%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT254-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 20.02s 3.08s
% Output : Proof 20.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% 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 : 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 : 298 ( 26 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(meet(X,join(Y,meet(X,Z))),meet(Z,U))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H79) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(meet(X,join(Y,meet(X,Z))),meet(Z,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(meet(X,join(Y,meet(X,Z))),meet(Z,U))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(meet(X0,join(X1,meet(X0,X2))),meet(X2,X3))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(meet(X1,join(X2,meet(X1,X3))),meet(X3,X4))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t47,plain,
meet(X1,join(meet(X1,join(X2,meet(X1,X3))),meet(X3,X4))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t13]) ).
cnf(t83,plain,
meet(X1,join(meet(X1,join(X2,meet(X1,X3))),meet(X3,X4))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(rw,[status(thm)],[t47]) ).
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(t80,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t2287,plain,
meet(X1,join(meet(X3,X4),meet(X1,join(X2,meet(X1,X3))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(step,[status(thm)],[t83,t80]) ).
cnf(t692,plain,
meet(X1,join(meet(X2,X3),meet(X1,join(X4,meet(X1,X2))))) = meet(X1,join(X4,meet(X2,join(X1,X3)))),
inference(orient,[status(thm)],[t2287]) ).
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(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(t104,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t105,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t15,t104]) ).
cnf(t117,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t105]) ).
cnf(t708,plain,
meet(X1,join(X2,meet(X3,join(X1,one)))) = meet(X1,join(X3,meet(X1,join(X2,meet(X1,X3))))),
inference(cp,[status(thm)],[t692,t117]) ).
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(t2109,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t10,t80]) ).
cnf(t84,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t2109]) ).
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(t87,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t84,t16]) ).
cnf(t2113,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t87,t84]) ).
cnf(t2114,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t2113,t80]) ).
cnf(t137,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t2114]) ).
cnf(t140,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t137,t104]) ).
cnf(t2115,plain,
one = join(X1,one),
inference(step,[status(thm)],[t140,t104]) ).
cnf(t147,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t2115]) ).
cnf(t2288,plain,
meet(X1,join(X2,meet(X3,one))) = meet(X1,join(X3,meet(X1,join(X2,meet(X1,X3))))),
inference(step,[status(thm)],[t708,t147]) ).
cnf(t2289,plain,
meet(X1,join(X2,X3)) = meet(X1,join(X3,meet(X1,join(X2,meet(X1,X3))))),
inference(step,[status(thm)],[t2288,t117]) ).
cnf(t751,plain,
meet(X1,join(X2,meet(X1,join(X3,meet(X1,X2))))) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t2289]) ).
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(t66,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t771,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(complement(X1),meet(X1,join(X2,zero)))),
inference(cp,[status(thm)],[t751,t66]) ).
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(t67,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t66]) ).
cnf(t108,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t67]) ).
cnf(t2331,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(step,[status(thm)],[t771,t108]) ).
cnf(t1134,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t2331]) ).
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(t2108,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)],[t2108]) ).
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(t2110,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t30,t27]) ).
cnf(t2111,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t2110,t24]) ).
cnf(t122,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t2111]) ).
cnf(t125,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t122,t66]) ).
cnf(t2112,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t125,t66]) ).
cnf(t132,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t2112]) ).
cnf(t767,plain,
meet(X1,join(X2,zero)) = meet(X1,join(zero,meet(X1,join(X2,zero)))),
inference(cp,[status(thm)],[t751,t132]) ).
cnf(t2290,plain,
meet(X1,X2) = meet(X1,join(zero,meet(X1,join(X2,zero)))),
inference(step,[status(thm)],[t767,t108]) ).
cnf(t2291,plain,
meet(X1,X2) = meet(X1,join(zero,meet(X1,X2))),
inference(step,[status(thm)],[t2290,t108]) ).
cnf(t793,plain,
meet(X1,join(zero,meet(X1,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t2291]) ).
cnf(t810,plain,
meet(X1,join(zero,X2)) = meet(X1,join(X2,meet(X1,X2))),
inference(cp,[status(thm)],[t751,t793]) ).
cnf(t2300,plain,
meet(X1,join(X2,zero)) = meet(X1,join(X2,meet(X1,X2))),
inference(step,[status(thm)],[t810,t80]) ).
cnf(t2301,plain,
meet(X1,X2) = meet(X1,join(X2,meet(X1,X2))),
inference(step,[status(thm)],[t2300,t108]) ).
cnf(t871,plain,
meet(X1,join(X2,meet(X1,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t2301]) ).
cnf(t893,plain,
meet(X1,join(X2,meet(X2,join(X1,X3)))) = meet(X1,join(meet(X2,X3),meet(X1,X2))),
inference(cp,[status(thm)],[t692,t871]) ).
cnf(t2307,plain,
meet(X1,X2) = meet(X1,join(meet(X2,X3),meet(X1,X2))),
inference(step,[status(thm)],[t893,t17]) ).
cnf(t2308,plain,
meet(X1,X2) = meet(X1,join(meet(X1,X2),meet(X2,X3))),
inference(step,[status(thm)],[t2307,t80]) ).
cnf(t906,plain,
meet(X1,join(meet(X1,X2),meet(X2,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t2308]) ).
cnf(t922,plain,
meet(X1,complement(X1)) = meet(X1,join(zero,meet(complement(X1),X2))),
inference(cp,[status(thm)],[t906,t66]) ).
cnf(t2310,plain,
zero = meet(X1,join(zero,meet(complement(X1),X2))),
inference(step,[status(thm)],[t922,t66]) ).
cnf(t2311,plain,
zero = meet(X1,join(zero,meet(X2,complement(X1)))),
inference(step,[status(thm)],[t2310,t24]) ).
cnf(t975,plain,
meet(X1,join(zero,meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t2311]) ).
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(t2206,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1),
inference(step,[status(thm)],[t26,t80]) ).
cnf(t362,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t2206]) ).
cnf(t371,plain,
X1 = ifeq(zero,zero,ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t362,t66]) ).
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(t2207,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t371,t18]) ).
cnf(t2208,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t2207,t104]) ).
cnf(t2209,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t2208,t18]) ).
cnf(t391,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t2209]) ).
cnf(t978,plain,
zero = meet(complement(X1),join(zero,meet(X2,X1))),
inference(cp,[status(thm)],[t975,t391]) ).
cnf(t2315,plain,
zero = meet(complement(X1),join(zero,meet(X1,X2))),
inference(step,[status(thm)],[t978,t24]) ).
cnf(t1028,plain,
meet(complement(X1),join(zero,meet(X1,X2))) = zero,
inference(orient,[status(thm)],[t2315]) ).
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(t73,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t1033,plain,
zero = meet(complement(b),join(zero,a)),
inference(cp,[status(thm)],[t1028,t73]) ).
cnf(t1048,plain,
meet(complement(b),join(zero,a)) = zero,
inference(orient,[status(thm)],[t1033]) ).
cnf(t106,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t84,t104]) ).
cnf(t2122,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t106,t80]) ).
cnf(t2123,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t2122,t147]) ).
cnf(t171,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t2123]) ).
cnf(t175,plain,
join(X1,complement(X2)) = ifeq(meet(X2,join(X1,complement(X2))),zero,ifeq(one,one,complement(X2),join(X1,complement(X2))),join(X1,complement(X2))),
inference(cp,[status(thm)],[t19,t171]) ).
cnf(t2253,plain,
join(X1,complement(X2)) = ifeq(meet(X2,join(X1,complement(X2))),zero,complement(X2),join(X1,complement(X2))),
inference(step,[status(thm)],[t175,t18]) ).
cnf(t593,plain,
ifeq(meet(X1,join(X2,complement(X1))),zero,complement(X1),join(X2,complement(X1))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t2253]) ).
cnf(t595,plain,
join(X1,complement(complement(X2))) = ifeq(meet(complement(X2),join(X1,X2)),zero,complement(complement(X2)),join(X1,complement(complement(X2)))),
inference(cp,[status(thm)],[t593,t391]) ).
cnf(t2254,plain,
join(X1,X2) = ifeq(meet(complement(X2),join(X1,X2)),zero,complement(complement(X2)),join(X1,complement(complement(X2)))),
inference(step,[status(thm)],[t595,t391]) ).
cnf(t2255,plain,
join(X1,X2) = ifeq(meet(complement(X2),join(X1,X2)),zero,X2,join(X1,complement(complement(X2)))),
inference(step,[status(thm)],[t2254,t391]) ).
cnf(t2256,plain,
join(X1,X2) = ifeq(meet(complement(X2),join(X1,X2)),zero,X2,join(X1,X2)),
inference(step,[status(thm)],[t2255,t391]) ).
cnf(t602,plain,
ifeq(meet(complement(X1),join(X2,X1)),zero,X1,join(X2,X1)) = join(X2,X1),
inference(orient,[status(thm)],[t2256]) ).
cnf(t931,plain,
meet(X1,b) = meet(X1,join(meet(X1,b),a)),
inference(cp,[status(thm)],[t906,t73]) ).
cnf(t2309,plain,
meet(X1,b) = meet(X1,join(a,meet(X1,b))),
inference(step,[status(thm)],[t931,t80]) ).
cnf(t953,plain,
meet(X1,join(a,meet(X1,b))) = meet(X1,b),
inference(orient,[status(thm)],[t2309]) ).
cnf(t1138,plain,
meet(X1,join(join(a,meet(X1,b)),complement(X1))) = meet(X1,join(complement(X1),meet(X1,b))),
inference(cp,[status(thm)],[t1134,t953]) ).
cnf(t2434,plain,
meet(X1,join(complement(X1),join(a,meet(X1,b)))) = meet(X1,join(complement(X1),meet(X1,b))),
inference(step,[status(thm)],[t1138,t80]) ).
cnf(t2435,plain,
meet(X1,join(a,join(meet(X1,b),complement(X1)))) = meet(X1,join(complement(X1),meet(X1,b))),
inference(step,[status(thm)],[t2434,t84]) ).
cnf(t2436,plain,
meet(X1,join(a,join(complement(X1),meet(X1,b)))) = meet(X1,join(complement(X1),meet(X1,b))),
inference(step,[status(thm)],[t2435,t80]) ).
cnf(t2437,plain,
meet(X1,join(a,join(complement(X1),meet(X1,b)))) = meet(X1,join(b,complement(X1))),
inference(step,[status(thm)],[t2436,t1134]) ).
cnf(t1957,plain,
meet(X1,join(a,join(complement(X1),meet(X1,b)))) = meet(X1,join(b,complement(X1))),
inference(orient,[status(thm)],[t2437]) ).
cnf(t1958,plain,
meet(a,join(b,complement(a))) = a,
inference(cp,[status(thm)],[t1957,t15]) ).
cnf(t1984,plain,
meet(a,join(b,complement(a))) = a,
inference(orient,[status(thm)],[t1958]) ).
cnf(t1987,plain,
zero = meet(complement(a),join(zero,a)),
inference(cp,[status(thm)],[t1028,t1984]) ).
cnf(t2031,plain,
meet(complement(a),join(zero,a)) = zero,
inference(orient,[status(thm)],[t1987]) ).
cnf(t2035,plain,
join(zero,a) = ifeq(zero,zero,a,join(zero,a)),
inference(cp,[status(thm)],[t602,t2031]) ).
cnf(t2439,plain,
join(zero,a) = a,
inference(step,[status(thm)],[t2035,t18]) ).
cnf(t2046,plain,
join(zero,a) = a,
inference(orient,[status(thm)],[t2439]) ).
cnf(t2441,plain,
meet(complement(b),a) = zero,
inference(step,[status(thm)],[t1048,t2046]) ).
cnf(t2058,plain,
meet(complement(b),a) = zero,
inference(rw,[status(thm)],[t2441]) ).
cnf(t2443,plain,
meet(a,complement(b)) = zero,
inference(step,[status(thm)],[t2058,t24]) ).
cnf(t2060,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t2443]) ).
cnf(t2061,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),zero)),
inference(cp,[status(thm)],[t1134,t2060]) ).
cnf(t2444,plain,
meet(a,join(complement(b),complement(a))) = meet(a,complement(a)),
inference(step,[status(thm)],[t2061,t108]) ).
cnf(t2445,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(step,[status(thm)],[t2444,t66]) ).
cnf(t2072,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t2445]) ).
cnf(t2073,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,t2072]) ).
cnf(t2446,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)],[t2073,t18]) ).
cnf(t2447,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t2446,t171]) ).
cnf(t2448,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t2447,t18]) ).
cnf(t2089,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t2448]) ).
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,t2089]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT254-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n006.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 20:41:41 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.02/3.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.02/3.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------