%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT210-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 46.91s 6.48s
% Output : Proof 46.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 80
% Number of leaves : 13
% Syntax : Number of formulae : 331 ( 327 unt; 0 def)
% Number of atoms : 339 ( 338 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 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 : 705 ( 87 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t53,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t14,t52]) ).
cnf(t118,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t53]) ).
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(f11,axiom,
meet(X,join(Y,Z)) = meet(X,join(Y,meet(X,join(Z,meet(X,Y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H68) ).
fof(f11_nnf,plain,
! [X,Y,Z] : meet(X,join(Y,Z)) = meet(X,join(Y,meet(X,join(Z,meet(X,Y))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] : meet(X,join(Y,Z)) = meet(X,join(Y,meet(X,join(Z,meet(X,Y))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,X2)) = meet(X0,join(X1,meet(X0,join(X2,meet(X0,X1))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X1,X2))))) = meet(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X1,X2))))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
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(t41,plain,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(X1,join(X3,meet(X2,X1))))),
inference(cp,[status(thm)],[t35,t23]) ).
cnf(t49461,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X2,X1))))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t41]) ).
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(t46,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t49588,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),join(X1,meet(complement(X1),join(X2,zero)))),
inference(cp,[status(thm)],[t49461,t46]) ).
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(t49,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t16,t46]) ).
cnf(t71,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t49]) ).
cnf(t109555,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),join(X1,meet(complement(X1),X2))),
inference(step,[status(thm)],[t49588,t71]) ).
cnf(t49841,plain,
meet(complement(X1),join(X1,meet(complement(X1),X2))) = meet(complement(X1),join(X1,X2)),
inference(orient,[status(thm)],[t109555]) ).
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(t10276,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t10328,plain,
X1 = ifeq(zero,zero,ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t10276,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(t109498,plain,
X1 = ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t10328,t17]) ).
cnf(t109499,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t109498,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(t67,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t109500,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t109499,t67]) ).
cnf(t109501,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t109500,t17]) ).
cnf(t18789,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t109501]) ).
cnf(t49845,plain,
meet(complement(complement(X1)),join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(complement(complement(X1)),X2))),
inference(cp,[status(thm)],[t49841,t18789]) ).
cnf(t109556,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t49845,t18789]) ).
cnf(t109557,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(step,[status(thm)],[t109556,t18789]) ).
cnf(t50112,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(orient,[status(thm)],[t109557]) ).
cnf(t120,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t118,t16]) ).
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(t109319,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t120,t26]) ).
cnf(t145,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t109319]) ).
cnf(t48,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t26,t46]) ).
cnf(t72,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t71,t52]) ).
cnf(t80,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t72]) ).
cnf(t82,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t80,t16]) ).
cnf(t99,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t82]) ).
cnf(t109324,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t48,t99]) ).
cnf(t156,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t109324]) ).
cnf(t159,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t145,t156]) ).
cnf(t109325,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t159,t26]) ).
cnf(t109326,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t109325,t26]) ).
cnf(t100,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t99,t23]) ).
cnf(t106,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t100]) ).
cnf(t109327,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t109326,t106]) ).
cnf(t109328,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t109327,t106]) ).
cnf(t169,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t109328]) ).
cnf(t174,plain,
zero = meet(complement(join(X1,X2)),X1),
inference(cp,[status(thm)],[t169,t14]) ).
cnf(t109329,plain,
zero = meet(X1,complement(join(X1,X2))),
inference(step,[status(thm)],[t174,t23]) ).
cnf(t183,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t109329]) ).
cnf(t50197,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t50112,t183]) ).
cnf(t109558,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t50197,t71]) ).
cnf(t109559,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(step,[status(thm)],[t109558,t46]) ).
cnf(t50416,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t109559]) ).
cnf(t50473,plain,
join(complement(X1),complement(join(X1,X2))) = ifeq(zero,zero,ifeq(join(X1,join(complement(X1),complement(join(X1,X2)))),one,complement(X1),join(complement(X1),complement(join(X1,X2)))),join(complement(X1),complement(join(X1,X2)))),
inference(cp,[status(thm)],[t18,t50416]) ).
cnf(t109560,plain,
join(complement(X1),complement(join(X1,X2))) = ifeq(join(X1,join(complement(X1),complement(join(X1,X2)))),one,complement(X1),join(complement(X1),complement(join(X1,X2)))),
inference(step,[status(thm)],[t50473,t17]) ).
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(t56,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t70,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t56,t67]) ).
cnf(t69,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t14,t67]) ).
cnf(t75,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t69]) ).
cnf(t76,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t75,t23]) ).
cnf(t89,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t76]) ).
cnf(t91,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t89,t14]) ).
cnf(t102,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t91]) ).
cnf(t109331,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t70,t102]) ).
cnf(t208,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t109331]) ).
cnf(t109561,plain,
join(complement(X1),complement(join(X1,X2))) = ifeq(one,one,complement(X1),join(complement(X1),complement(join(X1,X2)))),
inference(step,[status(thm)],[t109560,t208]) ).
cnf(t109562,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(step,[status(thm)],[t109561,t17]) ).
cnf(t50601,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t109562]) ).
cnf(t58,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(cp,[status(thm)],[t56,t16]) ).
cnf(t2322,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(orient,[status(thm)],[t58]) ).
cnf(t62,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t56,t52]) ).
cnf(t109382,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t62,t56]) ).
cnf(t1931,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t109382]) ).
cnf(t2324,plain,
join(X1,X2) = join(X2,join(X1,meet(join(X1,X2),X3))),
inference(cp,[status(thm)],[t2322,t1931]) ).
cnf(t4245,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(orient,[status(thm)],[t2324]) ).
cnf(t24,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t16,t23]) ).
cnf(t111,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t24]) ).
cnf(t31,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t300,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t31]) ).
cnf(t313,plain,
meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)),
inference(cp,[status(thm)],[t111,t300]) ).
cnf(t109502,plain,
meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)),
inference(step,[status(thm)],[t313,t52]) ).
cnf(t18813,plain,
join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2),
inference(orient,[status(thm)],[t109502]) ).
cnf(t18835,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))),
inference(cp,[status(thm)],[t18813,t14]) ).
cnf(t38219,plain,
join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)),
inference(orient,[status(thm)],[t18835]) ).
cnf(t38404,plain,
join(X1,X2) = join(X2,meet(join(X1,X2),join(X1,X3))),
inference(cp,[status(thm)],[t4245,t38219]) ).
cnf(t38453,plain,
join(X1,meet(join(X2,X1),join(X2,X3))) = join(X2,X1),
inference(orient,[status(thm)],[t38404]) ).
cnf(t115,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t111,t26]) ).
cnf(t254,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t115]) ).
cnf(t267,plain,
meet(X1,join(meet(X2,X3),X3)) = meet(X1,join(meet(X2,X3),meet(X1,X3))),
inference(cp,[status(thm)],[t35,t254]) ).
cnf(t109539,plain,
meet(X1,join(X3,meet(X2,X3))) = meet(X1,join(meet(X2,X3),meet(X1,X3))),
inference(step,[status(thm)],[t267,t52]) ).
cnf(t109540,plain,
meet(X1,X3) = meet(X1,join(meet(X2,X3),meet(X1,X3))),
inference(step,[status(thm)],[t109539,t111]) ).
cnf(t33369,plain,
meet(X1,join(meet(X2,X3),meet(X1,X3))) = meet(X1,X3),
inference(orient,[status(thm)],[t109540]) ).
cnf(t33527,plain,
meet(X1,X2) = meet(X1,join(meet(X3,X2),meet(X2,X1))),
inference(cp,[status(thm)],[t33369,t23]) ).
cnf(t34217,plain,
meet(X1,join(meet(X2,X3),meet(X3,X1))) = meet(X1,X3),
inference(orient,[status(thm)],[t33527]) ).
cnf(t34258,plain,
meet(X1,join(X2,X3)) = meet(X1,join(X3,meet(join(X2,X3),X1))),
inference(cp,[status(thm)],[t34217,t118]) ).
cnf(t36479,plain,
meet(X1,join(X2,meet(join(X3,X2),X1))) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t34258]) ).
cnf(t38465,plain,
join(X1,X2) = join(X2,meet(join(X1,X2),join(X3,X1))),
inference(cp,[status(thm)],[t38453,t36479]) ).
cnf(t39173,plain,
join(X1,meet(join(X2,X1),join(X3,X2))) = join(X2,X1),
inference(orient,[status(thm)],[t38465]) ).
cnf(t39299,plain,
join(X1,X2) = join(X2,meet(join(X2,X1),join(X3,X1))),
inference(cp,[status(thm)],[t39173,t52]) ).
cnf(t40674,plain,
join(X1,meet(join(X1,X2),join(X3,X2))) = join(X2,X1),
inference(orient,[status(thm)],[t39299]) ).
cnf(t50607,plain,
complement(X1) = join(complement(X1),complement(join(X2,X1))),
inference(cp,[status(thm)],[t50601,t40674]) ).
cnf(t51112,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(orient,[status(thm)],[t50607]) ).
cnf(t51180,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t118,t51112]) ).
cnf(t109568,plain,
complement(join(X1,X2)) = meet(complement(X2),complement(join(X1,X2))),
inference(step,[status(thm)],[t51180,t23]) ).
cnf(t52601,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(orient,[status(thm)],[t109568]) ).
cnf(t47,plain,
zero = meet(X1,meet(X2,complement(meet(X1,X2)))),
inference(cp,[status(thm)],[t46,t26]) ).
cnf(t538,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(orient,[status(thm)],[t47]) ).
cnf(t50191,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t50112,t538]) ).
cnf(t109651,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t50191,t71]) ).
cnf(t109652,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(step,[status(thm)],[t109651,t46]) ).
cnf(t92406,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(orient,[status(thm)],[t109652]) ).
cnf(t92580,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = ifeq(zero,zero,ifeq(join(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))),one,complement(X1),join(complement(X1),meet(X2,complement(meet(X1,X2))))),join(complement(X1),meet(X2,complement(meet(X1,X2))))),
inference(cp,[status(thm)],[t18,t92406]) ).
cnf(t109653,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = ifeq(join(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))),one,complement(X1),join(complement(X1),meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t92580,t17]) ).
cnf(t109654,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = ifeq(one,one,complement(X1),join(complement(X1),meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t109653,t208]) ).
cnf(t109655,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(step,[status(thm)],[t109654,t17]) ).
cnf(t92726,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(orient,[status(thm)],[t109655]) ).
cnf(t92860,plain,
complement(join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(cp,[status(thm)],[t52601,t92726]) ).
cnf(t109657,plain,
complement(complement(X1)) = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t92860,t92726]) ).
cnf(t109658,plain,
X1 = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t109657,t18789]) ).
cnf(t109659,plain,
X1 = meet(complement(complement(X1)),complement(meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t109658,t23]) ).
cnf(t109660,plain,
X1 = meet(X1,complement(meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t109659,t18789]) ).
cnf(t93388,plain,
meet(X1,complement(meet(X2,complement(meet(X1,X2))))) = X1,
inference(orient,[status(thm)],[t109660]) ).
cnf(t176,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t169,t118]) ).
cnf(t109330,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t176,t23]) ).
cnf(t191,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t109330]) ).
cnf(t194,plain,
zero = meet(X1,complement(join(X2,join(X3,X1)))),
inference(cp,[status(thm)],[t191,t56]) ).
cnf(t674,plain,
meet(X1,complement(join(X2,join(X3,X1)))) = zero,
inference(orient,[status(thm)],[t194]) ).
cnf(t150,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,X1)),
inference(cp,[status(thm)],[t111,t145]) ).
cnf(t418,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t150]) ).
cnf(t686,plain,
zero = meet(meet(X1,X2),complement(join(X3,meet(X2,X1)))),
inference(cp,[status(thm)],[t674,t418]) ).
cnf(t109432,plain,
zero = meet(X1,meet(X2,complement(join(X3,meet(X2,X1))))),
inference(step,[status(thm)],[t686,t26]) ).
cnf(t8077,plain,
meet(X1,meet(X2,complement(join(X3,meet(X2,X1))))) = zero,
inference(orient,[status(thm)],[t109432]) ).
cnf(t50633,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t118,t50601]) ).
cnf(t109564,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t50633,t23]) ).
cnf(t51315,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t109564]) ).
cnf(t51486,plain,
zero = meet(X1,complement(join(X2,meet(complement(X2),X1)))),
inference(cp,[status(thm)],[t8077,t51315]) ).
cnf(t55598,plain,
meet(X1,complement(join(X2,meet(complement(X2),X1)))) = zero,
inference(orient,[status(thm)],[t51486]) ).
cnf(t93399,plain,
X1 = meet(X1,complement(meet(complement(join(X2,meet(complement(X2),X1))),complement(zero)))),
inference(cp,[status(thm)],[t93388,t55598]) ).
cnf(t109661,plain,
X1 = meet(X1,complement(meet(complement(zero),complement(join(X2,meet(complement(X2),X1)))))),
inference(step,[status(thm)],[t93399,t23]) ).
cnf(t81,plain,
complement(zero) = one,
inference(cp,[status(thm)],[t80,t67]) ).
cnf(t87,plain,
complement(zero) = one,
inference(orient,[status(thm)],[t81]) ).
cnf(t109662,plain,
X1 = meet(X1,complement(meet(one,complement(join(X2,meet(complement(X2),X1)))))),
inference(step,[status(thm)],[t109661,t87]) ).
cnf(t109663,plain,
X1 = meet(X1,complement(complement(join(X2,meet(complement(X2),X1))))),
inference(step,[status(thm)],[t109662,t89]) ).
cnf(t109664,plain,
X1 = meet(X1,join(X2,meet(complement(X2),X1))),
inference(step,[status(thm)],[t109663,t18789]) ).
cnf(t93767,plain,
meet(X1,join(X2,meet(complement(X2),X1))) = X1,
inference(orient,[status(thm)],[t109664]) ).
cnf(t49948,plain,
join(X1,meet(complement(X1),X2)) = join(join(X1,meet(complement(X1),X2)),meet(complement(X1),join(X1,X2))),
inference(cp,[status(thm)],[t111,t49841]) ).
cnf(t109608,plain,
join(X1,meet(complement(X1),X2)) = join(X1,join(meet(complement(X1),X2),meet(complement(X1),join(X1,X2)))),
inference(step,[status(thm)],[t49948,t56]) ).
cnf(t151,plain,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3),
inference(cp,[status(thm)],[t26,t145]) ).
cnf(t109372,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3),
inference(step,[status(thm)],[t151,t26]) ).
cnf(t109373,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t109372,t26]) ).
cnf(t1308,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t109373]) ).
cnf(t1361,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,meet(X3,X2))),
inference(cp,[status(thm)],[t254,t1308]) ).
cnf(t3902,plain,
join(meet(X1,X2),meet(X1,meet(X3,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t1361]) ).
cnf(t3961,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X1,X3)),
inference(cp,[status(thm)],[t3902,t118]) ).
cnf(t109533,plain,
meet(X1,join(X2,X3)) = join(meet(X1,X3),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t3961,t52]) ).
cnf(t31002,plain,
join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t109533]) ).
cnf(t109609,plain,
join(X1,meet(complement(X1),X2)) = join(X1,meet(complement(X1),join(X1,X2))),
inference(step,[status(thm)],[t109608,t31002]) ).
cnf(t69910,plain,
join(X1,meet(complement(X1),join(X1,X2))) = join(X1,meet(complement(X1),X2)),
inference(orient,[status(thm)],[t109609]) ).
cnf(t93772,plain,
join(X1,X2) = meet(join(X1,X2),join(X1,meet(complement(X1),X2))),
inference(cp,[status(thm)],[t93767,t69910]) ).
cnf(t121,plain,
X1 = meet(X1,join(X2,join(X3,X1))),
inference(cp,[status(thm)],[t118,t56]) ).
cnf(t268,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(orient,[status(thm)],[t121]) ).
cnf(t92,plain,
join(X1,meet(one,join(X2,meet(one,X1)))) = meet(one,join(X1,X2)),
inference(cp,[status(thm)],[t89,t35]) ).
cnf(t109316,plain,
join(X1,join(X2,meet(one,X1))) = meet(one,join(X1,X2)),
inference(step,[status(thm)],[t92,t89]) ).
cnf(t109317,plain,
join(X1,join(X2,X1)) = meet(one,join(X1,X2)),
inference(step,[status(thm)],[t109316,t89]) ).
cnf(t109318,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(step,[status(thm)],[t109317,t89]) ).
cnf(t138,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t109318]) ).
cnf(t143,plain,
join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3),
inference(cp,[status(thm)],[t56,t138]) ).
cnf(t109370,plain,
join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3),
inference(step,[status(thm)],[t143,t56]) ).
cnf(t109371,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t109370,t56]) ).
cnf(t1194,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t109371]) ).
cnf(t1246,plain,
join(X1,X2) = meet(join(X1,X2),join(X1,join(X3,X2))),
inference(cp,[status(thm)],[t268,t1194]) ).
cnf(t3686,plain,
meet(join(X1,X2),join(X1,join(X3,X2))) = join(X1,X2),
inference(orient,[status(thm)],[t1246]) ).
cnf(t3738,plain,
join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X3)),
inference(cp,[status(thm)],[t3686,t111]) ).
cnf(t109529,plain,
join(X1,meet(X2,X3)) = meet(join(X1,X3),join(X1,meet(X2,X3))),
inference(step,[status(thm)],[t3738,t23]) ).
cnf(t29485,plain,
meet(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(orient,[status(thm)],[t109529]) ).
cnf(t109665,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(step,[status(thm)],[t93772,t29485]) ).
cnf(t94142,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t109665]) ).
cnf(t94214,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(cp,[status(thm)],[t94142,t1308]) ).
cnf(t109703,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t94214,t94142]) ).
cnf(t100641,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t109703]) ).
cnf(t94359,plain,
join(X1,join(X2,meet(complement(X1),X3))) = join(X1,join(X2,join(X1,X3))),
inference(cp,[status(thm)],[t1194,t94142]) ).
cnf(t109706,plain,
join(X1,join(X2,meet(complement(X1),X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t94359,t1194]) ).
cnf(t101845,plain,
join(X1,join(X2,meet(complement(X1),X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t109706]) ).
cnf(t101874,plain,
join(X1,join(complement(X2),complement(meet(X2,complement(X1))))) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t101845,t92726]) ).
cnf(t51154,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t51112,t16]) ).
cnf(t109565,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t51154,t52]) ).
cnf(t51494,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t109565]) ).
cnf(t109707,plain,
join(X1,complement(meet(X2,complement(X1)))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t101874,t51494]) ).
cnf(t51518,plain,
complement(X1) = meet(complement(X1),complement(meet(X1,X2))),
inference(cp,[status(thm)],[t14,t51494]) ).
cnf(t51658,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t51518]) ).
cnf(t51659,plain,
complement(complement(X1)) = meet(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t51658,t18789]) ).
cnf(t109566,plain,
X1 = meet(X1,complement(meet(complement(X1),X2))),
inference(step,[status(thm)],[t51659,t18789]) ).
cnf(t51824,plain,
meet(X1,complement(meet(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t109566]) ).
cnf(t28,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t2204,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(t109381,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t32,t26]) ).
cnf(t1675,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t109381]) ).
cnf(t2206,plain,
meet(X1,X2) = meet(X2,meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t2204,t1675]) ).
cnf(t4093,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t2206]) ).
cnf(t51829,plain,
X1 = meet(X1,complement(meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t51824,t4093]) ).
cnf(t51999,plain,
meet(X1,complement(meet(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t51829]) ).
cnf(t52004,plain,
complement(meet(X1,complement(X2))) = join(complement(meet(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t111,t51999]) ).
cnf(t109571,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(meet(X1,complement(X2)))),
inference(step,[status(thm)],[t52004,t52]) ).
cnf(t53348,plain,
join(X1,complement(meet(X2,complement(X1)))) = complement(meet(X2,complement(X1))),
inference(orient,[status(thm)],[t109571]) ).
cnf(t109708,plain,
complement(meet(X2,complement(X1))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t109707,t53348]) ).
cnf(t102234,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t109708]) ).
cnf(t102268,plain,
meet(X1,complement(X2)) = complement(join(X2,complement(X1))),
inference(cp,[status(thm)],[t18789,t102234]) ).
cnf(t103015,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t102268]) ).
cnf(t103028,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t103015,t52]) ).
cnf(t103200,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t103028]) ).
cnf(t50190,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(cp,[status(thm)],[t50112,t145]) ).
cnf(t109611,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t50190,t50112]) ).
cnf(t71384,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),X2)),
inference(orient,[status(thm)],[t109611]) ).
cnf(t94168,plain,
join(X1,join(complement(complement(X1)),meet(X2,complement(X1)))) = join(X1,meet(complement(X1),join(complement(complement(X1)),X2))),
inference(cp,[status(thm)],[t94142,t71384]) ).
cnf(t109666,plain,
join(X1,join(X1,meet(X2,complement(X1)))) = join(X1,meet(complement(X1),join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t94168,t18789]) ).
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(t60,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t56,t15]) ).
cnf(t133,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t60]) ).
cnf(t109667,plain,
join(X1,meet(X2,complement(X1))) = join(X1,meet(complement(X1),join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t109666,t133]) ).
cnf(t109668,plain,
join(X1,meet(X2,complement(X1))) = join(X1,join(complement(complement(X1)),X2)),
inference(step,[status(thm)],[t109667,t94142]) ).
cnf(t109669,plain,
join(X1,meet(X2,complement(X1))) = join(X1,join(X1,X2)),
inference(step,[status(thm)],[t109668,t18789]) ).
cnf(t109670,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(step,[status(thm)],[t109669,t133]) ).
cnf(t94478,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t109670]) ).
cnf(t94503,plain,
join(complement(X1),X2) = join(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t94478,t18789]) ).
cnf(t95066,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t94503]) ).
cnf(t103207,plain,
meet(X1,complement(meet(X2,X1))) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t103200,t95066]) ).
cnf(t109775,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t103207,t103200]) ).
cnf(t103721,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t109775]) ).
cnf(t173,plain,
zero = meet(complement(meet(X1,X2)),meet(X2,X1)),
inference(cp,[status(thm)],[t169,t145]) ).
cnf(t109350,plain,
zero = meet(meet(X2,X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t173,t23]) ).
cnf(t109351,plain,
zero = meet(X2,meet(X1,complement(meet(X1,X2)))),
inference(step,[status(thm)],[t109350,t26]) ).
cnf(t588,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(orient,[status(thm)],[t109351]) ).
cnf(t92800,plain,
complement(X1) = join(complement(X1),meet(meet(X2,complement(meet(X2,X1))),complement(zero))),
inference(cp,[status(thm)],[t92726,t588]) ).
cnf(t109699,plain,
complement(X1) = join(complement(X1),meet(X2,meet(complement(meet(X2,X1)),complement(zero)))),
inference(step,[status(thm)],[t92800,t26]) ).
cnf(t109700,plain,
complement(X1) = join(complement(X1),meet(X2,meet(complement(zero),complement(meet(X2,X1))))),
inference(step,[status(thm)],[t109699,t23]) ).
cnf(t109701,plain,
complement(X1) = join(complement(X1),meet(X2,meet(one,complement(meet(X2,X1))))),
inference(step,[status(thm)],[t109700,t87]) ).
cnf(t109702,plain,
complement(X1) = join(complement(X1),meet(X2,complement(meet(X2,X1)))),
inference(step,[status(thm)],[t109701,t89]) ).
cnf(t100288,plain,
join(complement(X1),meet(X2,complement(meet(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t109702]) ).
cnf(t101875,plain,
join(X1,join(complement(X2),complement(meet(complement(X1),X2)))) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t101845,t100288]) ).
cnf(t51155,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t51112,t111]) ).
cnf(t109567,plain,
complement(meet(X1,X2)) = join(complement(X2),complement(meet(X1,X2))),
inference(step,[status(thm)],[t51155,t52]) ).
cnf(t52383,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(orient,[status(thm)],[t109567]) ).
cnf(t109720,plain,
join(X1,complement(meet(complement(X1),X2))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t101875,t52383]) ).
cnf(t51495,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t51494,t18789]) ).
cnf(t53179,plain,
join(X1,complement(meet(complement(X1),X2))) = complement(meet(complement(X1),X2)),
inference(orient,[status(thm)],[t51495]) ).
cnf(t109721,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(step,[status(thm)],[t109720,t53179]) ).
cnf(t102484,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t109721]) ).
cnf(t103725,plain,
meet(X1,complement(complement(X2))) = meet(X1,join(X2,complement(X1))),
inference(cp,[status(thm)],[t103721,t102484]) ).
cnf(t109776,plain,
meet(X1,X2) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t103725,t18789]) ).
cnf(t104032,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t109776]) ).
cnf(t104145,plain,
join(X1,meet(X2,join(X3,complement(complement(X1))))) = join(X1,meet(X2,meet(complement(X1),X3))),
inference(cp,[status(thm)],[t100641,t104032]) ).
cnf(t109791,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,meet(complement(X1),X3))),
inference(step,[status(thm)],[t104145,t18789]) ).
cnf(t109792,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t109791,t100641]) ).
cnf(t106382,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t109792]) ).
cnf(t104044,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t104032,t52]) ).
cnf(t104239,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t104044]) ).
cnf(t104250,plain,
meet(X1,join(X2,meet(complement(complement(X1)),X3))) = meet(X1,join(complement(X1),join(X2,X3))),
inference(cp,[status(thm)],[t104239,t101845]) ).
cnf(t109801,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(complement(X1),join(X2,X3))),
inference(step,[status(thm)],[t104250,t18789]) ).
cnf(t109802,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t109801,t104239]) ).
cnf(t106761,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t109802]) ).
cnf(t106965,plain,
join(meet(X1,X2),meet(X1,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))),
inference(cp,[status(thm)],[t106382,t106761]) ).
cnf(t109838,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(step,[status(thm)],[t106965,t31002]) ).
cnf(t108753,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t109838]) ).
cnf(f12,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f12_nnf,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
join(meet(a,b),meet(a,c)) != meet(a,join(b,c)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
meet(a,join(c,b)) != meet(a,join(b,c)),
inference(rw,[status(thm)],[goal_0,t108753]) ).
cnf(g0_1,plain,
meet(a,join(c,b)) != meet(a,join(c,b)),
inference(rw,[status(thm)],[g0_0,t52]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT210-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.46 % Computer : n015.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Wed Sep 23 20:37:25 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 46.91/6.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.91/6.48 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------