%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT196-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:55:51 PM UTC 2026
% Result : Unsatisfiable 52.66s 7.10s
% Output : Proof 52.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 13
% Syntax : Number of formulae : 310 ( 306 unt; 0 def)
% Number of atoms : 318 ( 317 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 : 657 ( 77 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t59,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
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(t61,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(cp,[status(thm)],[t59,t16]) ).
cnf(t2326,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(orient,[status(thm)],[t61]) ).
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(t54,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t65,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t59,t54]) ).
cnf(t112094,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t65,t59]) ).
cnf(t1935,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t112094]) ).
cnf(t2328,plain,
join(X1,X2) = join(X2,join(X1,meet(join(X1,X2),X3))),
inference(cp,[status(thm)],[t2326,t1935]) ).
cnf(t4249,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(orient,[status(thm)],[t2328]) ).
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(t24,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t16,t23]) ).
cnf(t113,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t24]) ).
cnf(f6,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
fof(f6_nnf,plain,
! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t10,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(f2,axiom,
meet(X,join(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
fof(f2_nnf,plain,
! [X,Y] : meet(X,join(X,Y)) = X,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : meet(X,join(X,Y)) = X,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
meet(X0,join(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t8,plain,
meet(X1,join(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t14,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t31,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t304,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t31]) ).
cnf(t317,plain,
meet(join(X1,X2),X3) = join(meet(join(X1,X2),X3),meet(X1,X3)),
inference(cp,[status(thm)],[t113,t304]) ).
cnf(t112208,plain,
meet(join(X1,X2),X3) = join(meet(X1,X3),meet(join(X1,X2),X3)),
inference(step,[status(thm)],[t317,t54]) ).
cnf(t18823,plain,
join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2),
inference(orient,[status(thm)],[t112208]) ).
cnf(t18845,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))),
inference(cp,[status(thm)],[t18823,t14]) ).
cnf(t34788,plain,
join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)),
inference(orient,[status(thm)],[t18845]) ).
cnf(t34965,plain,
join(X1,X2) = join(X2,meet(join(X1,X2),join(X1,X3))),
inference(cp,[status(thm)],[t4249,t34788]) ).
cnf(t35016,plain,
join(X1,meet(join(X2,X1),join(X2,X3))) = join(X2,X1),
inference(orient,[status(thm)],[t34965]) ).
cnf(t35143,plain,
join(X1,X2) = join(X2,meet(join(X2,X1),join(X1,X3))),
inference(cp,[status(thm)],[t35016,t54]) ).
cnf(t35717,plain,
join(X1,meet(join(X1,X2),join(X2,X3))) = join(X2,X1),
inference(orient,[status(thm)],[t35143]) ).
cnf(t35872,plain,
join(X1,X2) = join(X2,meet(join(X2,X1),join(X3,X1))),
inference(cp,[status(thm)],[t35717,t35016]) ).
cnf(t37184,plain,
join(X1,meet(join(X1,X2),join(X3,X2))) = join(X2,X1),
inference(orient,[status(thm)],[t35872]) ).
cnf(t37423,plain,
join(meet(X1,X2),X3) = join(X3,meet(join(X3,meet(X1,X2)),X2)),
inference(cp,[status(thm)],[t37184,t113]) ).
cnf(t112264,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t37423,t23]) ).
cnf(t41908,plain,
join(X1,meet(X2,join(X1,meet(X3,X2)))) = join(meet(X3,X2),X1),
inference(orient,[status(thm)],[t112264]) ).
cnf(t55,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t14,t54]) ).
cnf(t122,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t55]) ).
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,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Z))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H39) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Z))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Z))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(X1,meet(X2,join(X3,meet(X0,X2))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X1,X3))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X1,X3))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t12]) ).
cnf(t42196,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(meet(X1,X3),X2)),
inference(cp,[status(thm)],[t35,t41908]) ).
cnf(t51528,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(meet(X1,X3),X2)),
inference(orient,[status(thm)],[t42196]) ).
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(t70,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t51653,plain,
meet(X1,join(meet(X1,X2),complement(X1))) = meet(X1,join(complement(X1),meet(X2,one))),
inference(cp,[status(thm)],[t51528,t70]) ).
cnf(t112267,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),meet(X2,one))),
inference(step,[status(thm)],[t51653,t54]) ).
cnf(t72,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t14,t70]) ).
cnf(t78,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t72]) ).
cnf(t112268,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t112267,t78]) ).
cnf(t51917,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(orient,[status(thm)],[t112268]) ).
cnf(t124,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t122,t16]) ).
cnf(t112040,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t124,t26]) ).
cnf(t149,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t112040]) ).
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(t48,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t50,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t26,t48]) ).
cnf(t51,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t16,t48]) ).
cnf(t74,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t51]) ).
cnf(t75,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t74,t54]) ).
cnf(t83,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t75]) ).
cnf(t85,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t83,t16]) ).
cnf(t102,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t85]) ).
cnf(t112045,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t50,t102]) ).
cnf(t160,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t112045]) ).
cnf(t163,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t149,t160]) ).
cnf(t112046,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t163,t26]) ).
cnf(t112047,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t112046,t26]) ).
cnf(t103,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t102,t23]) ).
cnf(t109,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t103]) ).
cnf(t112048,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t112047,t109]) ).
cnf(t112049,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t112048,t109]) ).
cnf(t173,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t112049]) ).
cnf(t178,plain,
zero = meet(complement(join(X1,X2)),X1),
inference(cp,[status(thm)],[t173,t14]) ).
cnf(t112050,plain,
zero = meet(X1,complement(join(X1,X2))),
inference(step,[status(thm)],[t178,t23]) ).
cnf(t187,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t112050]) ).
cnf(t52003,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t51917,t187]) ).
cnf(t112269,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t52003,t74]) ).
cnf(t112270,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(step,[status(thm)],[t112269,t48]) ).
cnf(t52225,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t112270]) ).
cnf(t52284,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,t52225]) ).
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(t112271,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)],[t52284,t17]) ).
cnf(t73,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t59,t70]) ).
cnf(t79,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t78,t23]) ).
cnf(t92,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t79]) ).
cnf(t94,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t92,t14]) ).
cnf(t105,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t94]) ).
cnf(t112052,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t73,t105]) ).
cnf(t212,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t112052]) ).
cnf(t112272,plain,
join(complement(X1),complement(join(X1,X2))) = ifeq(one,one,complement(X1),join(complement(X1),complement(join(X1,X2)))),
inference(step,[status(thm)],[t112271,t212]) ).
cnf(t112273,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(step,[status(thm)],[t112272,t17]) ).
cnf(t52414,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t112273]) ).
cnf(t52421,plain,
complement(X1) = join(complement(X1),complement(join(X2,X1))),
inference(cp,[status(thm)],[t52414,t37184]) ).
cnf(t52944,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(orient,[status(thm)],[t52421]) ).
cnf(t53012,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t122,t52944]) ).
cnf(t112279,plain,
complement(join(X1,X2)) = meet(complement(X2),complement(join(X1,X2))),
inference(step,[status(thm)],[t53012,t23]) ).
cnf(t54458,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(orient,[status(thm)],[t112279]) ).
cnf(t49,plain,
zero = meet(X1,meet(X2,complement(meet(X1,X2)))),
inference(cp,[status(thm)],[t48,t26]) ).
cnf(t543,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(orient,[status(thm)],[t49]) ).
cnf(t51997,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t51917,t543]) ).
cnf(t112356,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t51997,t74]) ).
cnf(t112357,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(step,[status(thm)],[t112356,t48]) ).
cnf(t94150,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(orient,[status(thm)],[t112357]) ).
cnf(t94324,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,t94150]) ).
cnf(t112358,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)],[t94324,t17]) ).
cnf(t112359,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)],[t112358,t212]) ).
cnf(t112360,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(step,[status(thm)],[t112359,t17]) ).
cnf(t94471,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(orient,[status(thm)],[t112360]) ).
cnf(t94605,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)],[t54458,t94471]) ).
cnf(t112362,plain,
complement(complement(X1)) = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t94605,t94471]) ).
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(t10282,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t10334,plain,
X1 = ifeq(zero,zero,ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t10282,t48]) ).
cnf(t112204,plain,
X1 = ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t10334,t17]) ).
cnf(t112205,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t112204,t54]) ).
cnf(t112206,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t112205,t70]) ).
cnf(t112207,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t112206,t17]) ).
cnf(t18799,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t112207]) ).
cnf(t112363,plain,
X1 = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t112362,t18799]) ).
cnf(t112364,plain,
X1 = meet(complement(complement(X1)),complement(meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t112363,t23]) ).
cnf(t112365,plain,
X1 = meet(X1,complement(meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t112364,t18799]) ).
cnf(t95139,plain,
meet(X1,complement(meet(X2,complement(meet(X1,X2))))) = X1,
inference(orient,[status(thm)],[t112365]) ).
cnf(t180,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t173,t122]) ).
cnf(t112051,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t180,t23]) ).
cnf(t195,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t112051]) ).
cnf(t198,plain,
zero = meet(X1,complement(join(X2,join(X3,X1)))),
inference(cp,[status(thm)],[t195,t59]) ).
cnf(t679,plain,
meet(X1,complement(join(X2,join(X3,X1)))) = zero,
inference(orient,[status(thm)],[t198]) ).
cnf(t154,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,X1)),
inference(cp,[status(thm)],[t113,t149]) ).
cnf(t422,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t154]) ).
cnf(t691,plain,
zero = meet(meet(X1,X2),complement(join(X3,meet(X2,X1)))),
inference(cp,[status(thm)],[t679,t422]) ).
cnf(t112138,plain,
zero = meet(X1,meet(X2,complement(join(X3,meet(X2,X1))))),
inference(step,[status(thm)],[t691,t26]) ).
cnf(t8083,plain,
meet(X1,meet(X2,complement(join(X3,meet(X2,X1))))) = zero,
inference(orient,[status(thm)],[t112138]) ).
cnf(t52448,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t122,t52414]) ).
cnf(t112275,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t52448,t23]) ).
cnf(t53152,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t112275]) ).
cnf(t53325,plain,
zero = meet(X1,complement(join(X2,meet(complement(X2),X1)))),
inference(cp,[status(thm)],[t8083,t53152]) ).
cnf(t57529,plain,
meet(X1,complement(join(X2,meet(complement(X2),X1)))) = zero,
inference(orient,[status(thm)],[t53325]) ).
cnf(t95149,plain,
X1 = meet(X1,complement(meet(complement(join(X2,meet(complement(X2),X1))),complement(zero)))),
inference(cp,[status(thm)],[t95139,t57529]) ).
cnf(t112366,plain,
X1 = meet(X1,complement(meet(complement(zero),complement(join(X2,meet(complement(X2),X1)))))),
inference(step,[status(thm)],[t95149,t23]) ).
cnf(t84,plain,
complement(zero) = one,
inference(cp,[status(thm)],[t83,t70]) ).
cnf(t90,plain,
complement(zero) = one,
inference(orient,[status(thm)],[t84]) ).
cnf(t112367,plain,
X1 = meet(X1,complement(meet(one,complement(join(X2,meet(complement(X2),X1)))))),
inference(step,[status(thm)],[t112366,t90]) ).
cnf(t112368,plain,
X1 = meet(X1,complement(complement(join(X2,meet(complement(X2),X1))))),
inference(step,[status(thm)],[t112367,t92]) ).
cnf(t112369,plain,
X1 = meet(X1,join(X2,meet(complement(X2),X1))),
inference(step,[status(thm)],[t112368,t18799]) ).
cnf(t95520,plain,
meet(X1,join(X2,meet(complement(X2),X1))) = X1,
inference(orient,[status(thm)],[t112369]) ).
cnf(t95819,plain,
join(meet(complement(X1),X2),X1) = join(X1,X2),
inference(cp,[status(thm)],[t41908,t95520]) ).
cnf(t112370,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(step,[status(thm)],[t95819,t54]) ).
cnf(t95901,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t112370]) ).
cnf(t155,plain,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3),
inference(cp,[status(thm)],[t26,t149]) ).
cnf(t112090,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3),
inference(step,[status(thm)],[t155,t26]) ).
cnf(t112091,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t112090,t26]) ).
cnf(t1313,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t112091]) ).
cnf(t95973,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(cp,[status(thm)],[t95901,t1313]) ).
cnf(t112408,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t95973,t95901]) ).
cnf(t102562,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t112408]) ).
cnf(t115,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t113,t14]) ).
cnf(t112039,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t115,t59]) ).
cnf(t142,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t112039]) ).
cnf(t147,plain,
join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3),
inference(cp,[status(thm)],[t59,t142]) ).
cnf(t112088,plain,
join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3),
inference(step,[status(thm)],[t147,t59]) ).
cnf(t112089,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t112088,t59]) ).
cnf(t1199,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t112089]) ).
cnf(t96123,plain,
join(X1,join(X2,meet(complement(X1),X3))) = join(X1,join(X2,join(X1,X3))),
inference(cp,[status(thm)],[t1199,t95901]) ).
cnf(t112411,plain,
join(X1,join(X2,meet(complement(X1),X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t96123,t1199]) ).
cnf(t103778,plain,
join(X1,join(X2,meet(complement(X1),X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t112411]) ).
cnf(t103807,plain,
join(X1,join(complement(X2),complement(meet(X2,complement(X1))))) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t103778,t94471]) ).
cnf(t52986,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t52944,t16]) ).
cnf(t112276,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t52986,t54]) ).
cnf(t53334,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t112276]) ).
cnf(t112412,plain,
join(X1,complement(meet(X2,complement(X1)))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t103807,t53334]) ).
cnf(t53359,plain,
complement(X1) = meet(complement(X1),complement(meet(X1,X2))),
inference(cp,[status(thm)],[t14,t53334]) ).
cnf(t53502,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t53359]) ).
cnf(t53503,plain,
complement(complement(X1)) = meet(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t53502,t18799]) ).
cnf(t112277,plain,
X1 = meet(X1,complement(meet(complement(X1),X2))),
inference(step,[status(thm)],[t53503,t18799]) ).
cnf(t53671,plain,
meet(X1,complement(meet(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t112277]) ).
cnf(t28,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t2208,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t28]) ).
cnf(t32,plain,
meet(X1,meet(X2,X3)) = meet(meet(X2,X1),X3),
inference(cp,[status(thm)],[t26,t23]) ).
cnf(t112093,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t32,t26]) ).
cnf(t1679,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t112093]) ).
cnf(t2210,plain,
meet(X1,X2) = meet(X2,meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t2208,t1679]) ).
cnf(t4097,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t2210]) ).
cnf(t53677,plain,
X1 = meet(X1,complement(meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t53671,t4097]) ).
cnf(t53849,plain,
meet(X1,complement(meet(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t53677]) ).
cnf(t53854,plain,
complement(meet(X1,complement(X2))) = join(complement(meet(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t113,t53849]) ).
cnf(t112282,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(meet(X1,complement(X2)))),
inference(step,[status(thm)],[t53854,t54]) ).
cnf(t55214,plain,
join(X1,complement(meet(X2,complement(X1)))) = complement(meet(X2,complement(X1))),
inference(orient,[status(thm)],[t112282]) ).
cnf(t112413,plain,
complement(meet(X2,complement(X1))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t112412,t55214]) ).
cnf(t104170,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t112413]) ).
cnf(t104204,plain,
meet(X1,complement(X2)) = complement(join(X2,complement(X1))),
inference(cp,[status(thm)],[t18799,t104170]) ).
cnf(t104956,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t104204]) ).
cnf(t104969,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t104956,t54]) ).
cnf(t105141,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t104969]) ).
cnf(t51996,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(cp,[status(thm)],[t51917,t149]) ).
cnf(t112319,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t51996,t51917]) ).
cnf(t72625,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X1,join(complement(X1),X2)),
inference(orient,[status(thm)],[t112319]) ).
cnf(t95926,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)],[t95901,t72625]) ).
cnf(t112371,plain,
join(X1,join(X1,meet(X2,complement(X1)))) = join(X1,meet(complement(X1),join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t95926,t18799]) ).
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(t63,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t59,t15]) ).
cnf(t137,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t63]) ).
cnf(t112372,plain,
join(X1,meet(X2,complement(X1))) = join(X1,meet(complement(X1),join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t112371,t137]) ).
cnf(t112373,plain,
join(X1,meet(X2,complement(X1))) = join(X1,join(complement(complement(X1)),X2)),
inference(step,[status(thm)],[t112372,t95901]) ).
cnf(t112374,plain,
join(X1,meet(X2,complement(X1))) = join(X1,join(X1,X2)),
inference(step,[status(thm)],[t112373,t18799]) ).
cnf(t112375,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(step,[status(thm)],[t112374,t137]) ).
cnf(t96248,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t112375]) ).
cnf(t96273,plain,
join(complement(X1),X2) = join(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t96248,t18799]) ).
cnf(t96847,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t96273]) ).
cnf(t105148,plain,
meet(X1,complement(meet(X2,X1))) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t105141,t96847]) ).
cnf(t112480,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t105148,t105141]) ).
cnf(t105667,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t112480]) ).
cnf(t177,plain,
zero = meet(complement(meet(X1,X2)),meet(X2,X1)),
inference(cp,[status(thm)],[t173,t149]) ).
cnf(t112068,plain,
zero = meet(meet(X2,X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t177,t23]) ).
cnf(t112069,plain,
zero = meet(X2,meet(X1,complement(meet(X1,X2)))),
inference(step,[status(thm)],[t112068,t26]) ).
cnf(t593,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(orient,[status(thm)],[t112069]) ).
cnf(t94544,plain,
complement(X1) = join(complement(X1),meet(meet(X2,complement(meet(X2,X1))),complement(zero))),
inference(cp,[status(thm)],[t94471,t593]) ).
cnf(t112404,plain,
complement(X1) = join(complement(X1),meet(X2,meet(complement(meet(X2,X1)),complement(zero)))),
inference(step,[status(thm)],[t94544,t26]) ).
cnf(t112405,plain,
complement(X1) = join(complement(X1),meet(X2,meet(complement(zero),complement(meet(X2,X1))))),
inference(step,[status(thm)],[t112404,t23]) ).
cnf(t112406,plain,
complement(X1) = join(complement(X1),meet(X2,meet(one,complement(meet(X2,X1))))),
inference(step,[status(thm)],[t112405,t90]) ).
cnf(t112407,plain,
complement(X1) = join(complement(X1),meet(X2,complement(meet(X2,X1)))),
inference(step,[status(thm)],[t112406,t92]) ).
cnf(t102204,plain,
join(complement(X1),meet(X2,complement(meet(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t112407]) ).
cnf(t103808,plain,
join(X1,join(complement(X2),complement(meet(complement(X1),X2)))) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t103778,t102204]) ).
cnf(t52987,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t52944,t113]) ).
cnf(t112278,plain,
complement(meet(X1,X2)) = join(complement(X2),complement(meet(X1,X2))),
inference(step,[status(thm)],[t52987,t54]) ).
cnf(t54237,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(orient,[status(thm)],[t112278]) ).
cnf(t112425,plain,
join(X1,complement(meet(complement(X1),X2))) = join(X1,complement(X2)),
inference(step,[status(thm)],[t103808,t54237]) ).
cnf(t53335,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t53334,t18799]) ).
cnf(t55041,plain,
join(X1,complement(meet(complement(X1),X2))) = complement(meet(complement(X1),X2)),
inference(orient,[status(thm)],[t53335]) ).
cnf(t112426,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(step,[status(thm)],[t112425,t55041]) ).
cnf(t104420,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t112426]) ).
cnf(t105671,plain,
meet(X1,complement(complement(X2))) = meet(X1,join(X2,complement(X1))),
inference(cp,[status(thm)],[t105667,t104420]) ).
cnf(t112481,plain,
meet(X1,X2) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t105671,t18799]) ).
cnf(t105982,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t112481]) ).
cnf(t106098,plain,
join(X1,meet(X2,join(X3,complement(complement(X1))))) = join(X1,meet(X2,meet(complement(X1),X3))),
inference(cp,[status(thm)],[t102562,t105982]) ).
cnf(t112496,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,meet(complement(X1),X3))),
inference(step,[status(thm)],[t106098,t18799]) ).
cnf(t112497,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t112496,t102562]) ).
cnf(t108995,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t112497]) ).
cnf(t105994,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t105982,t54]) ).
cnf(t106196,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t105994]) ).
cnf(t106206,plain,
meet(X1,join(X2,meet(complement(complement(X1)),X3))) = meet(X1,join(complement(X1),join(X2,X3))),
inference(cp,[status(thm)],[t106196,t103778]) ).
cnf(t112508,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(complement(X1),join(X2,X3))),
inference(step,[status(thm)],[t106206,t18799]) ).
cnf(t112509,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t112508,t106196]) ).
cnf(t109392,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t112509]) ).
cnf(t109601,plain,
join(meet(X1,X2),meet(X1,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))),
inference(cp,[status(thm)],[t108995,t109392]) ).
cnf(t117,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t113,t26]) ).
cnf(t258,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t117]) ).
cnf(t1366,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,meet(X3,X2))),
inference(cp,[status(thm)],[t258,t1313]) ).
cnf(t3826,plain,
join(meet(X1,X2),meet(X1,meet(X3,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t1366]) ).
cnf(t3885,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X1,X3)),
inference(cp,[status(thm)],[t3826,t122]) ).
cnf(t112239,plain,
meet(X1,join(X2,X3)) = join(meet(X1,X3),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t3885,t54]) ).
cnf(t31018,plain,
join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t112239]) ).
cnf(t112541,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(step,[status(thm)],[t109601,t31018]) ).
cnf(t111473,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t112541]) ).
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,t111473]) ).
cnf(g0_1,plain,
meet(a,join(c,b)) != meet(a,join(c,b)),
inference(rw,[status(thm)],[g0_0,t54]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT196-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.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 20:34:23 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 52.66/7.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.66/7.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------