%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT213-1 : 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 01:56:09 PM UTC 2026
% Result : Unsatisfiable 23.95s 8.58s
% Output : Proof 23.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 13
% Syntax : Number of formulae : 349 ( 345 unt; 0 def)
% Number of atoms : 357 ( 356 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 : 740 ( 82 sgn 46 !; 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(t56,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(t10284,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(t50,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t10336,plain,
X1 = ifeq(zero,zero,ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t10284,t50]) ).
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(t87224,plain,
X1 = ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t10336,t17]) ).
cnf(t87225,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t87224,t56]) ).
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(t71,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t87226,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t87225,t71]) ).
cnf(t87227,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t87226,t17]) ).
cnf(t18801,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t87227]) ).
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(t57,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t14,t56]) ).
cnf(t121,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t57]) ).
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(t123,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t121,t16]) ).
cnf(t87060,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t123,t26]) ).
cnf(t148,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t87060]) ).
cnf(t154,plain,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3),
inference(cp,[status(thm)],[t26,t148]) ).
cnf(t87110,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3),
inference(step,[status(thm)],[t154,t26]) ).
cnf(t87111,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t87110,t26]) ).
cnf(t1312,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t87111]) ).
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(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H76) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,join(X1,X3)))) = meet(X0,join(X1,meet(X2,join(X3,meet(X0,X1))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X1,X2))))) = meet(X1,join(X2,meet(X3,join(X2,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X1,X2))))) = meet(X1,join(X2,meet(X3,join(X2,X4)))),
inference(orient,[status(thm)],[t12]) ).
cnf(t41,plain,
meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t35,t16]) ).
cnf(t33417,plain,
meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X3,X1))),
inference(orient,[status(thm)],[t41]) ).
cnf(t33521,plain,
meet(complement(X1),join(X1,meet(X2,complement(X1)))) = meet(complement(X1),join(X1,meet(X2,one))),
inference(cp,[status(thm)],[t33417,t71]) ).
cnf(t73,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t14,t71]) ).
cnf(t79,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t73]) ).
cnf(t87264,plain,
meet(complement(X1),join(X1,meet(X2,complement(X1)))) = meet(complement(X1),join(X1,X2)),
inference(step,[status(thm)],[t33521,t79]) ).
cnf(t33731,plain,
meet(complement(X1),join(X1,meet(X2,complement(X1)))) = meet(complement(X1),join(X1,X2)),
inference(orient,[status(thm)],[t87264]) ).
cnf(t33744,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,t33731]) ).
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(t60,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t87267,plain,
join(X1,meet(X2,complement(X1))) = join(X1,join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2)))),
inference(step,[status(thm)],[t33744,t60]) ).
cnf(t124,plain,
X1 = meet(X1,join(X2,join(X3,X1))),
inference(cp,[status(thm)],[t121,t60]) ).
cnf(t271,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(orient,[status(thm)],[t124]) ).
cnf(t276,plain,
meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)),
inference(cp,[status(thm)],[t271,t16]) ).
cnf(t87083,plain,
meet(X1,X2) = meet(X1,meet(X2,join(X3,X1))),
inference(step,[status(thm)],[t276,t26]) ).
cnf(t476,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t87083]) ).
cnf(t494,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X3,X1)),
inference(cp,[status(thm)],[t114,t476]) ).
cnf(t87235,plain,
meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t494,t56]) ).
cnf(t22250,plain,
join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X3,X1)),
inference(orient,[status(thm)],[t87235]) ).
cnf(t87268,plain,
join(X1,meet(X2,complement(X1))) = join(X1,meet(complement(X1),join(X1,X2))),
inference(step,[status(thm)],[t87267,t22250]) ).
cnf(t34141,plain,
join(X1,meet(complement(X1),join(X1,X2))) = join(X1,meet(X2,complement(X1))),
inference(orient,[status(thm)],[t87268]) ).
cnf(t116,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t114,t14]) ).
cnf(t87059,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t116,t60]) ).
cnf(t141,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t87059]) ).
cnf(t74,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t60,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(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(t87072,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t74,t106]) ).
cnf(t211,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t87072]) ).
cnf(t214,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t141,t211]) ).
cnf(t87073,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t214,t60]) ).
cnf(t87074,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t87073,t60]) ).
cnf(t107,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t106,t56]) ).
cnf(t112,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t107]) ).
cnf(t87075,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t87074,t112]) ).
cnf(t87076,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t87075,t112]) ).
cnf(t222,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t87076]) ).
cnf(t227,plain,
one = join(complement(meet(X1,X2)),X1),
inference(cp,[status(thm)],[t222,t16]) ).
cnf(t87077,plain,
one = join(X1,complement(meet(X1,X2))),
inference(step,[status(thm)],[t227,t56]) ).
cnf(t234,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(orient,[status(thm)],[t87077]) ).
cnf(t34217,plain,
join(X1,meet(complement(meet(X1,X2)),complement(X1))) = join(X1,meet(complement(X1),one)),
inference(cp,[status(thm)],[t34141,t234]) ).
cnf(t87269,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = join(X1,meet(complement(X1),one)),
inference(step,[status(thm)],[t34217,t23]) ).
cnf(t87270,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = join(X1,complement(X1)),
inference(step,[status(thm)],[t87269,t79]) ).
cnf(t87271,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = one,
inference(step,[status(thm)],[t87270,t71]) ).
cnf(t34418,plain,
join(X1,meet(complement(X1),complement(meet(X1,X2)))) = one,
inference(orient,[status(thm)],[t87271]) ).
cnf(t34465,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,t34418]) ).
cnf(t52,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t26,t50]) ).
cnf(t53,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t16,t50]) ).
cnf(t75,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t53]) ).
cnf(t76,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t75,t56]) ).
cnf(t84,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t76]) ).
cnf(t86,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t84,t16]) ).
cnf(t103,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t86]) ).
cnf(t87065,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t52,t103]) ).
cnf(t159,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t87065]) ).
cnf(t87272,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)],[t34465,t159]) ).
cnf(t87273,plain,
meet(complement(X1),complement(meet(X1,X2))) = ifeq(one,one,complement(X1),meet(complement(X1),complement(meet(X1,X2)))),
inference(step,[status(thm)],[t87272,t17]) ).
cnf(t87274,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(step,[status(thm)],[t87273,t17]) ).
cnf(t34569,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t87274]) ).
cnf(t28,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t2208,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(t87113,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t32,t26]) ).
cnf(t1679,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t87113]) ).
cnf(t2210,plain,
meet(X1,X2) = meet(X2,meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t2208,t1679]) ).
cnf(t4099,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t2210]) ).
cnf(t34571,plain,
complement(X1) = meet(complement(X1),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t34569,t4099]) ).
cnf(t34982,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(orient,[status(thm)],[t34571]) ).
cnf(t35033,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t114,t34982]) ).
cnf(t87280,plain,
complement(meet(X1,X2)) = join(complement(X2),complement(meet(X1,X2))),
inference(step,[status(thm)],[t35033,t56]) ).
cnf(t36136,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(orient,[status(thm)],[t87280]) ).
cnf(t72,plain,
one = join(X1,join(X2,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t71,t60]) ).
cnf(t558,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(orient,[status(thm)],[t72]) ).
cnf(t34211,plain,
join(X1,meet(join(X2,complement(join(X1,X2))),complement(X1))) = join(X1,meet(complement(X1),one)),
inference(cp,[status(thm)],[t34141,t558]) ).
cnf(t87358,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = join(X1,meet(complement(X1),one)),
inference(step,[status(thm)],[t34211,t23]) ).
cnf(t87359,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = join(X1,complement(X1)),
inference(step,[status(thm)],[t87358,t79]) ).
cnf(t87360,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = one,
inference(step,[status(thm)],[t87359,t71]) ).
cnf(t67754,plain,
join(X1,meet(complement(X1),join(X2,complement(join(X1,X2))))) = one,
inference(orient,[status(thm)],[t87360]) ).
cnf(t67908,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,t67754]) ).
cnf(t87361,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)],[t67908,t159]) ).
cnf(t87362,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)],[t87361,t17]) ).
cnf(t87363,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = complement(X1),
inference(step,[status(thm)],[t87362,t17]) ).
cnf(t68025,plain,
meet(complement(X1),join(X2,complement(join(X1,X2)))) = complement(X1),
inference(orient,[status(thm)],[t87363]) ).
cnf(t68139,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)],[t36136,t68025]) ).
cnf(t87365,plain,
complement(complement(X1)) = join(complement(join(X2,complement(join(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t68139,t68025]) ).
cnf(t87366,plain,
X1 = join(complement(join(X2,complement(join(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t87365,t18801]) ).
cnf(t87367,plain,
X1 = join(complement(complement(X1)),complement(join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t87366,t56]) ).
cnf(t87368,plain,
X1 = join(X1,complement(join(X2,complement(join(X1,X2))))),
inference(step,[status(thm)],[t87367,t18801]) ).
cnf(t68574,plain,
join(X1,complement(join(X2,complement(join(X1,X2))))) = X1,
inference(orient,[status(thm)],[t87368]) ).
cnf(t228,plain,
one = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t222,t114]) ).
cnf(t87078,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t228,t56]) ).
cnf(t241,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t87078]) ).
cnf(t245,plain,
one = join(X1,complement(meet(X2,meet(X3,X1)))),
inference(cp,[status(thm)],[t241,t26]) ).
cnf(t827,plain,
join(X1,complement(meet(X2,meet(X3,X1)))) = one,
inference(orient,[status(thm)],[t245]) ).
cnf(t145,plain,
join(X1,X2) = meet(join(X1,X2),join(X2,X1)),
inference(cp,[status(thm)],[t121,t141]) ).
cnf(t393,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t145]) ).
cnf(t840,plain,
one = join(join(X1,X2),complement(meet(X3,join(X2,X1)))),
inference(cp,[status(thm)],[t827,t393]) ).
cnf(t87183,plain,
one = join(X1,join(X2,complement(meet(X3,join(X2,X1))))),
inference(step,[status(thm)],[t840,t60]) ).
cnf(t9828,plain,
join(X1,join(X2,complement(meet(X3,join(X2,X1))))) = one,
inference(orient,[status(thm)],[t87183]) ).
cnf(t34591,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t114,t34569]) ).
cnf(t87276,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t34591,t56]) ).
cnf(t35144,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t87276]) ).
cnf(t35263,plain,
one = join(X1,complement(meet(X2,join(complement(X2),X1)))),
inference(cp,[status(thm)],[t9828,t35144]) ).
cnf(t38494,plain,
join(X1,complement(meet(X2,join(complement(X2),X1)))) = one,
inference(orient,[status(thm)],[t35263]) ).
cnf(t68583,plain,
X1 = join(X1,complement(join(complement(meet(X2,join(complement(X2),X1))),complement(one)))),
inference(cp,[status(thm)],[t68574,t38494]) ).
cnf(t87369,plain,
X1 = join(X1,complement(join(complement(one),complement(meet(X2,join(complement(X2),X1)))))),
inference(step,[status(thm)],[t68583,t56]) ).
cnf(t94,plain,
complement(one) = zero,
inference(cp,[status(thm)],[t93,t50]) ).
cnf(t101,plain,
complement(one) = zero,
inference(orient,[status(thm)],[t94]) ).
cnf(t87370,plain,
X1 = join(X1,complement(join(zero,complement(meet(X2,join(complement(X2),X1)))))),
inference(step,[status(thm)],[t87369,t101]) ).
cnf(t87371,plain,
X1 = join(X1,complement(complement(meet(X2,join(complement(X2),X1))))),
inference(step,[status(thm)],[t87370,t84]) ).
cnf(t87372,plain,
X1 = join(X1,meet(X2,join(complement(X2),X1))),
inference(step,[status(thm)],[t87371,t18801]) ).
cnf(t68894,plain,
join(X1,meet(X2,join(complement(X2),X1))) = X1,
inference(orient,[status(thm)],[t87372]) ).
cnf(t33732,plain,
meet(complement(complement(X1)),join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(cp,[status(thm)],[t33731,t18801]) ).
cnf(t87265,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t33732,t18801]) ).
cnf(t87266,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X2,X1))),
inference(step,[status(thm)],[t87265,t18801]) ).
cnf(t33876,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),X2)),
inference(orient,[status(thm)],[t87266]) ).
cnf(t68898,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,join(complement(X2),X1))),
inference(cp,[status(thm)],[t68894,t33876]) ).
cnf(t87373,plain,
meet(X1,X2) = meet(X2,join(complement(X2),X1)),
inference(step,[status(thm)],[t68898,t22250]) ).
cnf(t69201,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(orient,[status(thm)],[t87373]) ).
cnf(t69480,plain,
meet(X1,meet(X2,join(complement(X1),X3))) = meet(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t1312,t69201]) ).
cnf(t152,plain,
meet(X1,meet(X2,X3)) = meet(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t148,t26]) ).
cnf(t1259,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t152]) ).
cnf(t87446,plain,
meet(X1,meet(X2,join(complement(X1),X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t69480,t1259]) ).
cnf(t77526,plain,
meet(X1,meet(X2,join(complement(X1),X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t87446]) ).
cnf(t77572,plain,
meet(X1,meet(complement(X2),complement(join(X2,complement(X1))))) = meet(X1,complement(X2)),
inference(cp,[status(thm)],[t77526,t68025]) ).
cnf(t35010,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t34982,t14]) ).
cnf(t87277,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t35010,t23]) ).
cnf(t35274,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t87277]) ).
cnf(t87447,plain,
meet(X1,complement(join(X2,complement(X1)))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t77572,t35274]) ).
cnf(t35298,plain,
complement(X1) = join(complement(X1),complement(join(X1,X2))),
inference(cp,[status(thm)],[t16,t35274]) ).
cnf(t35409,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t35298]) ).
cnf(t35410,plain,
complement(complement(X1)) = join(X1,complement(join(complement(X1),X2))),
inference(cp,[status(thm)],[t35409,t18801]) ).
cnf(t87278,plain,
X1 = join(X1,complement(join(complement(X1),X2))),
inference(step,[status(thm)],[t35410,t18801]) ).
cnf(t35539,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t87278]) ).
cnf(t62,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(cp,[status(thm)],[t60,t16]) ).
cnf(t2327,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(orient,[status(thm)],[t62]) ).
cnf(t66,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t60,t56]) ).
cnf(t87114,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t66,t60]) ).
cnf(t1935,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t87114]) ).
cnf(t2329,plain,
join(X1,X2) = join(X2,join(X1,meet(join(X1,X2),X3))),
inference(cp,[status(thm)],[t2327,t1935]) ).
cnf(t4251,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(orient,[status(thm)],[t2329]) ).
cnf(t35541,plain,
X1 = join(X1,complement(join(X2,complement(X1)))),
inference(cp,[status(thm)],[t35539,t4251]) ).
cnf(t35678,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t35541]) ).
cnf(t35683,plain,
complement(join(X1,complement(X2))) = meet(complement(join(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t121,t35678]) ).
cnf(t87283,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(join(X1,complement(X2)))),
inference(step,[status(thm)],[t35683,t23]) ).
cnf(t36697,plain,
meet(X1,complement(join(X2,complement(X1)))) = complement(join(X2,complement(X1))),
inference(orient,[status(thm)],[t87283]) ).
cnf(t87448,plain,
complement(join(X2,complement(X1))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t87447,t36697]) ).
cnf(t77888,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t87448]) ).
cnf(t77922,plain,
join(X1,complement(X2)) = complement(meet(X2,complement(X1))),
inference(cp,[status(thm)],[t18801,t77888]) ).
cnf(t78611,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t77922]) ).
cnf(t78624,plain,
join(X1,complement(X2)) = complement(meet(complement(X1),X2)),
inference(cp,[status(thm)],[t78611,t23]) ).
cnf(t78796,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t78624]) ).
cnf(t34209,plain,
join(X1,meet(join(X2,X1),complement(X1))) = join(X1,meet(complement(X1),join(X1,X2))),
inference(cp,[status(thm)],[t34141,t141]) ).
cnf(t87320,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X1,meet(complement(X1),join(X1,X2))),
inference(step,[status(thm)],[t34209,t23]) ).
cnf(t87321,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X1,meet(X2,complement(X1))),
inference(step,[status(thm)],[t87320,t34141]) ).
cnf(t50948,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X1,meet(X2,complement(X1))),
inference(orient,[status(thm)],[t87321]) ).
cnf(t69300,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)],[t69201,t50948]) ).
cnf(t87378,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)],[t69300,t26]) ).
cnf(t29,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(cp,[status(thm)],[t26,t23]) ).
cnf(t1506,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(orient,[status(thm)],[t29]) ).
cnf(t1531,plain,
meet(meet(X1,X2),meet(X3,X2)) = meet(X3,meet(X2,X1)),
inference(cp,[status(thm)],[t1506,t148]) ).
cnf(t87115,plain,
meet(X1,meet(X2,meet(X3,X2))) = meet(X3,meet(X2,X1)),
inference(step,[status(thm)],[t1531,t26]) ).
cnf(t87116,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(step,[status(thm)],[t87115,t148]) ).
cnf(t2021,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X2,X1)),
inference(orient,[status(thm)],[t87116]) ).
cnf(t87379,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)],[t87378,t2021]) ).
cnf(t87380,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)],[t87379,t23]) ).
cnf(t87381,plain,
meet(X1,meet(X1,join(X2,complement(X1)))) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t87380,t18801]) ).
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(t87382,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(complement(X1),meet(X2,complement(complement(X1))))),
inference(step,[status(thm)],[t87381,t130]) ).
cnf(t87383,plain,
meet(X1,join(X2,complement(X1))) = meet(meet(X2,complement(complement(X1))),X1),
inference(step,[status(thm)],[t87382,t69201]) ).
cnf(t87384,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,meet(complement(complement(X1)),X1)),
inference(step,[status(thm)],[t87383,t26]) ).
cnf(t87385,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,meet(X1,complement(complement(X1)))),
inference(step,[status(thm)],[t87384,t23]) ).
cnf(t87386,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,meet(X1,X1)),
inference(step,[status(thm)],[t87385,t18801]) ).
cnf(t87387,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,X1),
inference(step,[status(thm)],[t87386,t13]) ).
cnf(t69576,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,X1),
inference(orient,[status(thm)],[t87387]) ).
cnf(t242,plain,
one = join(X1,join(X2,complement(meet(X3,join(X1,X2))))),
inference(cp,[status(thm)],[t241,t60]) ).
cnf(t4984,plain,
join(X1,join(X2,complement(meet(X3,join(X1,X2))))) = one,
inference(orient,[status(thm)],[t242]) ).
cnf(t34570,plain,
complement(complement(X1)) = meet(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t34569,t18801]) ).
cnf(t87275,plain,
X1 = meet(X1,complement(meet(complement(X1),X2))),
inference(step,[status(thm)],[t34570,t18801]) ).
cnf(t34702,plain,
meet(X1,complement(meet(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t87275]) ).
cnf(t34711,plain,
complement(meet(complement(X1),X2)) = join(complement(meet(complement(X1),X2)),X1),
inference(cp,[status(thm)],[t114,t34702]) ).
cnf(t87281,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(meet(complement(X1),X2))),
inference(step,[status(thm)],[t34711,t56]) ).
cnf(t36302,plain,
join(X1,complement(meet(complement(X1),X2))) = complement(meet(complement(X1),X2)),
inference(orient,[status(thm)],[t87281]) ).
cnf(t36428,plain,
one = join(X1,complement(meet(complement(X2),join(X1,X2)))),
inference(cp,[status(thm)],[t4984,t36302]) ).
cnf(t40984,plain,
join(X1,complement(meet(complement(X2),join(X1,X2)))) = one,
inference(orient,[status(thm)],[t36428]) ).
cnf(t69588,plain,
meet(X1,meet(complement(X2),join(X1,X2))) = meet(meet(complement(X2),join(X1,X2)),one),
inference(cp,[status(thm)],[t69576,t40984]) ).
cnf(t31,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t303,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t31]) ).
cnf(t308,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,meet(join(X1,X3),X2)),
inference(cp,[status(thm)],[t303,t148]) ).
cnf(t87084,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(step,[status(thm)],[t308,t303]) ).
cnf(t504,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t87084]) ).
cnf(t87388,plain,
meet(X1,complement(X2)) = meet(meet(complement(X2),join(X1,X2)),one),
inference(step,[status(thm)],[t69588,t504]) ).
cnf(t87389,plain,
meet(X1,complement(X2)) = meet(complement(X2),meet(join(X1,X2),one)),
inference(step,[status(thm)],[t87388,t26]) ).
cnf(t87390,plain,
meet(X1,complement(X2)) = meet(one,meet(join(X1,X2),complement(X2))),
inference(step,[status(thm)],[t87389,t2021]) ).
cnf(t87391,plain,
meet(X1,complement(X2)) = meet(join(X1,X2),complement(X2)),
inference(step,[status(thm)],[t87390,t93]) ).
cnf(t87392,plain,
meet(X1,complement(X2)) = meet(complement(X2),join(X1,X2)),
inference(step,[status(thm)],[t87391,t23]) ).
cnf(t70213,plain,
meet(complement(X1),join(X2,X1)) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t87392]) ).
cnf(t78803,plain,
join(X1,complement(join(X2,X1))) = complement(meet(X2,complement(X1))),
inference(cp,[status(thm)],[t78796,t70213]) ).
cnf(t87515,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t78803,t78611]) ).
cnf(t79252,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t87515]) ).
cnf(t226,plain,
one = join(complement(join(X1,X2)),join(X2,X1)),
inference(cp,[status(thm)],[t222,t141]) ).
cnf(t87096,plain,
one = join(join(X2,X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t226,t56]) ).
cnf(t87097,plain,
one = join(X2,join(X1,complement(join(X1,X2)))),
inference(step,[status(thm)],[t87096,t60]) ).
cnf(t737,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(orient,[status(thm)],[t87097]) ).
cnf(t68084,plain,
complement(X1) = meet(complement(X1),join(join(X2,complement(join(X2,X1))),complement(one))),
inference(cp,[status(thm)],[t68025,t737]) ).
cnf(t87437,plain,
complement(X1) = meet(complement(X1),join(X2,join(complement(join(X2,X1)),complement(one)))),
inference(step,[status(thm)],[t68084,t60]) ).
cnf(t87438,plain,
complement(X1) = meet(complement(X1),join(X2,join(complement(one),complement(join(X2,X1))))),
inference(step,[status(thm)],[t87437,t56]) ).
cnf(t87439,plain,
complement(X1) = meet(complement(X1),join(X2,join(zero,complement(join(X2,X1))))),
inference(step,[status(thm)],[t87438,t101]) ).
cnf(t87440,plain,
complement(X1) = meet(complement(X1),join(X2,complement(join(X2,X1)))),
inference(step,[status(thm)],[t87439,t84]) ).
cnf(t75822,plain,
meet(complement(X1),join(X2,complement(join(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t87440]) ).
cnf(t77573,plain,
meet(X1,meet(complement(X2),complement(join(complement(X1),X2)))) = meet(X1,complement(X2)),
inference(cp,[status(thm)],[t77526,t75822]) ).
cnf(t35013,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t34982,t121]) ).
cnf(t87279,plain,
complement(join(X1,X2)) = meet(complement(X2),complement(join(X1,X2))),
inference(step,[status(thm)],[t35013,t23]) ).
cnf(t35970,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(orient,[status(thm)],[t87279]) ).
cnf(t87460,plain,
meet(X1,complement(join(complement(X1),X2))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t77573,t35970]) ).
cnf(t35275,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(join(complement(X1),X2))),
inference(cp,[status(thm)],[t35274,t18801]) ).
cnf(t36560,plain,
meet(X1,complement(join(complement(X1),X2))) = complement(join(complement(X1),X2)),
inference(orient,[status(thm)],[t35275]) ).
cnf(t87461,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t87460,t36560]) ).
cnf(t78138,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t87461]) ).
cnf(t79256,plain,
join(X1,complement(complement(X2))) = join(X1,meet(X2,complement(X1))),
inference(cp,[status(thm)],[t79252,t78138]) ).
cnf(t87516,plain,
join(X1,X2) = join(X1,meet(X2,complement(X1))),
inference(step,[status(thm)],[t79256,t18801]) ).
cnf(t79514,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t87516]) ).
cnf(t79526,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t79514,t23]) ).
cnf(t80255,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t79526]) ).
cnf(t80265,plain,
join(X1,meet(X2,join(complement(complement(X1)),X3))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(cp,[status(thm)],[t80255,t77526]) ).
cnf(t87546,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(step,[status(thm)],[t80265,t18801]) ).
cnf(t87547,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t87546,t80255]) ).
cnf(t83489,plain,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t87547]) ).
cnf(t146,plain,
join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3),
inference(cp,[status(thm)],[t60,t141]) ).
cnf(t87108,plain,
join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3),
inference(step,[status(thm)],[t146,t60]) ).
cnf(t87109,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t87108,t60]) ).
cnf(t1198,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t87109]) ).
cnf(t69334,plain,
meet(join(X1,join(complement(X2),X3)),X2) = meet(X2,join(complement(X2),join(X1,X3))),
inference(cp,[status(thm)],[t69201,t1198]) ).
cnf(t87441,plain,
meet(X2,join(X1,join(complement(X2),X3))) = meet(X2,join(complement(X2),join(X1,X3))),
inference(step,[status(thm)],[t69334,t23]) ).
cnf(t87442,plain,
meet(X2,join(X1,join(complement(X2),X3))) = meet(join(X1,X3),X2),
inference(step,[status(thm)],[t87441,t69201]) ).
cnf(t76125,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(join(X2,X3),X1),
inference(orient,[status(thm)],[t87442]) ).
cnf(t79611,plain,
meet(join(X1,meet(X2,complement(complement(X3)))),X3) = meet(X3,join(X1,join(complement(X3),X2))),
inference(cp,[status(thm)],[t76125,t79514]) ).
cnf(t87541,plain,
meet(X3,join(X1,meet(X2,complement(complement(X3))))) = meet(X3,join(X1,join(complement(X3),X2))),
inference(step,[status(thm)],[t79611,t23]) ).
cnf(t87542,plain,
meet(X3,join(X1,meet(X2,X3))) = meet(X3,join(X1,join(complement(X3),X2))),
inference(step,[status(thm)],[t87541,t18801]) ).
cnf(t87543,plain,
meet(X3,join(X1,meet(X2,X3))) = meet(join(X1,X2),X3),
inference(step,[status(thm)],[t87542,t76125]) ).
cnf(t83078,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(join(X2,X3),X1),
inference(orient,[status(thm)],[t87543]) ).
cnf(t83143,plain,
meet(join(X1,X2),X3) = meet(X3,join(meet(X2,X3),X1)),
inference(cp,[status(thm)],[t83078,t56]) ).
cnf(t84274,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(join(X3,X2),X1),
inference(orient,[status(thm)],[t83143]) ).
cnf(t84607,plain,
join(meet(X1,X2),meet(X2,X3)) = join(meet(X1,X2),meet(join(X3,X1),X2)),
inference(cp,[status(thm)],[t83489,t84274]) ).
cnf(t125,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)],[t125]) ).
cnf(t385,plain,
meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X2,X3)),
inference(cp,[status(thm)],[t114,t365]) ).
cnf(t87231,plain,
meet(join(X1,X2),X3) = join(meet(X2,X3),meet(join(X1,X2),X3)),
inference(step,[status(thm)],[t385,t56]) ).
cnf(t20365,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(orient,[status(thm)],[t87231]) ).
cnf(t87572,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(join(X3,X1),X2),
inference(step,[status(thm)],[t84607,t20365]) ).
cnf(t86477,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(join(X3,X1),X2),
inference(orient,[status(thm)],[t87572]) ).
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,t56]) ).
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,t86477]) ).
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 : LAT213-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n017.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 20:29:51 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.95/8.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.95/8.58 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------