%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT250-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:56:25 PM UTC 2026
% Result : Unsatisfiable 16.02s 2.42s
% Output : Proof 16.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 15
% Syntax : Number of formulae : 186 ( 182 unt; 0 def)
% Number of atoms : 194 ( 193 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 : 306 ( 62 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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,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(t13,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X1,X2))))) = meet(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t47,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X1,X2))))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
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(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(complement(X1),X2)) = meet(X1,join(complement(X1),meet(X1,join(X2,zero)))),
inference(cp,[status(thm)],[t47,t58]) ).
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(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(t1451,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(complement(X1),meet(X1,join(X2,zero)))),
inference(step,[status(thm)],[t61,t70]) ).
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(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(t1452,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(step,[status(thm)],[t1451,t98]) ).
cnf(t732,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t1452]) ).
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(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/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(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(t1302,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)],[t1302]) ).
cnf(t62,plain,
meet(X1,meet(complement(X1),X2)) = meet(X2,zero),
inference(cp,[status(thm)],[t27,t58]) ).
cnf(t1314,plain,
meet(X1,meet(X2,complement(X1))) = meet(X2,zero),
inference(step,[status(thm)],[t62,t24]) ).
cnf(f0,axiom,
meet(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
fof(f0_nnf,plain,
! [X] : meet(X,X) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : meet(X,X) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
meet(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
meet(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(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(t1304,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t30,t27]) ).
cnf(t1305,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t1304,t24]) ).
cnf(t113,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t1305]) ).
cnf(t116,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t113,t58]) ).
cnf(t1306,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t116,t58]) ).
cnf(t124,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t1306]) ).
cnf(t1315,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t1314,t124]) ).
cnf(t157,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t1315]) ).
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(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(t163,plain,
meet(X1,meet(meet(X2,complement(X1)),X3)) = meet(X3,zero),
inference(cp,[status(thm)],[t27,t157]) ).
cnf(t1324,plain,
meet(X1,meet(X3,meet(X2,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t163,t24]) ).
cnf(t1325,plain,
meet(X1,meet(X2,meet(complement(X1),X3))) = meet(X3,zero),
inference(step,[status(thm)],[t1324,t27]) ).
cnf(t1326,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = meet(X3,zero),
inference(step,[status(thm)],[t1325,t24]) ).
cnf(t1327,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(step,[status(thm)],[t1326,t124]) ).
cnf(t199,plain,
meet(X1,meet(X2,meet(X3,complement(X1)))) = zero,
inference(orient,[status(thm)],[t1327]) ).
cnf(t745,plain,
meet(X1,join(meet(X2,meet(X3,complement(X1))),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t732,t199]) ).
cnf(t1473,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t745,t70]) ).
cnf(t1474,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t1473,t98]) ).
cnf(t1475,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = zero,
inference(step,[status(thm)],[t1474,t58]) ).
cnf(t849,plain,
meet(X1,join(complement(X1),meet(X2,meet(X3,complement(X1))))) = zero,
inference(orient,[status(thm)],[t1475]) ).
cnf(t31,plain,
meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t1318,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X3,X1),
inference(step,[status(thm)],[t31,t27]) ).
cnf(t1319,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X3,X1),
inference(step,[status(thm)],[t1318,t24]) ).
cnf(t1320,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X1,X3),
inference(step,[status(thm)],[t1319,t24]) ).
cnf(t172,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t1320]) ).
cnf(t750,plain,
meet(X1,join(meet(X2,join(X1,X3)),complement(X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(cp,[status(thm)],[t732,t172]) ).
cnf(t1498,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(step,[status(thm)],[t750,t70]) ).
cnf(t1499,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t1498,t732]) ).
cnf(t983,plain,
meet(X1,join(complement(X1),meet(X2,join(X1,X3)))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t1499]) ).
cnf(t749,plain,
meet(X1,join(meet(X2,complement(X1)),complement(X1))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t732,t157]) ).
cnf(t1458,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = meet(X1,join(complement(X1),zero)),
inference(step,[status(thm)],[t749,t70]) ).
cnf(t1459,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t1458,t98]) ).
cnf(t1460,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(step,[status(thm)],[t1459,t58]) ).
cnf(t804,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t1460]) ).
cnf(t991,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = meet(complement(X1),join(complement(complement(X1)),zero)),
inference(cp,[status(thm)],[t983,t804]) ).
cnf(t1500,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = meet(complement(X1),complement(complement(X1))),
inference(step,[status(thm)],[t991,t98]) ).
cnf(t1501,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = zero,
inference(step,[status(thm)],[t1500,t58]) ).
cnf(t1026,plain,
meet(complement(X1),join(X1,complement(complement(X1)))) = zero,
inference(orient,[status(thm)],[t1501]) ).
cnf(t1027,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,t1026]) ).
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(t1502,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)],[t1027,t18]) ).
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(t10,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t1303,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)],[t1303]) ).
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(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(t1316,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/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(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(t1307,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t77,t74]) ).
cnf(t1308,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t1307,t70]) ).
cnf(t130,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1308]) ).
cnf(t133,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t130,t94]) ).
cnf(t1309,plain,
one = join(X1,one),
inference(step,[status(thm)],[t133,t94]) ).
cnf(t140,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t1309]) ).
cnf(t1317,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t1316,t140]) ).
cnf(t165,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t1317]) ).
cnf(t1503,plain,
join(X1,complement(complement(X1))) = ifeq(one,one,complement(complement(X1)),join(X1,complement(complement(X1)))),
inference(step,[status(thm)],[t1502,t165]) ).
cnf(t1504,plain,
join(X1,complement(complement(X1))) = complement(complement(X1)),
inference(step,[status(thm)],[t1503,t18]) ).
cnf(t1036,plain,
join(X1,complement(complement(X1))) = complement(complement(X1)),
inference(orient,[status(thm)],[t1504]) ).
cnf(t1037,plain,
X1 = meet(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t15,t1036]) ).
cnf(t1050,plain,
meet(X1,complement(complement(X1))) = X1,
inference(orient,[status(thm)],[t1037]) ).
cnf(t1067,plain,
zero = meet(complement(X1),join(complement(complement(X1)),meet(X2,X1))),
inference(cp,[status(thm)],[t849,t1050]) ).
cnf(t1510,plain,
zero = meet(complement(X1),join(meet(X2,X1),complement(complement(X1)))),
inference(step,[status(thm)],[t1067,t70]) ).
cnf(t1511,plain,
zero = meet(complement(X1),join(meet(X1,X2),complement(complement(X1)))),
inference(step,[status(thm)],[t1510,t24]) ).
cnf(t1169,plain,
meet(complement(X1),join(meet(X1,X2),complement(complement(X1)))) = zero,
inference(orient,[status(thm)],[t1511]) ).
cnf(t1180,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,t1169]) ).
cnf(t1512,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)],[t1180,t18]) ).
cnf(t1513,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)],[t1512,t165]) ).
cnf(t1514,plain,
join(meet(X1,X2),complement(complement(X1))) = complement(complement(X1)),
inference(step,[status(thm)],[t1513,t18]) ).
cnf(t1192,plain,
join(meet(X1,X2),complement(complement(X1))) = complement(complement(X1)),
inference(orient,[status(thm)],[t1514]) ).
cnf(f12,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/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(a,X1)) = meet(b,join(a,meet(b,join(X1,a)))),
inference(cp,[status(thm)],[t47,t64]) ).
cnf(t1363,plain,
meet(b,join(X1,a)) = meet(b,join(a,meet(b,join(X1,a)))),
inference(step,[status(thm)],[t67,t70]) ).
cnf(t314,plain,
meet(b,join(a,meet(b,join(X1,a)))) = meet(b,join(X1,a)),
inference(orient,[status(thm)],[t1363]) ).
cnf(t320,plain,
meet(a,b) = meet(a,meet(b,join(X1,a))),
inference(cp,[status(thm)],[t172,t314]) ).
cnf(t1364,plain,
meet(b,a) = meet(a,meet(b,join(X1,a))),
inference(step,[status(thm)],[t320,t24]) ).
cnf(t1365,plain,
a = meet(a,meet(b,join(X1,a))),
inference(step,[status(thm)],[t1364,t64]) ).
cnf(t1366,plain,
a = meet(b,meet(join(X1,a),a)),
inference(step,[status(thm)],[t1365,t27]) ).
cnf(t1367,plain,
a = meet(b,meet(a,join(X1,a))),
inference(step,[status(thm)],[t1366,t24]) ).
cnf(t325,plain,
meet(b,meet(a,join(X1,a))) = a,
inference(orient,[status(thm)],[t1367]) ).
cnf(t1194,plain,
complement(complement(b)) = join(a,complement(complement(b))),
inference(cp,[status(thm)],[t1192,t325]) ).
cnf(t1216,plain,
join(a,complement(complement(b))) = complement(complement(b)),
inference(orient,[status(thm)],[t1194]) ).
cnf(t1217,plain,
a = meet(a,complement(complement(b))),
inference(cp,[status(thm)],[t15,t1216]) ).
cnf(t1231,plain,
meet(a,complement(complement(b))) = a,
inference(orient,[status(thm)],[t1217]) ).
cnf(t1236,plain,
zero = meet(complement(b),a),
inference(cp,[status(thm)],[t157,t1231]) ).
cnf(t1515,plain,
zero = meet(a,complement(b)),
inference(step,[status(thm)],[t1236,t24]) ).
cnf(t1254,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t1515]) ).
cnf(t1256,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),zero)),
inference(cp,[status(thm)],[t732,t1254]) ).
cnf(t1516,plain,
meet(a,join(complement(b),complement(a))) = meet(a,complement(a)),
inference(step,[status(thm)],[t1256,t98]) ).
cnf(t1517,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(step,[status(thm)],[t1516,t58]) ).
cnf(t1275,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t1517]) ).
cnf(t1276,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,t1275]) ).
cnf(t1518,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)],[t1276,t18]) ).
cnf(t1519,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t1518,t165]) ).
cnf(t1520,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t1519,t18]) ).
cnf(t1287,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t1520]) ).
cnf(f13,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/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,t1287]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT250-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 20:37:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.02/2.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.02/2.42 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------