%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT195-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 01:55:51 PM UTC 2026
% Result : Unsatisfiable 40.26s 5.64s
% Output : Proof 40.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 13
% Syntax : Number of formulae : 312 ( 308 unt; 0 def)
% Number of atoms : 320 ( 319 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 16 ~; 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 : 678 ( 82 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox2/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(t51,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(f4,axiom,
meet(X,Y) = meet(Y,X),
file('/export/starexec/sandbox2/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/sandbox2/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(t10278,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/sandbox2/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(t46,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t10330,plain,
X1 = ifeq(zero,zero,ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t10278,t46]) ).
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(t93504,plain,
X1 = ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t10330,t17]) ).
cnf(t93505,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t93504,t51]) ).
cnf(f8,axiom,
join(X,complement(X)) = one,
file('/export/starexec/sandbox2/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(t67,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t93506,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t93505,t67]) ).
cnf(t93507,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t93506,t17]) ).
cnf(t18794,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t93507]) ).
cnf(f2,axiom,
meet(X,join(X,Y)) = X,
file('/export/starexec/sandbox2/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(t52,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t14,t51]) ).
cnf(t121,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t52]) ).
cnf(f7,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('/export/starexec/sandbox2/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(t55,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t125,plain,
X1 = meet(X1,join(X2,join(X3,X1))),
inference(cp,[status(thm)],[t121,t55]) ).
cnf(t271,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(orient,[status(thm)],[t125]) ).
cnf(f3,axiom,
join(X,meet(X,Y)) = X,
file('/export/starexec/sandbox2/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(t24,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t16,t23]) ).
cnf(t113,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t24]) ).
cnf(t124,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t121,t16]) ).
cnf(f6,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('/export/starexec/sandbox2/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(t93340,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)],[t93340]) ).
cnf(t154,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,X1)),
inference(cp,[status(thm)],[t113,t149]) ).
cnf(t419,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t154]) ).
cnf(t445,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,meet(X2,X1))),
inference(cp,[status(thm)],[t271,t419]) ).
cnf(t93400,plain,
meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X2,X1)))),
inference(step,[status(thm)],[t445,t26]) ).
cnf(t3160,plain,
meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2),
inference(orient,[status(thm)],[t93400]) ).
cnf(t115,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t113,t14]) ).
cnf(t93339,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t115,t55]) ).
cnf(t141,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t93339]) ).
cnf(t146,plain,
join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3),
inference(cp,[status(thm)],[t55,t141]) ).
cnf(t93388,plain,
join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3),
inference(step,[status(thm)],[t146,t55]) ).
cnf(t93389,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t93388,t55]) ).
cnf(t1197,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t93389]) ).
cnf(t1249,plain,
join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))),
inference(cp,[status(thm)],[t271,t1197]) ).
cnf(t3608,plain,
meet(join(X1,X2),join(X1,join(X3,X2))) = join(X1,X2),
inference(orient,[status(thm)],[t1249]) ).
cnf(t3660,plain,
join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)),
inference(cp,[status(thm)],[t3608,t16]) ).
cnf(t93534,plain,
join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,meet(X2,X3))),
inference(step,[status(thm)],[t3660,t23]) ).
cnf(t29180,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t93534]) ).
cnf(f11,axiom,
meet(X,join(Y,meet(Z,U))) = meet(X,join(Y,meet(Z,join(Y,meet(U,join(Y,Z)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H34) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,U))) = meet(X,join(Y,meet(Z,join(Y,meet(U,join(Y,Z)))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,U))) = meet(X,join(Y,meet(Z,join(Y,meet(U,join(Y,Z)))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,X3))) = meet(X0,join(X1,meet(X2,join(X1,meet(X3,join(X1,X2)))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
meet(X1,join(X2,meet(X3,join(X2,meet(X4,join(X2,X3)))))) = meet(X1,join(X2,meet(X3,X4))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
meet(X1,join(X2,meet(X3,join(X2,meet(X4,join(X2,X3)))))) = meet(X1,join(X2,meet(X3,X4))),
inference(orient,[status(thm)],[t12]) ).
cnf(f0,axiom,
meet(X,X) = X,
file('/export/starexec/sandbox2/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(t36,plain,
meet(join(X1,meet(X2,join(X1,meet(X3,join(X1,X2))))),join(X1,meet(X2,X3))) = join(X1,meet(X2,join(X1,meet(X3,join(X1,X2))))),
inference(cp,[status(thm)],[t35,t13]) ).
cnf(t93542,plain,
meet(join(X1,meet(X2,X3)),join(X1,meet(X2,join(X1,meet(X3,join(X1,X2)))))) = join(X1,meet(X2,join(X1,meet(X3,join(X1,X2))))),
inference(step,[status(thm)],[t36,t23]) ).
cnf(t93543,plain,
meet(join(X1,meet(X2,X3)),join(X1,meet(X2,X3))) = join(X1,meet(X2,join(X1,meet(X3,join(X1,X2))))),
inference(step,[status(thm)],[t93542,t35]) ).
cnf(t93544,plain,
join(X1,meet(X2,X3)) = join(X1,meet(X2,join(X1,meet(X3,join(X1,X2))))),
inference(step,[status(thm)],[t93543,t13]) ).
cnf(t32863,plain,
join(X1,meet(X2,join(X1,meet(X3,join(X1,X2))))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t93544]) ).
cnf(t32954,plain,
join(X1,meet(complement(X1),X2)) = join(X1,meet(complement(X1),join(X1,meet(X2,one)))),
inference(cp,[status(thm)],[t32863,t67]) ).
cnf(t69,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t14,t67]) ).
cnf(t77,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t69]) ).
cnf(t93545,plain,
join(X1,meet(complement(X1),X2)) = join(X1,meet(complement(X1),join(X1,X2))),
inference(step,[status(thm)],[t32954,t77]) ).
cnf(t33170,plain,
join(X1,meet(complement(X1),join(X1,X2))) = join(X1,meet(complement(X1),X2)),
inference(orient,[status(thm)],[t93545]) ).
cnf(t70,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t55,t67]) ).
cnf(t78,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t77,t23]) ).
cnf(t91,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t78]) ).
cnf(t93,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t91,t14]) ).
cnf(t105,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t93]) ).
cnf(t93352,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t70,t105]) ).
cnf(t205,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t93352]) ).
cnf(t208,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t141,t205]) ).
cnf(t93353,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t208,t55]) ).
cnf(t93354,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t93353,t55]) ).
cnf(t106,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t105,t51]) ).
cnf(t110,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t106]) ).
cnf(t93355,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t93354,t110]) ).
cnf(t93356,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t93355,t110]) ).
cnf(t218,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t93356]) ).
cnf(t223,plain,
one = join(complement(meet(X1,X2)),X1),
inference(cp,[status(thm)],[t218,t16]) ).
cnf(t93357,plain,
one = join(X1,complement(meet(X1,X2))),
inference(step,[status(thm)],[t223,t51]) ).
cnf(t231,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(orient,[status(thm)],[t93357]) ).
cnf(t33229,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = join(X1,meet(complement(X1),one)),
inference(cp,[status(thm)],[t33170,t231]) ).
cnf(t93546,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = join(X1,complement(X1)),
inference(step,[status(thm)],[t33229,t77]) ).
cnf(t93547,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = one,
inference(step,[status(thm)],[t93546,t67]) ).
cnf(t33411,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = one,
inference(orient,[status(thm)],[t93547]) ).
cnf(t33458,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,t33411]) ).
cnf(t48,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t26,t46]) ).
cnf(t49,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t16,t46]) ).
cnf(t72,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t49]) ).
cnf(t73,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t72,t51]) ).
cnf(t81,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t73]) ).
cnf(t83,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t81,t16]) ).
cnf(t101,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t83]) ).
cnf(t93345,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t48,t101]) ).
cnf(t159,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t93345]) ).
cnf(t93548,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)],[t33458,t159]) ).
cnf(t93549,plain,
meet(complement(X1),complement(meet(X1,X2))) = ifeq(one,one,complement(X1),meet(complement(X1),complement(meet(X1,X2)))),
inference(step,[status(thm)],[t93548,t17]) ).
cnf(t93550,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(step,[status(thm)],[t93549,t17]) ).
cnf(t33561,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t93550]) ).
cnf(t28,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t2205,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(t93393,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t32,t26]) ).
cnf(t1674,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t93393]) ).
cnf(t2207,plain,
meet(X1,X2) = meet(X2,meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t2205,t1674]) ).
cnf(t4091,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t2207]) ).
cnf(t33563,plain,
complement(X1) = meet(complement(X1),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t33561,t4091]) ).
cnf(t33968,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(orient,[status(thm)],[t33563]) ).
cnf(t34014,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t113,t33968]) ).
cnf(t93556,plain,
complement(meet(X1,X2)) = join(complement(X2),complement(meet(X1,X2))),
inference(step,[status(thm)],[t34014,t51]) ).
cnf(t35103,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(orient,[status(thm)],[t93556]) ).
cnf(t68,plain,
one = join(X1,join(X2,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t67,t55]) ).
cnf(t555,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(orient,[status(thm)],[t68]) ).
cnf(t33223,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = join(X1,meet(complement(X1),one)),
inference(cp,[status(thm)],[t33170,t555]) ).
cnf(t93633,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = join(X1,complement(X1)),
inference(step,[status(thm)],[t33223,t77]) ).
cnf(t93634,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = one,
inference(step,[status(thm)],[t93633,t67]) ).
cnf(t66306,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = one,
inference(orient,[status(thm)],[t93634]) ).
cnf(t66461,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,t66306]) ).
cnf(t93635,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)],[t66461,t159]) ).
cnf(t93636,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)],[t93635,t17]) ).
cnf(t93637,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = complement(X1),
inference(step,[status(thm)],[t93636,t17]) ).
cnf(t66578,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = complement(X1),
inference(orient,[status(thm)],[t93637]) ).
cnf(t66697,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)],[t35103,t66578]) ).
cnf(t93639,plain,
complement(complement(X1)) = join(complement(join(X2,complement(join(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t66697,t66578]) ).
cnf(t93640,plain,
X1 = join(complement(join(X2,complement(join(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t93639,t18794]) ).
cnf(t93641,plain,
X1 = join(complement(complement(X1)),complement(join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t93640,t51]) ).
cnf(t93642,plain,
X1 = join(X1,complement(join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t93641,t18794]) ).
cnf(t67129,plain,
join(X1,complement(join(X2,complement(join(X1,X2))))) = X1,
inference(orient,[status(thm)],[t93642]) ).
cnf(t224,plain,
one = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t218,t113]) ).
cnf(t93358,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t224,t51]) ).
cnf(t239,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t93358]) ).
cnf(t243,plain,
one = join(X1,complement(meet(X2,meet(X3,X1)))),
inference(cp,[status(thm)],[t239,t26]) ).
cnf(t823,plain,
join(X1,complement(meet(X2,meet(X3,X1)))) = one,
inference(orient,[status(thm)],[t243]) ).
cnf(t145,plain,
join(X1,X2) = meet(join(X1,X2),join(X2,X1)),
inference(cp,[status(thm)],[t121,t141]) ).
cnf(t391,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t145]) ).
cnf(t836,plain,
one = join(join(X1,X2),complement(meet(X3,join(X2,X1)))),
inference(cp,[status(thm)],[t823,t391]) ).
cnf(t93463,plain,
one = join(X1,join(X2,complement(meet(X3,join(X2,X1))))),
inference(step,[status(thm)],[t836,t55]) ).
cnf(t9817,plain,
join(X1,join(X2,complement(meet(X3,join(X2,X1))))) = one,
inference(orient,[status(thm)],[t93463]) ).
cnf(t33583,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t113,t33561]) ).
cnf(t93552,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t33583,t51]) ).
cnf(t34123,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t93552]) ).
cnf(t34240,plain,
one = join(X1,complement(meet(X2,join(complement(X2),X1)))),
inference(cp,[status(thm)],[t9817,t34123]) ).
cnf(t37430,plain,
join(X1,complement(meet(X2,join(complement(X2),X1)))) = one,
inference(orient,[status(thm)],[t34240]) ).
cnf(t67138,plain,
X1 = join(X1,complement(join(complement(meet(X2,join(complement(X2),X1))),complement(one)))),
inference(cp,[status(thm)],[t67129,t37430]) ).
cnf(t93643,plain,
X1 = join(X1,complement(join(complement(one),complement(meet(X2,join(complement(X2),X1)))))),
inference(step,[status(thm)],[t67138,t51]) ).
cnf(t92,plain,
complement(one) = zero,
inference(cp,[status(thm)],[t91,t46]) ).
cnf(t99,plain,
complement(one) = zero,
inference(orient,[status(thm)],[t92]) ).
cnf(t93644,plain,
X1 = join(X1,complement(join(zero,complement(meet(X2,join(complement(X2),X1)))))),
inference(step,[status(thm)],[t93643,t99]) ).
cnf(t93645,plain,
X1 = join(X1,complement(complement(meet(X2,join(complement(X2),X1))))),
inference(step,[status(thm)],[t93644,t81]) ).
cnf(t93646,plain,
X1 = join(X1,meet(X2,join(complement(X2),X1))),
inference(step,[status(thm)],[t93645,t18794]) ).
cnf(t67453,plain,
join(X1,meet(X2,join(complement(X2),X1))) = X1,
inference(orient,[status(thm)],[t93646]) ).
cnf(t67589,plain,
join(X1,meet(meet(X2,join(complement(X2),X1)),X3)) = meet(X1,join(X1,meet(meet(X2,join(complement(X2),X1)),X3))),
inference(cp,[status(thm)],[t29180,t67453]) ).
cnf(t93696,plain,
join(X1,meet(X2,meet(join(complement(X2),X1),X3))) = meet(X1,join(X1,meet(meet(X2,join(complement(X2),X1)),X3))),
inference(step,[status(thm)],[t67589,t26]) ).
cnf(t93697,plain,
join(X1,meet(X2,meet(join(complement(X2),X1),X3))) = X1,
inference(step,[status(thm)],[t93696,t14]) ).
cnf(t72546,plain,
join(X1,meet(X2,meet(join(complement(X2),X1),X3))) = X1,
inference(orient,[status(thm)],[t93697]) ).
cnf(t72837,plain,
meet(meet(join(complement(X1),X2),X3),X1) = meet(meet(join(complement(X1),X2),X3),meet(X1,X2)),
inference(cp,[status(thm)],[t3160,t72546]) ).
cnf(t93698,plain,
meet(join(complement(X1),X2),meet(X3,X1)) = meet(meet(join(complement(X1),X2),X3),meet(X1,X2)),
inference(step,[status(thm)],[t72837,t26]) ).
cnf(t29,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(cp,[status(thm)],[t26,t23]) ).
cnf(t1503,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(orient,[status(thm)],[t29]) ).
cnf(t1528,plain,
meet(meet(X1,X2),meet(X3,X2)) = meet(X3,meet(X2,X1)),
inference(cp,[status(thm)],[t1503,t149]) ).
cnf(t93395,plain,
meet(X1,meet(X2,meet(X3,X2))) = meet(X3,meet(X2,X1)),
inference(step,[status(thm)],[t1528,t26]) ).
cnf(t93396,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(step,[status(thm)],[t93395,t149]) ).
cnf(t2018,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(orient,[status(thm)],[t93396]) ).
cnf(t93699,plain,
meet(X1,meet(X3,join(complement(X1),X2))) = meet(meet(join(complement(X1),X2),X3),meet(X1,X2)),
inference(step,[status(thm)],[t93698,t2018]) ).
cnf(t93700,plain,
meet(X1,meet(X3,join(complement(X1),X2))) = meet(join(complement(X1),X2),meet(X3,meet(X1,X2))),
inference(step,[status(thm)],[t93699,t26]) ).
cnf(t126,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t26,t121]) ).
cnf(t365,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t126]) ).
cnf(t1520,plain,
meet(meet(join(X1,X2),X3),meet(X4,X2)) = meet(X4,meet(X2,X3)),
inference(cp,[status(thm)],[t1503,t365]) ).
cnf(t93525,plain,
meet(join(X1,X2),meet(X3,meet(X4,X2))) = meet(X4,meet(X2,X3)),
inference(step,[status(thm)],[t1520,t26]) ).
cnf(t24751,plain,
meet(join(X1,X2),meet(X3,meet(X4,X2))) = meet(X4,meet(X2,X3)),
inference(orient,[status(thm)],[t93525]) ).
cnf(t93701,plain,
meet(X1,meet(X3,join(complement(X1),X2))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t93700,t24751]) ).
cnf(t72870,plain,
meet(X1,meet(X2,join(complement(X1),X3))) = meet(X1,meet(X3,X2)),
inference(orient,[status(thm)],[t93701]) ).
cnf(t66579,plain,
complement(complement(X1)) = meet(X1,join(X2,complement(join(complement(X1),X2)))),
inference(cp,[status(thm)],[t66578,t18794]) ).
cnf(t93638,plain,
X1 = meet(X1,join(X2,complement(join(complement(X1),X2)))),
inference(step,[status(thm)],[t66579,t18794]) ).
cnf(t66851,plain,
meet(X1,join(X2,complement(join(complement(X1),X2)))) = X1,
inference(orient,[status(thm)],[t93638]) ).
cnf(t72888,plain,
meet(X1,meet(complement(join(complement(X2),complement(X1))),X2)) = meet(X1,X2),
inference(cp,[status(thm)],[t72870,t66851]) ).
cnf(t93759,plain,
meet(X1,meet(X2,complement(join(complement(X2),complement(X1))))) = meet(X1,X2),
inference(step,[status(thm)],[t72888,t23]) ).
cnf(t33994,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t33968,t14]) ).
cnf(t93553,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t33994,t23]) ).
cnf(t34251,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t93553]) ).
cnf(t34252,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(join(complement(X1),X2))),
inference(cp,[status(thm)],[t34251,t18794]) ).
cnf(t35516,plain,
meet(X1,complement(join(complement(X1),X2))) = complement(join(complement(X1),X2)),
inference(orient,[status(thm)],[t34252]) ).
cnf(t93760,plain,
meet(X1,complement(join(complement(X2),complement(X1)))) = meet(X1,X2),
inference(step,[status(thm)],[t93759,t35516]) ).
cnf(t34275,plain,
complement(X1) = join(complement(X1),complement(join(X1,X2))),
inference(cp,[status(thm)],[t16,t34251]) ).
cnf(t34384,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t34275]) ).
cnf(t34385,plain,
complement(complement(X1)) = join(X1,complement(join(complement(X1),X2))),
inference(cp,[status(thm)],[t34384,t18794]) ).
cnf(t93554,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(step,[status(thm)],[t34385,t18794]) ).
cnf(t34512,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t93554]) ).
cnf(t57,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(cp,[status(thm)],[t55,t16]) ).
cnf(t2322,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(orient,[status(thm)],[t57]) ).
cnf(t61,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t55,t51]) ).
cnf(t93394,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t61,t55]) ).
cnf(t1931,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t93394]) ).
cnf(t2324,plain,
join(X1,X2) = join(X2,join(X1,meet(join(X1,X2),X3))),
inference(cp,[status(thm)],[t2322,t1931]) ).
cnf(t4242,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(orient,[status(thm)],[t2324]) ).
cnf(t34514,plain,
X1 = join(X1,complement(join(X2,complement(X1)))),
inference(cp,[status(thm)],[t34512,t4242]) ).
cnf(t34649,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t34514]) ).
cnf(t34654,plain,
complement(join(X1,complement(X2))) = meet(complement(join(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t121,t34649]) ).
cnf(t93559,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(join(X1,complement(X2)))),
inference(step,[status(thm)],[t34654,t23]) ).
cnf(t35649,plain,
meet(X1,complement(join(X2,complement(X1)))) = complement(join(X2,complement(X1))),
inference(orient,[status(thm)],[t93559]) ).
cnf(t93761,plain,
complement(join(complement(X2),complement(X1))) = meet(X1,X2),
inference(step,[status(thm)],[t93760,t35649]) ).
cnf(t86259,plain,
complement(join(complement(X1),complement(X2))) = meet(X2,X1),
inference(orient,[status(thm)],[t93761]) ).
cnf(t86302,plain,
meet(X1,complement(X2)) = complement(join(X2,complement(X1))),
inference(cp,[status(thm)],[t86259,t18794]) ).
cnf(t86564,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t86302]) ).
cnf(t86599,plain,
join(X1,complement(X2)) = complement(meet(X2,complement(X1))),
inference(cp,[status(thm)],[t18794,t86564]) ).
cnf(t87293,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t86599]) ).
cnf(t87310,plain,
join(X1,complement(X2)) = complement(meet(complement(X1),X2)),
inference(cp,[status(thm)],[t87293,t23]) ).
cnf(t87488,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t87310]) ).
cnf(t72900,plain,
meet(X1,meet(X2,join(X2,complement(X1)))) = meet(X1,join(X2,complement(X1))),
inference(cp,[status(thm)],[t72870,t391]) ).
cnf(t93705,plain,
meet(X1,X2) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t72900,t14]) ).
cnf(t73511,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t93705]) ).
cnf(t73536,plain,
meet(complement(X1),X2) = meet(complement(X1),join(X2,X1)),
inference(cp,[status(thm)],[t73511,t18794]) ).
cnf(t74004,plain,
meet(complement(X1),join(X2,X1)) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t73536]) ).
cnf(t87501,plain,
join(X1,complement(join(X2,X1))) = complement(meet(complement(X1),X2)),
inference(cp,[status(thm)],[t87488,t74004]) ).
cnf(t93826,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t87501,t87488]) ).
cnf(t87969,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t93826]) ).
cnf(t86593,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t86564,t51]) ).
cnf(t86828,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t86593]) ).
cnf(t87973,plain,
join(X1,complement(complement(X2))) = join(X1,meet(X2,complement(X1))),
inference(cp,[status(thm)],[t87969,t86828]) ).
cnf(t93827,plain,
join(X1,X2) = join(X1,meet(X2,complement(X1))),
inference(step,[status(thm)],[t87973,t18794]) ).
cnf(t88244,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t93827]) ).
cnf(t88260,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t88244,t23]) ).
cnf(t88409,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t88260]) ).
cnf(t155,plain,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3),
inference(cp,[status(thm)],[t26,t149]) ).
cnf(t93390,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3),
inference(step,[status(thm)],[t155,t26]) ).
cnf(t93391,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t93390,t26]) ).
cnf(t1311,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t93391]) ).
cnf(t74214,plain,
meet(complement(X1),meet(X2,join(X3,X1))) = meet(complement(X1),meet(X2,meet(complement(X1),X3))),
inference(cp,[status(thm)],[t1311,t74004]) ).
cnf(t93741,plain,
meet(complement(X1),meet(X2,join(X3,X1))) = meet(complement(X1),meet(X2,X3)),
inference(step,[status(thm)],[t74214,t1311]) ).
cnf(t82479,plain,
meet(complement(X1),meet(X2,join(X3,X1))) = meet(complement(X1),meet(X2,X3)),
inference(orient,[status(thm)],[t93741]) ).
cnf(t88417,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(cp,[status(thm)],[t88409,t82479]) ).
cnf(t93851,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t88417,t88409]) ).
cnf(t91283,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t93851]) ).
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(t72871,plain,
meet(X1,meet(X2,X1)) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t72870,t130]) ).
cnf(t93703,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t72871,t149]) ).
cnf(t73251,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t93703]) ).
cnf(t73298,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(X1,join(complement(X1),join(X2,X3))),
inference(cp,[status(thm)],[t73251,t1197]) ).
cnf(t93733,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t73298,t73251]) ).
cnf(t79359,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t93733]) ).
cnf(t88348,plain,
meet(X1,join(X2,meet(X3,complement(complement(X1))))) = meet(X1,join(X2,join(complement(X1),X3))),
inference(cp,[status(thm)],[t79359,t88244]) ).
cnf(t93842,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,join(complement(X1),X3))),
inference(step,[status(thm)],[t88348,t18794]) ).
cnf(t93843,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t93842,t79359]) ).
cnf(t89916,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t93843]) ).
cnf(t91290,plain,
join(meet(X1,X2),meet(X2,X3)) = join(meet(X1,X2),meet(X2,join(X3,X1))),
inference(cp,[status(thm)],[t91283,t89916]) ).
cnf(t276,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)),
inference(cp,[status(thm)],[t271,t16]) ).
cnf(t93363,plain,
meet(X1,X2) = meet(X1,meet(X2,join(X3,X1))),
inference(step,[status(thm)],[t276,t26]) ).
cnf(t475,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t93363]) ).
cnf(t493,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X3,X1)),
inference(cp,[status(thm)],[t113,t475]) ).
cnf(t93515,plain,
meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t493,t51]) ).
cnf(t22239,plain,
join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X3,X1)),
inference(orient,[status(thm)],[t93515]) ).
cnf(t93858,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X3,X1)),
inference(step,[status(thm)],[t91290,t22239]) ).
cnf(t92824,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X3,X1)),
inference(orient,[status(thm)],[t93858]) ).
cnf(f12,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox2/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,t51]) ).
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(a,join(b,c)) != meet(a,join(b,c)),
inference(rw,[status(thm)],[g0_1,t92824]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT195-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.40 % Computer : n019.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Wed Sep 23 20:31:19 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 40.26/5.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.26/5.64 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------