[status(thm)],[t119353]) ).
cnf(t119518,plain,
complement(join(X2,complement(X1))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t119517,t57437]) ).
cnf(t108530,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t119518]) ).
cnf(t108564,plain,
join(X1,complement(X2)) = complement(meet(X2,complement(X1))),
inference(cp,[status(thm)],[t18820,t108530]) ).
cnf(t109323,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t108564]) ).
cnf(t109336,plain,
join(X1,complement(X2)) = complement(meet(complement(X1),X2)),
inference(cp,[status(thm)],[t109323,t23]) ).
cnf(t109508,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t109336]) ).
cnf(t54103,plain,
join(X1,meet(join(X2,X1),complement(X1))) = join(X1,meet(complement(X1),join(X1,X2))),
inference(cp,[status(thm)],[t54002,t141]) ).
cnf(t119389,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X1,meet(complement(X1),join(X1,X2))),
inference(step,[status(thm)],[t54103,t23]) ).
cnf(t119390,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X1,meet(X2,complement(X1))),
inference(step,[status(thm)],[t119389,t54002]) ).
cnf(t75718,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X1,meet(X2,complement(X1))),
inference(orient,[status(thm)],[t119390]) ).
cnf(t98384,plain,
meet(meet(complement(complement(X1)),join(X2,complement(X1))),X1) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(cp,[status(thm)],[t98278,t75718]) ).
cnf(t119448,plain,
meet(complement(complement(X1)),meet(join(X2,complement(X1)),X1)) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t98384,t26]) ).
cnf(t29,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(cp,[status(thm)],[t26,t23]) ).
cnf(t1505,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(orient,[status(thm)],[t29]) ).
cnf(t1530,plain,
meet(meet(X1,X2),meet(X3,X2)) = meet(X3,meet(X2,X1)),
inference(cp,[status(thm)],[t1505,t149]) ).
cnf(t119165,plain,
meet(X1,meet(X2,meet(X3,X2))) = meet(X3,meet(X2,X1)),
inference(step,[status(thm)],[t1530,t26]) ).
cnf(t119166,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(step,[status(thm)],[t119165,t149]) ).
cnf(t2020,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(orient,[status(thm)],[t119166]) ).
cnf(t119449,plain,
meet(X1,meet(join(X2,complement(X1)),complement(complement(X1)))) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t119448,t2020]) ).
cnf(t119450,plain,
meet(X1,meet(complement(complement(X1)),join(X2,complement(X1)))) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t119449,t23]) ).
cnf(t119451,plain,
meet(X1,meet(X1,join(X2,complement(X1)))) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t119450,t18820]) ).
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(t30,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(cp,[status(thm)],[t26,t13]) ).
cnf(t130,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t30]) ).
cnf(t119452,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t119451,t130]) ).
cnf(t119453,plain,
meet(X1,join(X2,complement(X1))) = meet(meet(X2,complement(complement(X1))),X1),
inference(step,[status(thm)],[t119452,t98278]) ).
cnf(t119454,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,meet(complement(complement(X1)),X1)),
inference(step,[status(thm)],[t119453,t26]) ).
cnf(t119455,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,meet(X1,complement(complement(X1)))),
inference(step,[status(thm)],[t119454,t23]) ).
cnf(t119456,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,meet(X1,X1)),
inference(step,[status(thm)],[t119455,t18820]) ).
cnf(t119457,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,X1),
inference(step,[status(thm)],[t119456,t13]) ).
cnf(t98724,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,X1),
inference(orient,[status(thm)],[t119457]) ).
cnf(t240,plain,
one = join(X1,join(X2,complement(meet(X3,join(X1,X2))))),
inference(cp,[status(thm)],[t239,t57]) ).
cnf(t4983,plain,
join(X1,join(X2,complement(meet(X3,join(X1,X2))))) = one,
inference(orient,[status(thm)],[t240]) ).
cnf(t54543,plain,
complement(complement(X1)) = meet(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t54542,t18820]) ).
cnf(t119345,plain,
X1 = meet(X1,complement(meet(complement(X1),X2))),
inference(step,[status(thm)],[t54543,t18820]) ).
cnf(t54724,plain,
meet(X1,complement(meet(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t119345]) ).
cnf(t54747,plain,
complement(meet(complement(X1),X2)) = join(complement(meet(complement(X1),X2)),X1),
inference(cp,[status(thm)],[t114,t54724]) ).
cnf(t119351,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(meet(complement(X1),X2))),
inference(step,[status(thm)],[t54747,t52]) ).
cnf(t56891,plain,
join(X1,complement(meet(complement(X1),X2))) = complement(meet(complement(X1),X2)),
inference(orient,[status(thm)],[t119351]) ).
cnf(t57071,plain,
one = join(X1,complement(meet(complement(X2),join(X1,X2)))),
inference(cp,[status(thm)],[t4983,t56891]) ).
cnf(t63061,plain,
join(X1,complement(meet(complement(X2),join(X1,X2)))) = one,
inference(orient,[status(thm)],[t57071]) ).
cnf(t98740,plain,
meet(X1,meet(complement(X2),join(X1,X2))) = meet(meet(complement(X2),join(X1,X2)),one),
inference(cp,[status(thm)],[t98724,t63061]) ).
cnf(t307,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,meet(join(X1,X3),X2)),
inference(cp,[status(thm)],[t302,t149]) ).
cnf(t119134,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(step,[status(thm)],[t307,t302]) ).
cnf(t504,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t119134]) ).
cnf(t119458,plain,
meet(X1,complement(X2)) = meet(meet(complement(X2),join(X1,X2)),one),
inference(step,[status(thm)],[t98740,t504]) ).
cnf(t119459,plain,
meet(X1,complement(X2)) = meet(complement(X2),meet(join(X1,X2),one)),
inference(step,[status(thm)],[t119458,t26]) ).
cnf(t119460,plain,
meet(X1,complement(X2)) = meet(one,meet(join(X1,X2),complement(X2))),
inference(step,[status(thm)],[t119459,t2020]) ).
cnf(t119461,plain,
meet(X1,complement(X2)) = meet(join(X1,X2),complement(X2)),
inference(step,[status(thm)],[t119460,t93]) ).
cnf(t119462,plain,
meet(X1,complement(X2)) = meet(complement(X2),join(X1,X2)),
inference(step,[status(thm)],[t119461,t23]) ).
cnf(t99470,plain,
meet(complement(X1),join(X2,X1)) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t119462]) ).
cnf(t109515,plain,
join(X1,complement(join(X2,X1))) = complement(meet(X2,complement(X1))),
inference(cp,[status(thm)],[t109508,t99470]) ).
cnf(t119586,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t109515,t109323]) ).
cnf(t110757,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t119586]) ).
cnf(t222,plain,
one = join(complement(join(X1,X2)),join(X2,X1)),
inference(cp,[status(thm)],[t218,t141]) ).
cnf(t119146,plain,
one = join(join(X2,X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t222,t52]) ).
cnf(t119147,plain,
one = join(X2,join(X1,complement(join(X1,X2)))),
inference(step,[status(thm)],[t119146,t57]) ).
cnf(t730,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(orient,[status(thm)],[t119147]) ).
cnf(t96931,plain,
complement(X1) = meet(complement(X1),join(join(X2,complement(join(X2,X1))),complement(one))),
inference(cp,[status(thm)],[t96858,t730]) ).
cnf(t119507,plain,
complement(X1) = meet(complement(X1),join(X2,join(complement(join(X2,X1)),complement(one)))),
inference(step,[status(thm)],[t96931,t57]) ).
cnf(t119508,plain,
complement(X1) = meet(complement(X1),join(X2,join(complement(one),complement(join(X2,X1))))),
inference(step,[status(thm)],[t119507,t52]) ).
cnf(t119509,plain,
complement(X1) = meet(complement(X1),join(X2,join(zero,complement(join(X2,X1))))),
inference(step,[status(thm)],[t119508,t101]) ).
cnf(t119510,plain,
complement(X1) = meet(complement(X1),join(X2,complement(join(X2,X1)))),
inference(step,[status(thm)],[t119509,t83]) ).
cnf(t106138,plain,
meet(complement(X1),join(X2,complement(join(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t119510]) ).
cnf(t108164,plain,
meet(X1,meet(complement(X2),complement(join(complement(X1),X2)))) = meet(X1,complement(X2)),
inference(cp,[status(thm)],[t108117,t106138]) ).
cnf(t55148,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t55094,t122]) ).
cnf(t119349,plain,
complement(join(X1,X2)) = meet(complement(X2),complement(join(X1,X2))),
inference(step,[status(thm)],[t55148,t23]) ).
cnf(t56441,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(orient,[status(thm)],[t119349]) ).
cnf(t119530,plain,
meet(X1,complement(join(complement(X1),X2))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t108164,t56441]) ).
cnf(t55498,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(join(complement(X1),X2))),
inference(cp,[status(thm)],[t55497,t18820]) ).
cnf(t57249,plain,
meet(X1,complement(join(complement(X1),X2))) = complement(join(complement(X1),X2)),
inference(orient,[status(thm)],[t55498]) ).
cnf(t119531,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t119530,t57249]) ).
cnf(t108780,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t119531]) ).
cnf(t110761,plain,
join(X1,complement(complement(X2))) = join(X1,meet(X2,complement(X1))),
inference(cp,[status(thm)],[t110757,t108780]) ).
cnf(t119587,plain,
join(X1,X2) = join(X1,meet(X2,complement(X1))),
inference(step,[status(thm)],[t110761,t18820]) ).
cnf(t111066,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t119587]) ).
cnf(t111078,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t111066,t23]) ).
cnf(t111278,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t111078]) ).
cnf(t111292,plain,
join(X1,meet(X2,join(complement(complement(X1)),X3))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(cp,[status(thm)],[t111278,t108117]) ).
cnf(t119624,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(step,[status(thm)],[t111292,t18820]) ).
cnf(t119625,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t119624,t111278]) ).
cnf(t115243,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t119625]) ).
cnf(t146,plain,
join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3),
inference(cp,[status(thm)],[t57,t141]) ).
cnf(t119158,plain,
join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3),
inference(step,[status(thm)],[t146,t57]) ).
cnf(t119159,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t119158,t57]) ).
cnf(t1199,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t119159]) ).
cnf(t98444,plain,
meet(join(X1,join(complement(X2),X3)),X2) = meet(X2,join(complement(X2),join(X1,X3))),
inference(cp,[status(thm)],[t98278,t1199]) ).
cnf(t119511,plain,
meet(X2,join(X1,join(complement(X2),X3))) = meet(X2,join(complement(X2),join(X1,X3))),
inference(step,[status(thm)],[t98444,t23]) ).
cnf(t119512,plain,
meet(X2,join(X1,join(complement(X2),X3))) = meet(join(X1,X3),X2),
inference(step,[status(thm)],[t119511,t98278]) ).
cnf(t106495,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(join(X2,X3),X1),
inference(orient,[status(thm)],[t119512]) ).
cnf(t111184,plain,
meet(join(X1,meet(X2,complement(complement(X3)))),X3) = meet(X3,join(X1,join(complement(X3),X2))),
inference(cp,[status(thm)],[t106495,t111066]) ).
cnf(t119611,plain,
meet(X3,join(X1,meet(X2,complement(complement(X3))))) = meet(X3,join(X1,join(complement(X3),X2))),
inference(step,[status(thm)],[t111184,t23]) ).
cnf(t119612,plain,
meet(X3,join(X1,meet(X2,X3))) = meet(X3,join(X1,join(complement(X3),X2))),
inference(step,[status(thm)],[t119611,t18820]) ).
cnf(t119613,plain,
meet(X3,join(X1,meet(X2,X3))) = meet(join(X1,X2),X3),
inference(step,[status(thm)],[t119612,t106495]) ).
cnf(t114734,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(join(X2,X3),X1),
inference(orient,[status(thm)],[t119613]) ).
cnf(t114831,plain,
meet(join(X1,X2),X3) = meet(X3,join(meet(X2,X3),X1)),
inference(cp,[status(thm)],[t114734,t52]) ).
cnf(t116141,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(join(X3,X2),X1),
inference(orient,[status(thm)],[t114831]) ).
cnf(t116506,plain,
join(meet(X1,X2),meet(X2,X3)) = join(meet(X1,X2),meet(join(X3,X1),X2)),
inference(cp,[status(thm)],[t115243,t116141]) ).
cnf(t126,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t26,t122]) ).
cnf(t365,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t126]) ).
cnf(t385,plain,
meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)),
inference(cp,[status(thm)],[t114,t365]) ).
cnf(t119281,plain,
meet(join(X1,X2),X3) = join(meet(X2,X3),meet(join(X1,X2),X3)),
inference(step,[status(thm)],[t385,t52]) ).
cnf(t20384,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(orient,[status(thm)],[t119281]) ).
cnf(t119678,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(join(X3,X1),X2),
inference(step,[status(thm)],[t116506,t20384]) ).
cnf(t118506,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(join(X3,X1),X2),
inference(orient,[status(thm)],[t119678]) ).
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,
join(meet(a,c),meet(a,b)) != meet(a,join(b,c)),
inference(rw,[status(thm)],[goal_0,t52]) ).
cnf(g0_1,plain,
join(meet(c,a),meet(a,b)) != meet(a,join(b,c)),
inference(rw,[status(thm)],[g0_0,t23]) ).
cnf(g0_2,plain,
meet(join(b,c),a) != meet(a,join(b,c)),
inference(rw,[status(thm)],[g0_1,t118506]) ).
cnf(g0_3,plain,
meet(a,join(b,c)) != meet(a,join(b,c)),
inference(rw,[status(thm)],[g0_2,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT200-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Wed Sep 23 20:26:59 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 42.26/6.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.26/6.63 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------