%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT253-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:56:26 PM UTC 2026
% Result : Unsatisfiable 16.70s 2.52s
% Output : Proof 16.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 15
% Syntax : Number of formulae : 183 ( 179 unt; 0 def)
% Number of atoms : 191 ( 190 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 : 7 ( 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 : 317 ( 56 sgn 48 !; 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,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))),
file('/export/starexec/sandbox2/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(t13,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(t47,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)],[t13]) ).
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(t51,plain,
meet(X1,join(X2,meet(X3,join(X2,X1)))) = meet(X1,join(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t47,t17]) ).
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(t74,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t1675,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X3,X1))),
inference(step,[status(thm)],[t51,t74]) ).
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(t1676,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(step,[status(thm)],[t1675,t24]) ).
cnf(t305,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(orient,[status(thm)],[t1676]) ).
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(t98,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t319,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),meet(X2,one))),
inference(cp,[status(thm)],[t305,t98]) ).
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(t99,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t15,t98]) ).
cnf(t111,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t99]) ).
cnf(t1702,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t319,t111]) ).
cnf(t1703,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t1702,t74]) ).
cnf(t451,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t1703]) ).
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(t1621,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)],[t1621]) ).
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(t62,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t66,plain,
meet(X1,meet(complement(X1),X2)) = meet(X2,zero),
inference(cp,[status(thm)],[t27,t62]) ).
cnf(t1633,plain,
meet(X1,meet(X2,complement(X1))) = meet(X2,zero),
inference(step,[status(thm)],[t66,t24]) ).
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(t1623,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t30,t27]) ).
cnf(t1624,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t1623,t24]) ).
cnf(t117,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t1624]) ).
cnf(t120,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t117,t62]) ).
cnf(t1625,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t120,t62]) ).
cnf(t128,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t1625]) ).
cnf(t1634,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t1633,t128]) ).
cnf(t161,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t1634]) ).
cnf(t167,plain,
meet(X1,meet(meet(X2,complement(X1)),X3)) = meet(X3,zero),
inference(cp,[status(thm)],[t27,t161]) ).
cnf(t1643,plain,
meet(X1,meet(X3,meet(X2,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t167,t24]) ).
cnf(t1644,plain,
meet(X1,meet(X2,meet(complement(X1),X3))) = meet(X3,zero),
inference(step,[status(thm)],[t1643,t27]) ).
cnf(t1645,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t1644,t24]) ).
cnf(t1646,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(step,[status(thm)],[t1645,t128]) ).
cnf(t203,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(orient,[status(thm)],[t1646]) ).
cnf(t462,plain,
meet(X1,join(meet(X2,meet(X3,complement(X1))),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t451,t203]) ).
cnf(t1738,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t462,t74]) ).
cnf(t63,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t62]) ).
cnf(t102,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t63]) ).
cnf(t1739,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t1738,t102]) ).
cnf(t1740,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = zero,
inference(step,[status(thm)],[t1739,t62]) ).
cnf(t633,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = zero,
inference(orient,[status(thm)],[t1740]) ).
cnf(t31,plain,
meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t1637,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X3,X1),
inference(step,[status(thm)],[t31,t27]) ).
cnf(t1638,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X3,X1),
inference(step,[status(thm)],[t1637,t24]) ).
cnf(t1639,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X1,X3),
inference(step,[status(thm)],[t1638,t24]) ).
cnf(t176,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t1639]) ).
cnf(t467,plain,
meet(X1,join(meet(X2,join(X1,X3)),complement(X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(cp,[status(thm)],[t451,t176]) ).
cnf(t1870,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(step,[status(thm)],[t467,t74]) ).
cnf(t1871,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t1870,t451]) ).
cnf(t1331,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t1871]) ).
cnf(t466,plain,
meet(X1,join(meet(X2,complement(X1)),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t451,t161]) ).
cnf(t1724,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t466,t74]) ).
cnf(t1725,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t1724,t102]) ).
cnf(t1726,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(step,[status(thm)],[t1725,t62]) ).
cnf(t561,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t1726]) ).
cnf(t1342,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = meet(complement(X1),join(complement(complement(X1)),zero)),
inference(cp,[status(thm)],[t1331,t561]) ).
cnf(t1872,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = meet(complement(X1),complement(complement(X1))),
inference(step,[status(thm)],[t1342,t102]) ).
cnf(t1873,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = zero,
inference(step,[status(thm)],[t1872,t62]) ).
cnf(t1380,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = zero,
inference(orient,[status(thm)],[t1873]) ).
cnf(t1381,plain,
join(X1,complement(complement(X1))) = ifeq(zero,zero,ifeq(join(complement(X1),join(X1,complement(complement(X1)))),one,complement(complement(X1)),join(X1,complement(complement(X1)))),join(X1,complement(complement(X1)))),
inference(cp,[status(thm)],[t19,t1380]) ).
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(t1874,plain,
join(X1,complement(complement(X1))) = ifeq(join(complement(X1),join(X1,complement(complement(X1)))),one,complement(complement(X1)),join(X1,complement(complement(X1)))),
inference(step,[status(thm)],[t1381,t18]) ).
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(t1622,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t10,t74]) ).
cnf(t78,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t1622]) ).
cnf(t100,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t78,t98]) ).
cnf(t1635,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t100,t74]) ).
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(t81,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t78,t16]) ).
cnf(t1626,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t81,t78]) ).
cnf(t1627,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t1626,t74]) ).
cnf(t134,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1627]) ).
cnf(t137,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t134,t98]) ).
cnf(t1628,plain,
one = join(X1,one),
inference(step,[status(thm)],[t137,t98]) ).
cnf(t144,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t1628]) ).
cnf(t1636,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t1635,t144]) ).
cnf(t169,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t1636]) ).
cnf(t1875,plain,
join(X1,complement(complement(X1))) = ifeq(one,one,complement(complement(X1)),join(X1,complement(complement(X1)))),
inference(step,[status(thm)],[t1874,t169]) ).
cnf(t1876,plain,
join(X1,complement(complement(X1))) = complement(complement(X1)),
inference(step,[status(thm)],[t1875,t18]) ).
cnf(t1388,plain,
join(X1,complement(complement(X1))) = complement(complement(X1)),
inference(orient,[status(thm)],[t1876]) ).
cnf(t1389,plain,
X1 = meet(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t15,t1388]) ).
cnf(t1403,plain,
meet(X1,complement(complement(X1))) = X1,
inference(orient,[status(thm)],[t1389]) ).
cnf(t1427,plain,
zero = meet(complement(X1),join(complement(complement(X1)),meet(X2,X1))),
inference(cp,[status(thm)],[t633,t1403]) ).
cnf(t1878,plain,
zero = meet(complement(X1),join(meet(X2,X1),complement(complement(X1)))),
inference(step,[status(thm)],[t1427,t74]) ).
cnf(t1879,plain,
zero = meet(complement(X1),join(meet(X1,X2),complement(complement(X1)))),
inference(step,[status(thm)],[t1878,t24]) ).
cnf(t1506,plain,
meet(complement(X1),join(meet(X1,X2),complement(complement(X1)))) = zero,
inference(orient,[status(thm)],[t1879]) ).
cnf(t1514,plain,
join(meet(X1,X2),complement(complement(X1))) = ifeq(zero,zero,ifeq(join(complement(X1),join(meet(X1,X2),complement(complement(X1)))),one,complement(complement(X1)),join(meet(X1,X2),complement(complement(X1)))),join(meet(X1,X2),complement(complement(X1)))),
inference(cp,[status(thm)],[t19,t1506]) ).
cnf(t1880,plain,
join(meet(X1,X2),complement(complement(X1))) = ifeq(join(complement(X1),join(meet(X1,X2),complement(complement(X1)))),one,complement(complement(X1)),join(meet(X1,X2),complement(complement(X1)))),
inference(step,[status(thm)],[t1514,t18]) ).
cnf(t1881,plain,
join(meet(X1,X2),complement(complement(X1))) = ifeq(one,one,complement(complement(X1)),join(meet(X1,X2),complement(complement(X1)))),
inference(step,[status(thm)],[t1880,t169]) ).
cnf(t1882,plain,
join(meet(X1,X2),complement(complement(X1))) = complement(complement(X1)),
inference(step,[status(thm)],[t1881,t18]) ).
cnf(t1525,plain,
join(meet(X1,X2),complement(complement(X1))) = complement(complement(X1)),
inference(orient,[status(thm)],[t1882]) ).
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(t68,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t1527,plain,
complement(complement(b)) = join(a,complement(complement(b))),
inference(cp,[status(thm)],[t1525,t68]) ).
cnf(t1547,plain,
join(a,complement(complement(b))) = complement(complement(b)),
inference(orient,[status(thm)],[t1527]) ).
cnf(t1548,plain,
a = meet(a,complement(complement(b))),
inference(cp,[status(thm)],[t15,t1547]) ).
cnf(t1563,plain,
meet(a,complement(complement(b))) = a,
inference(orient,[status(thm)],[t1548]) ).
cnf(t1568,plain,
zero = meet(complement(b),a),
inference(cp,[status(thm)],[t161,t1563]) ).
cnf(t1883,plain,
zero = meet(a,complement(b)),
inference(step,[status(thm)],[t1568,t24]) ).
cnf(t1586,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t1883]) ).
cnf(t1588,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),zero)),
inference(cp,[status(thm)],[t451,t1586]) ).
cnf(t1884,plain,
meet(a,join(complement(b),complement(a))) = meet(a,complement(a)),
inference(step,[status(thm)],[t1588,t102]) ).
cnf(t1885,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(step,[status(thm)],[t1884,t62]) ).
cnf(t1594,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t1885]) ).
cnf(t1595,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,t1594]) ).
cnf(t1886,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)],[t1595,t18]) ).
cnf(t1887,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t1886,t169]) ).
cnf(t1888,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t1887,t18]) ).
cnf(t1605,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t1888]) ).
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,t1605]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT253-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 20:42:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.70/2.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.70/2.52 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------