%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT249-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:56:25 PM UTC 2026
% Result : Unsatisfiable 20.10s 3.14s
% Output : Proof 20.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 15
% Syntax : Number of formulae : 219 ( 215 unt; 0 def)
% Number of atoms : 227 ( 226 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 430 ( 107 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t12,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t19,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(f11,axiom,
meet(X,join(Y,Z)) = meet(X,join(Y,meet(X,join(Z,meet(X,join(Y,meet(X,Z))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H64) ).
fof(f11_nnf,plain,
! [X,Y,Z] : meet(X,join(Y,Z)) = meet(X,join(Y,meet(X,join(Z,meet(X,join(Y,meet(X,Z))))))),
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,join(Y,meet(X,Z))))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,X2)) = meet(X0,join(X1,meet(X0,join(X2,meet(X0,join(X1,meet(X0,X2))))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X1,join(X2,meet(X1,X3))))))) = meet(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t47,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X1,join(X2,meet(X1,X3))))))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
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(t4,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t58,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t61,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(X2,meet(X1,join(complement(X1),meet(X1,join(X2,zero)))))),
inference(cp,[status(thm)],[t47,t58]) ).
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(t7,plain,
join(X1,meet(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t17,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t59,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t58]) ).
cnf(t98,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t59]) ).
cnf(t10869,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(X2,meet(X1,join(complement(X1),meet(X1,X2))))),
inference(step,[status(thm)],[t61,t98]) ).
cnf(t9880,plain,
meet(X1,join(X2,meet(X1,join(complement(X1),meet(X1,X2))))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t10869]) ).
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(t11,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
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(t8,plain,
meet(X1,X2) = meet(X2,X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t24,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t10041,plain,
meet(X3,meet(X1,X2)) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t11,t24]) ).
cnf(t27,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(orient,[status(thm)],[t10041]) ).
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(t14,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t30,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(cp,[status(thm)],[t27,t14]) ).
cnf(t10043,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t30,t27]) ).
cnf(t10044,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t10043,t24]) ).
cnf(t113,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t10044]) ).
cnf(t116,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t113,t58]) ).
cnf(t10045,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t116,t58]) ).
cnf(t124,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t10045]) ).
cnf(t127,plain,
meet(X1,join(X2,zero)) = meet(X1,join(X2,meet(X1,join(zero,meet(X1,join(X2,zero)))))),
inference(cp,[status(thm)],[t47,t124]) ).
cnf(t10095,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,join(zero,meet(X1,join(X2,zero)))))),
inference(step,[status(thm)],[t127,t98]) ).
cnf(t10096,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,join(zero,meet(X1,X2))))),
inference(step,[status(thm)],[t10095,t98]) ).
cnf(t284,plain,
meet(X1,join(X2,meet(X1,join(zero,meet(X1,X2))))) = meet(X1,X2),
inference(orient,[status(thm)],[t10096]) ).
cnf(t300,plain,
meet(X1,join(zero,X2)) = meet(X1,join(zero,meet(X1,X2))),
inference(cp,[status(thm)],[t47,t284]) ).
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(t6,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t70,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t10097,plain,
meet(X1,join(X2,zero)) = meet(X1,join(zero,meet(X1,X2))),
inference(step,[status(thm)],[t300,t70]) ).
cnf(t10098,plain,
meet(X1,X2) = meet(X1,join(zero,meet(X1,X2))),
inference(step,[status(thm)],[t10097,t98]) ).
cnf(t305,plain,
meet(X1,join(zero,meet(X1,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t10098]) ).
cnf(t319,plain,
meet(X1,join(X2,zero)) = meet(X1,join(X2,meet(X1,join(X2,meet(X1,zero))))),
inference(cp,[status(thm)],[t47,t305]) ).
cnf(t10107,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,join(X2,meet(X1,zero))))),
inference(step,[status(thm)],[t319,t98]) ).
cnf(t10108,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,join(X2,zero)))),
inference(step,[status(thm)],[t10107,t124]) ).
cnf(t10109,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,X2))),
inference(step,[status(thm)],[t10108,t98]) ).
cnf(t355,plain,
meet(X1,join(X2,meet(X1,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t10109]) ).
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(t9,plain,
meet(X1,join(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t31,plain,
meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t10057,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X3,X1),
inference(step,[status(thm)],[t31,t27]) ).
cnf(t10058,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X3,X1),
inference(step,[status(thm)],[t10057,t24]) ).
cnf(t10059,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X1,X3),
inference(step,[status(thm)],[t10058,t24]) ).
cnf(t172,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t10059]) ).
cnf(t358,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,join(meet(X2,join(X1,X3)),meet(X1,X2))),
inference(cp,[status(thm)],[t355,t172]) ).
cnf(t10116,plain,
meet(X1,X2) = meet(X1,join(meet(X2,join(X1,X3)),meet(X1,X2))),
inference(step,[status(thm)],[t358,t172]) ).
cnf(t10117,plain,
meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(X2,join(X1,X3)))),
inference(step,[status(thm)],[t10116,t70]) ).
cnf(t445,plain,
meet(X1,join(meet(X1,X2),meet(X2,join(X1,X3)))) = meet(X1,X2),
inference(orient,[status(thm)],[t10117]) ).
cnf(t456,plain,
meet(X1,join(X2,meet(X1,X2))) = meet(X1,join(meet(X1,X2),meet(join(X2,meet(X1,X2)),join(X1,X3)))),
inference(cp,[status(thm)],[t445,t355]) ).
cnf(t10436,plain,
meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(join(X2,meet(X1,X2)),join(X1,X3)))),
inference(step,[status(thm)],[t456,t355]) ).
cnf(t10437,plain,
meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(join(X1,X3),join(X2,meet(X1,X2))))),
inference(step,[status(thm)],[t10436,t24]) ).
cnf(t3545,plain,
meet(X1,join(meet(X1,X2),meet(join(X1,X3),join(X2,meet(X1,X2))))) = meet(X1,X2),
inference(orient,[status(thm)],[t10437]) ).
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(t10,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t10042,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t10,t70]) ).
cnf(t74,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t10042]) ).
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(t3,plain,
join(X1,complement(X1)) = one,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t94,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t96,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t74,t94]) ).
cnf(t10055,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t96,t70]) ).
cnf(f1,axiom,
join(X,X) = X,
file('/export/starexec/sandbox2/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(t16,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t77,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t74,t16]) ).
cnf(t10046,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t77,t74]) ).
cnf(t10047,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t10046,t70]) ).
cnf(t130,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t10047]) ).
cnf(t133,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t130,t94]) ).
cnf(t10048,plain,
one = join(X1,one),
inference(step,[status(thm)],[t133,t94]) ).
cnf(t140,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t10048]) ).
cnf(t10056,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t10055,t140]) ).
cnf(t165,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t10056]) ).
cnf(t170,plain,
join(X1,join(join(X2,complement(X1)),X3)) = join(X3,one),
inference(cp,[status(thm)],[t74,t165]) ).
cnf(t10067,plain,
join(X1,join(X3,join(X2,complement(X1)))) = join(X3,one),
inference(step,[status(thm)],[t170,t70]) ).
cnf(t10068,plain,
join(X1,join(X2,join(complement(X1),X3))) = join(X3,one),
inference(step,[status(thm)],[t10067,t74]) ).
cnf(t10069,plain,
join(X1,join(X2,join(X3,complement(X1)))) = join(X3,one),
inference(step,[status(thm)],[t10068,t70]) ).
cnf(t10070,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(step,[status(thm)],[t10069,t140]) ).
cnf(t210,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(orient,[status(thm)],[t10070]) ).
cnf(t3623,plain,
meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(one,join(X2,meet(X1,X2))))),
inference(cp,[status(thm)],[t3545,t210]) ).
cnf(t3742,plain,
meet(X1,join(meet(X1,X2),meet(one,join(X2,meet(X1,X2))))) = meet(X1,X2),
inference(orient,[status(thm)],[t3623]) ).
cnf(t322,plain,
meet(X1,meet(join(zero,meet(X1,X2)),X3)) = meet(X3,meet(X1,X2)),
inference(cp,[status(thm)],[t27,t305]) ).
cnf(t10110,plain,
meet(X1,meet(X3,join(zero,meet(X1,X2)))) = meet(X3,meet(X1,X2)),
inference(step,[status(thm)],[t322,t24]) ).
cnf(t10111,plain,
meet(X1,meet(X3,join(zero,meet(X1,X2)))) = meet(X2,meet(X3,X1)),
inference(step,[status(thm)],[t10110,t27]) ).
cnf(t10112,plain,
meet(X1,meet(X3,join(zero,meet(X1,X2)))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t10111,t27]) ).
cnf(t372,plain,
meet(X1,meet(X2,join(zero,meet(X1,X3)))) = meet(X1,meet(X3,X2)),
inference(orient,[status(thm)],[t10112]) ).
cnf(t62,plain,
meet(X1,meet(complement(X1),X2)) = meet(X2,zero),
inference(cp,[status(thm)],[t27,t58]) ).
cnf(t10053,plain,
meet(X1,meet(X2,complement(X1))) = meet(X2,zero),
inference(step,[status(thm)],[t62,t24]) ).
cnf(t10054,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t10053,t124]) ).
cnf(t157,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t10054]) ).
cnf(t451,plain,
meet(X1,meet(X2,complement(X1))) = meet(X1,join(zero,meet(meet(X2,complement(X1)),join(X1,X3)))),
inference(cp,[status(thm)],[t445,t157]) ).
cnf(t10154,plain,
zero = meet(X1,join(zero,meet(meet(X2,complement(X1)),join(X1,X3)))),
inference(step,[status(thm)],[t451,t157]) ).
cnf(t10155,plain,
zero = meet(X1,join(zero,meet(join(X1,X3),meet(X2,complement(X1))))),
inference(step,[status(thm)],[t10154,t24]) ).
cnf(t10156,plain,
zero = meet(X1,join(zero,meet(complement(X1),meet(join(X1,X3),X2)))),
inference(step,[status(thm)],[t10155,t27]) ).
cnf(t10157,plain,
zero = meet(X1,join(zero,meet(X2,meet(complement(X1),join(X1,X3))))),
inference(step,[status(thm)],[t10156,t27]) ).
cnf(t606,plain,
meet(X1,join(zero,meet(X2,meet(complement(X1),join(X1,X3))))) = zero,
inference(orient,[status(thm)],[t10157]) ).
cnf(t613,plain,
zero = meet(X1,join(zero,meet(X2,meet(complement(X1),one)))),
inference(cp,[status(thm)],[t606,t210]) ).
cnf(t95,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t15,t94]) ).
cnf(t107,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t95]) ).
cnf(t10158,plain,
zero = meet(X1,join(zero,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t613,t107]) ).
cnf(t635,plain,
meet(X1,join(zero,meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t10158]) ).
cnf(t642,plain,
meet(X1,meet(join(zero,meet(X2,complement(X1))),X3)) = meet(X1,meet(X3,join(zero,zero))),
inference(cp,[status(thm)],[t372,t635]) ).
cnf(t10159,plain,
meet(X1,meet(X3,join(zero,meet(X2,complement(X1))))) = meet(X1,meet(X3,join(zero,zero))),
inference(step,[status(thm)],[t642,t24]) ).
cnf(t10160,plain,
meet(X1,meet(X3,join(zero,meet(X2,complement(X1))))) = meet(X1,meet(X3,zero)),
inference(step,[status(thm)],[t10159,t98]) ).
cnf(t10161,plain,
meet(X1,meet(X3,join(zero,meet(X2,complement(X1))))) = meet(X1,zero),
inference(step,[status(thm)],[t10160,t124]) ).
cnf(t10162,plain,
meet(X1,meet(X3,join(zero,meet(X2,complement(X1))))) = zero,
inference(step,[status(thm)],[t10161,t124]) ).
cnf(t647,plain,
meet(X1,meet(X2,join(zero,meet(X3,complement(X1))))) = zero,
inference(orient,[status(thm)],[t10162]) ).
cnf(t657,plain,
meet(X1,meet(meet(X2,join(zero,meet(X3,complement(X1)))),Y3)) = meet(X1,meet(Y3,join(zero,zero))),
inference(cp,[status(thm)],[t372,t647]) ).
cnf(t10167,plain,
meet(X1,meet(Y3,meet(X2,join(zero,meet(X3,complement(X1)))))) = meet(X1,meet(Y3,join(zero,zero))),
inference(step,[status(thm)],[t657,t24]) ).
cnf(t10168,plain,
meet(X1,meet(X2,meet(join(zero,meet(X3,complement(X1))),Y3))) = meet(X1,meet(Y3,join(zero,zero))),
inference(step,[status(thm)],[t10167,t27]) ).
cnf(t10169,plain,
meet(X1,meet(X2,meet(Y3,join(zero,meet(X3,complement(X1)))))) = meet(X1,meet(Y3,join(zero,zero))),
inference(step,[status(thm)],[t10168,t24]) ).
cnf(t10170,plain,
meet(X1,meet(X2,meet(Y3,join(zero,meet(X3,complement(X1)))))) = meet(X1,meet(Y3,zero)),
inference(step,[status(thm)],[t10169,t98]) ).
cnf(t10171,plain,
meet(X1,meet(X2,meet(Y3,join(zero,meet(X3,complement(X1)))))) = meet(X1,zero),
inference(step,[status(thm)],[t10170,t124]) ).
cnf(t10172,plain,
meet(X1,meet(X2,meet(Y3,join(zero,meet(X3,complement(X1)))))) = zero,
inference(step,[status(thm)],[t10171,t124]) ).
cnf(t689,plain,
meet(X1,meet(X2,meet(X3,join(zero,meet(Y3,complement(X1)))))) = zero,
inference(orient,[status(thm)],[t10172]) ).
cnf(t3766,plain,
meet(X1,meet(X2,meet(X3,join(zero,meet(Y3,complement(X1)))))) = meet(X1,join(zero,meet(one,join(meet(X2,meet(X3,join(zero,meet(Y3,complement(X1))))),meet(X1,meet(X2,meet(X3,join(zero,meet(Y3,complement(X1)))))))))),
inference(cp,[status(thm)],[t3742,t689]) ).
cnf(t10612,plain,
zero = meet(X1,join(zero,meet(one,join(meet(X2,meet(X3,join(zero,meet(Y3,complement(X1))))),meet(X1,meet(X2,meet(X3,join(zero,meet(Y3,complement(X1)))))))))),
inference(step,[status(thm)],[t3766,t689]) ).
cnf(t10613,plain,
zero = meet(X1,join(zero,meet(one,join(meet(X2,meet(X3,join(zero,meet(Y3,complement(X1))))),zero)))),
inference(step,[status(thm)],[t10612,t689]) ).
cnf(t10614,plain,
zero = meet(X1,join(zero,meet(one,meet(X2,meet(X3,join(zero,meet(Y3,complement(X1)))))))),
inference(step,[status(thm)],[t10613,t98]) ).
cnf(t10615,plain,
zero = meet(X1,join(zero,meet(X2,meet(meet(X3,join(zero,meet(Y3,complement(X1)))),one)))),
inference(step,[status(thm)],[t10614,t27]) ).
cnf(t10616,plain,
zero = meet(X1,join(zero,meet(X2,meet(X3,join(zero,meet(Y3,complement(X1))))))),
inference(step,[status(thm)],[t10615,t107]) ).
cnf(t6371,plain,
meet(X1,join(zero,meet(X2,meet(X3,join(zero,meet(Y3,complement(X1))))))) = zero,
inference(orient,[status(thm)],[t10616]) ).
cnf(t26,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1),
inference(cp,[status(thm)],[t19,t24]) ).
cnf(t10221,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1),
inference(step,[status(thm)],[t26,t70]) ).
cnf(t905,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t10221]) ).
cnf(t926,plain,
X1 = ifeq(zero,zero,ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t905,t58]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t10222,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t926,t18]) ).
cnf(t10223,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t10222,t94]) ).
cnf(t10224,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t10223,t18]) ).
cnf(t953,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t10224]) ).
cnf(t6378,plain,
zero = meet(complement(X1),join(zero,meet(X2,meet(X3,join(zero,meet(Y3,X1)))))),
inference(cp,[status(thm)],[t6371,t953]) ).
cnf(t10617,plain,
zero = meet(complement(X1),join(zero,meet(X2,meet(X3,join(zero,meet(X1,Y3)))))),
inference(step,[status(thm)],[t6378,t24]) ).
cnf(t6426,plain,
meet(complement(X1),join(zero,meet(X2,meet(X3,join(zero,meet(X1,Y3)))))) = zero,
inference(orient,[status(thm)],[t10617]) ).
cnf(f12,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
fof(f12_nnf,plain,
meet(b,a) = a,
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
meet(b,a) = a,
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t2,plain,
meet(b,a) = a,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t64,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t67,plain,
meet(b,join(X1,a)) = meet(b,join(X1,meet(b,join(a,meet(b,join(X1,a)))))),
inference(cp,[status(thm)],[t47,t64]) ).
cnf(t1596,plain,
meet(b,join(X1,meet(b,join(a,meet(b,join(X1,a)))))) = meet(b,join(X1,a)),
inference(orient,[status(thm)],[t67]) ).
cnf(t6435,plain,
zero = meet(complement(b),join(zero,meet(X1,meet(b,join(zero,a))))),
inference(cp,[status(thm)],[t6426,t1596]) ).
cnf(t312,plain,
meet(b,a) = meet(b,join(zero,a)),
inference(cp,[status(thm)],[t305,t64]) ).
cnf(t10100,plain,
a = meet(b,join(zero,a)),
inference(step,[status(thm)],[t312,t64]) ).
cnf(t325,plain,
meet(b,join(zero,a)) = a,
inference(orient,[status(thm)],[t10100]) ).
cnf(t10618,plain,
zero = meet(complement(b),join(zero,meet(X1,a))),
inference(step,[status(thm)],[t6435,t325]) ).
cnf(t6501,plain,
meet(complement(b),join(zero,meet(X1,a))) = zero,
inference(orient,[status(thm)],[t10618]) ).
cnf(t6502,plain,
zero = meet(complement(b),a),
inference(cp,[status(thm)],[t6501,t305]) ).
cnf(t10619,plain,
zero = meet(a,complement(b)),
inference(step,[status(thm)],[t6502,t24]) ).
cnf(t6536,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t10619]) ).
cnf(t9927,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(b),meet(a,join(complement(a),zero)))),
inference(cp,[status(thm)],[t9880,t6536]) ).
cnf(t10870,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(b),meet(a,complement(a)))),
inference(step,[status(thm)],[t9927,t98]) ).
cnf(t10871,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(b),zero)),
inference(step,[status(thm)],[t10870,t58]) ).
cnf(t10872,plain,
meet(a,join(complement(b),complement(a))) = meet(a,complement(b)),
inference(step,[status(thm)],[t10871,t98]) ).
cnf(t10873,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(step,[status(thm)],[t10872,t6536]) ).
cnf(t9985,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t10873]) ).
cnf(t9986,plain,
join(complement(b),complement(a)) = ifeq(zero,zero,ifeq(join(a,join(complement(b),complement(a))),one,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(cp,[status(thm)],[t19,t9985]) ).
cnf(t10874,plain,
join(complement(b),complement(a)) = ifeq(join(a,join(complement(b),complement(a))),one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t9986,t18]) ).
cnf(t10875,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t10874,t165]) ).
cnf(t10876,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t10875,t18]) ).
cnf(t10011,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t10876]) ).
cnf(f13,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f13_nnf,plain,
join(complement(b),complement(a)) != complement(a),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
join(complement(b),complement(a)) != complement(a),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
join(complement(b),complement(a)) != complement(a),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
complement(a) != complement(a),
inference(rw,[status(thm)],[goal_0,t10011]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT249-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 20:44:38 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.10/3.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.10/3.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------