%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT239-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:56:23 PM UTC 2026
% Result : Unsatisfiable 28.01s 4.02s
% Output : Proof 28.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 15
% Syntax : Number of formulae : 225 ( 221 unt; 0 def)
% Number of atoms : 233 ( 232 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 : 6 ( 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 : 359 ( 65 sgn 48 !; 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,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,join(Y,U))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H49) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,join(Y,U))))),
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,join(meet(X,Z),meet(Z,join(Y,U))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(X1,join(meet(X0,X2),meet(X2,join(X1,X3))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t47,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X3,join(X2,X4))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t13]) ).
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(t55,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,X2)))),
inference(cp,[status(thm)],[t47,t16]) ).
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(t2402,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X2,X3)))),
inference(step,[status(thm)],[t55,t24]) ).
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(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(t74,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t2170,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t10,t74]) ).
cnf(t79,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t2170]) ).
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(t83,plain,
join(meet(X1,X2),join(X3,X1)) = join(X3,X1),
inference(cp,[status(thm)],[t79,t17]) ).
cnf(t2188,plain,
join(X1,join(meet(X1,X2),X3)) = join(X3,X1),
inference(step,[status(thm)],[t83,t79]) ).
cnf(t2189,plain,
join(X1,join(X3,meet(X1,X2))) = join(X3,X1),
inference(step,[status(thm)],[t2188,t74]) ).
cnf(t2190,plain,
join(X1,join(X3,meet(X1,X2))) = join(X1,X3),
inference(step,[status(thm)],[t2189,t74]) ).
cnf(t201,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(orient,[status(thm)],[t2190]) ).
cnf(t2403,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(step,[status(thm)],[t2402,t201]) ).
cnf(t1497,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(orient,[status(thm)],[t2403]) ).
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(t102,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t1528,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),meet(X2,one))),
inference(cp,[status(thm)],[t1497,t102]) ).
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(t103,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t15,t102]) ).
cnf(t118,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t103]) ).
cnf(t2430,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t1528,t118]) ).
cnf(t2431,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t2430,t74]) ).
cnf(t1936,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t2431]) ).
cnf(t212,plain,
meet(X1,join(X2,meet(X2,join(X1,X3)))) = meet(X1,join(X2,meet(X1,X2))),
inference(cp,[status(thm)],[t47,t201]) ).
cnf(t2191,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,X2))),
inference(step,[status(thm)],[t212,t17]) ).
cnf(t216,plain,
meet(X1,join(X2,meet(X1,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t2191]) ).
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(t2169,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)],[t2169]) ).
cnf(t31,plain,
meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t2185,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X3,X1),
inference(step,[status(thm)],[t31,t27]) ).
cnf(t2186,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X3,X1),
inference(step,[status(thm)],[t2185,t24]) ).
cnf(t2187,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X1,X3),
inference(step,[status(thm)],[t2186,t24]) ).
cnf(t187,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t2187]) ).
cnf(t217,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,join(meet(X2,join(X1,X3)),meet(X1,X2))),
inference(cp,[status(thm)],[t216,t187]) ).
cnf(t2244,plain,
meet(X1,X2) = meet(X1,join(meet(X2,join(X1,X3)),meet(X1,X2))),
inference(step,[status(thm)],[t217,t187]) ).
cnf(t2245,plain,
meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(X2,join(X1,X3)))),
inference(step,[status(thm)],[t2244,t74]) ).
cnf(t435,plain,
meet(X1,join(meet(X1,X2),meet(X2,join(X1,X3)))) = meet(X1,X2),
inference(orient,[status(thm)],[t2245]) ).
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(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(t2181,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/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(t2171,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t30,t27]) ).
cnf(t2172,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t2171,t24]) ).
cnf(t124,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t2172]) ).
cnf(t127,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t124,t62]) ).
cnf(t2173,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t127,t62]) ).
cnf(t135,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t2173]) ).
cnf(t2182,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t2181,t135]) ).
cnf(t171,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t2182]) ).
cnf(t439,plain,
meet(X1,meet(X2,complement(X1))) = meet(X1,join(zero,meet(meet(X2,complement(X1)),join(X1,X3)))),
inference(cp,[status(thm)],[t435,t171]) ).
cnf(t2279,plain,
zero = meet(X1,join(zero,meet(meet(X2,complement(X1)),join(X1,X3)))),
inference(step,[status(thm)],[t439,t171]) ).
cnf(t2280,plain,
zero = meet(X1,join(zero,meet(join(X1,X3),meet(X2,complement(X1))))),
inference(step,[status(thm)],[t2279,t24]) ).
cnf(t2281,plain,
zero = meet(X1,join(zero,meet(complement(X1),meet(join(X1,X3),X2)))),
inference(step,[status(thm)],[t2280,t27]) ).
cnf(t2282,plain,
zero = meet(X1,join(zero,meet(X2,meet(complement(X1),join(X1,X3))))),
inference(step,[status(thm)],[t2281,t27]) ).
cnf(t584,plain,
meet(X1,join(zero,meet(X2,meet(complement(X1),join(X1,X3))))) = zero,
inference(orient,[status(thm)],[t2282]) ).
cnf(t105,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t79,t102]) ).
cnf(t2183,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t105,t74]) ).
cnf(t82,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t79,t16]) ).
cnf(t2174,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t82,t79]) ).
cnf(t2175,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t2174,t74]) ).
cnf(t141,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t2175]) ).
cnf(t144,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t141,t102]) ).
cnf(t2176,plain,
one = join(X1,one),
inference(step,[status(thm)],[t144,t102]) ).
cnf(t153,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t2176]) ).
cnf(t2184,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t2183,t153]) ).
cnf(t179,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t2184]) ).
cnf(t185,plain,
join(X1,join(join(X2,complement(X1)),X3)) = join(X3,one),
inference(cp,[status(thm)],[t79,t179]) ).
cnf(t2196,plain,
join(X1,join(X3,join(X2,complement(X1)))) = join(X3,one),
inference(step,[status(thm)],[t185,t74]) ).
cnf(t2197,plain,
join(X1,join(X2,join(complement(X1),X3))) = join(X3,one),
inference(step,[status(thm)],[t2196,t79]) ).
cnf(t2198,plain,
join(X1,join(X2,join(X3,complement(X1)))) = join(X3,one),
inference(step,[status(thm)],[t2197,t74]) ).
cnf(t2199,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(step,[status(thm)],[t2198,t153]) ).
cnf(t241,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(orient,[status(thm)],[t2199]) ).
cnf(t592,plain,
zero = meet(X1,join(zero,meet(X2,meet(complement(X1),one)))),
inference(cp,[status(thm)],[t584,t241]) ).
cnf(t2283,plain,
zero = meet(X1,join(zero,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t592,t118]) ).
cnf(t613,plain,
meet(X1,join(zero,meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t2283]) ).
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(t2333,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1),
inference(step,[status(thm)],[t26,t74]) ).
cnf(t962,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t2333]) ).
cnf(t983,plain,
X1 = ifeq(zero,zero,ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t962,t62]) ).
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(t2334,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t983,t18]) ).
cnf(t2335,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t2334,t102]) ).
cnf(t2336,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t2335,t18]) ).
cnf(t1011,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t2336]) ).
cnf(t1025,plain,
zero = meet(complement(X1),join(zero,meet(X2,X1))),
inference(cp,[status(thm)],[t613,t1011]) ).
cnf(t2338,plain,
zero = meet(complement(X1),join(zero,meet(X1,X2))),
inference(step,[status(thm)],[t1025,t24]) ).
cnf(t1039,plain,
meet(complement(X1),join(zero,meet(X1,X2))) = zero,
inference(orient,[status(thm)],[t2338]) ).
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(t68,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t71,plain,
meet(b,join(X1,meet(a,join(b,X2)))) = meet(b,join(X1,join(a,meet(a,join(X1,X2))))),
inference(cp,[status(thm)],[t47,t68]) ).
cnf(t2222,plain,
meet(b,join(X1,meet(a,join(X2,b)))) = meet(b,join(X1,join(a,meet(a,join(X1,X2))))),
inference(step,[status(thm)],[t71,t74]) ).
cnf(t2223,plain,
meet(b,join(X1,meet(a,join(X2,b)))) = meet(b,join(X1,a)),
inference(step,[status(thm)],[t2222,t17]) ).
cnf(t318,plain,
meet(b,join(X1,meet(a,join(X2,b)))) = meet(b,join(X1,a)),
inference(orient,[status(thm)],[t2223]) ).
cnf(t319,plain,
meet(b,join(meet(a,join(X1,b)),a)) = meet(b,meet(a,join(X1,b))),
inference(cp,[status(thm)],[t318,t16]) ).
cnf(t2241,plain,
meet(b,join(a,meet(a,join(X1,b)))) = meet(b,meet(a,join(X1,b))),
inference(step,[status(thm)],[t319,t74]) ).
cnf(t2242,plain,
meet(b,a) = meet(b,meet(a,join(X1,b))),
inference(step,[status(thm)],[t2241,t17]) ).
cnf(t2243,plain,
a = meet(b,meet(a,join(X1,b))),
inference(step,[status(thm)],[t2242,t68]) ).
cnf(t424,plain,
meet(b,meet(a,join(X1,b))) = a,
inference(orient,[status(thm)],[t2243]) ).
cnf(t1044,plain,
zero = meet(complement(b),join(zero,a)),
inference(cp,[status(thm)],[t1039,t424]) ).
cnf(t1061,plain,
meet(complement(b),join(zero,a)) = zero,
inference(orient,[status(thm)],[t1044]) ).
cnf(t1523,plain,
meet(X1,join(one,meet(X1,X2))) = meet(X1,join(one,meet(X2,one))),
inference(cp,[status(thm)],[t1497,t153]) ).
cnf(t2405,plain,
meet(X1,join(one,meet(X1,X2))) = meet(X1,join(one,X2)),
inference(step,[status(thm)],[t1523,t118]) ).
cnf(t2406,plain,
meet(X1,join(one,meet(X1,X2))) = meet(X1,join(X2,one)),
inference(step,[status(thm)],[t2405,t74]) ).
cnf(t2407,plain,
meet(X1,join(one,meet(X1,X2))) = meet(X1,one),
inference(step,[status(thm)],[t2406,t153]) ).
cnf(t2408,plain,
meet(X1,join(one,meet(X1,X2))) = X1,
inference(step,[status(thm)],[t2407,t118]) ).
cnf(t1590,plain,
meet(X1,join(one,meet(X1,X2))) = X1,
inference(orient,[status(thm)],[t2408]) ).
cnf(t1594,plain,
b = meet(b,join(one,a)),
inference(cp,[status(thm)],[t1590,t424]) ).
cnf(t1622,plain,
meet(b,join(one,a)) = b,
inference(orient,[status(thm)],[t1594]) ).
cnf(t1629,plain,
meet(one,join(a,meet(one,b))) = meet(one,join(a,b)),
inference(cp,[status(thm)],[t1497,t1622]) ).
cnf(t2409,plain,
meet(one,join(a,meet(one,b))) = meet(one,join(b,a)),
inference(step,[status(thm)],[t1629,t74]) ).
cnf(t69,plain,
b = join(b,a),
inference(cp,[status(thm)],[t17,t68]) ).
cnf(t113,plain,
join(b,a) = b,
inference(orient,[status(thm)],[t69]) ).
cnf(t2410,plain,
meet(one,join(a,meet(one,b))) = meet(one,b),
inference(step,[status(thm)],[t2409,t113]) ).
cnf(t1674,plain,
meet(one,join(a,meet(one,b))) = meet(one,b),
inference(orient,[status(thm)],[t2410]) ).
cnf(t1678,plain,
meet(a,one) = meet(a,meet(one,b)),
inference(cp,[status(thm)],[t187,t1674]) ).
cnf(t2411,plain,
a = meet(a,meet(one,b)),
inference(step,[status(thm)],[t1678,t118]) ).
cnf(t2412,plain,
a = meet(b,meet(a,one)),
inference(step,[status(thm)],[t2411,t27]) ).
cnf(t2413,plain,
a = meet(one,meet(b,a)),
inference(step,[status(thm)],[t2412,t27]) ).
cnf(t2414,plain,
a = meet(one,a),
inference(step,[status(thm)],[t2413,t68]) ).
cnf(t1692,plain,
meet(one,a) = a,
inference(orient,[status(thm)],[t2414]) ).
cnf(t1989,plain,
meet(one,join(a,complement(one))) = meet(one,join(complement(one),a)),
inference(cp,[status(thm)],[t1936,t1692]) ).
cnf(t137,plain,
zero = ifeq(zero,zero,ifeq(join(X1,zero),one,complement(X1),zero),zero),
inference(cp,[status(thm)],[t19,t135]) ).
cnf(t2177,plain,
zero = ifeq(join(X1,zero),one,complement(X1),zero),
inference(step,[status(thm)],[t137,t18]) ).
cnf(t63,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t62]) ).
cnf(t107,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t63]) ).
cnf(t2178,plain,
zero = ifeq(X1,one,complement(X1),zero),
inference(step,[status(thm)],[t2177,t107]) ).
cnf(t159,plain,
ifeq(X1,one,complement(X1),zero) = zero,
inference(orient,[status(thm)],[t2178]) ).
cnf(t160,plain,
zero = complement(one),
inference(cp,[status(thm)],[t159,t18]) ).
cnf(t161,plain,
complement(one) = zero,
inference(orient,[status(thm)],[t160]) ).
cnf(t2432,plain,
meet(one,join(a,zero)) = meet(one,join(complement(one),a)),
inference(step,[status(thm)],[t1989,t161]) ).
cnf(t2433,plain,
meet(one,a) = meet(one,join(complement(one),a)),
inference(step,[status(thm)],[t2432,t107]) ).
cnf(t2434,plain,
a = meet(one,join(complement(one),a)),
inference(step,[status(thm)],[t2433,t1692]) ).
cnf(t2435,plain,
a = meet(one,join(zero,a)),
inference(step,[status(thm)],[t2434,t161]) ).
cnf(t2026,plain,
meet(one,join(zero,a)) = a,
inference(orient,[status(thm)],[t2435]) ).
cnf(t2045,plain,
meet(join(zero,a),meet(X1,one)) = meet(X1,a),
inference(cp,[status(thm)],[t27,t2026]) ).
cnf(t2436,plain,
meet(join(zero,a),X1) = meet(X1,a),
inference(step,[status(thm)],[t2045,t118]) ).
cnf(t2437,plain,
meet(X1,join(zero,a)) = meet(X1,a),
inference(step,[status(thm)],[t2436,t24]) ).
cnf(t2046,plain,
meet(X1,join(zero,a)) = meet(X1,a),
inference(orient,[status(thm)],[t2437]) ).
cnf(t2439,plain,
meet(complement(b),a) = zero,
inference(step,[status(thm)],[t1061,t2046]) ).
cnf(t2074,plain,
meet(complement(b),a) = zero,
inference(rw,[status(thm)],[t2439]) ).
cnf(t2440,plain,
meet(a,complement(b)) = zero,
inference(step,[status(thm)],[t2074,t24]) ).
cnf(t2075,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t2440]) ).
cnf(t2077,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),zero)),
inference(cp,[status(thm)],[t1936,t2075]) ).
cnf(t2450,plain,
meet(a,join(complement(b),complement(a))) = meet(a,complement(a)),
inference(step,[status(thm)],[t2077,t107]) ).
cnf(t2451,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(step,[status(thm)],[t2450,t62]) ).
cnf(t2128,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t2451]) ).
cnf(t2129,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,t2128]) ).
cnf(t2452,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)],[t2129,t18]) ).
cnf(t2453,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t2452,t179]) ).
cnf(t2454,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t2453,t18]) ).
cnf(t2144,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t2454]) ).
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,t2144]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT239-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Wed Sep 23 20:39:35 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.01/4.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.01/4.02 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------