%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT230-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:56:22 PM UTC 2026
% Result : Unsatisfiable 231.32s 34.54s
% Output : Proof 231.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 17
% Syntax : Number of formulae : 230 ( 226 unt; 0 def)
% Number of atoms : 238 ( 237 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 17 ~; 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 : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 321 ( 55 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
sFlat0 = complement(b),
introduced(definition) ).
cnf(t100,plain,
complement(b) = sFlat0,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sFlat1 = complement(a),
introduced(definition) ).
cnf(t95,plain,
complement(a) = sFlat1,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat2 = join(complement(b),complement(a)),
introduced(definition) ).
cnf(t90,plain,
join(complement(b),complement(a)) = sFlat2,
inference(orient,[status(thm)],[t16]) ).
cnf(t650224,plain,
join(complement(b),sFlat1) = sFlat2,
inference(step,[status(thm)],[t90,t95]) ).
cnf(t99,plain,
join(complement(b),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t650224]) ).
cnf(f5,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
fof(f5_nnf,plain,
! [X,Y] : join(X,Y) = join(Y,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : join(X,Y) = join(Y,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t71,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t650235,plain,
join(sFlat1,complement(b)) = sFlat2,
inference(step,[status(thm)],[t99,t71]) ).
cnf(t650236,plain,
join(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t650235,t100]) ).
cnf(t650237,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t650236,t71]) ).
cnf(t173,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t650237]) ).
cnf(f3,axiom,
join(X,meet(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
fof(f3_nnf,plain,
! [X,Y] : join(X,meet(X,Y)) = X,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : join(X,meet(X,Y)) = X,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
join(X0,meet(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t7,plain,
join(X1,meet(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t20,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(f4,axiom,
meet(X,Y) = meet(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
fof(f4_nnf,plain,
! [X,Y] : meet(X,Y) = meet(Y,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : meet(X,Y) = meet(Y,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
meet(X0,X1) = meet(X1,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t8,plain,
meet(X1,X2) = meet(X2,X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t27,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t28,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t20,t27]) ).
cnf(t182,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t28]) ).
cnf(f6,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
fof(f6_nnf,plain,
! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t11,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t30,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(f2,axiom,
meet(X,join(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
fof(f2_nnf,plain,
! [X,Y] : meet(X,join(X,Y)) = X,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : meet(X,join(X,Y)) = X,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
meet(X0,join(X0,X1)) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t9,plain,
meet(X1,join(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t18,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(f7,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
fof(f7_nnf,plain,
! [X,Y,Z] : join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z] : join(join(X,Y),Z) = join(X,join(Y,Z)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t10,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t75,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t175,plain,
join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
inference(cp,[status(thm)],[t75,t173]) ).
cnf(t491,plain,
join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
inference(orient,[status(thm)],[t175]) ).
cnf(t499,plain,
sFlat0 = meet(sFlat0,join(sFlat2,X1)),
inference(cp,[status(thm)],[t18,t491]) ).
cnf(t528,plain,
meet(sFlat0,join(sFlat2,X1)) = sFlat0,
inference(orient,[status(thm)],[t499]) ).
cnf(t531,plain,
meet(sFlat0,meet(join(sFlat2,X1),X2)) = meet(sFlat0,X2),
inference(cp,[status(thm)],[t30,t528]) ).
cnf(t2719,plain,
meet(sFlat0,meet(join(sFlat2,X1),X2)) = meet(sFlat0,X2),
inference(orient,[status(thm)],[t531]) ).
cnf(t72,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t18,t71]) ).
cnf(t195,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t72]) ).
cnf(t197,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t195,t20]) ).
cnf(t650288,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t197,t30]) ).
cnf(t561,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t650288]) ).
cnf(t2722,plain,
meet(sFlat0,meet(X1,join(sFlat2,X2))) = meet(sFlat0,meet(join(sFlat2,X2),X1)),
inference(cp,[status(thm)],[t2719,t561]) ).
cnf(t650442,plain,
meet(sFlat0,meet(X1,join(sFlat2,X2))) = meet(sFlat0,X1),
inference(step,[status(thm)],[t2722,t2719]) ).
cnf(t4215,plain,
meet(sFlat0,meet(X1,join(sFlat2,X2))) = meet(sFlat0,X1),
inference(orient,[status(thm)],[t650442]) ).
cnf(t4222,plain,
meet(X1,join(sFlat2,X2)) = join(meet(X1,join(sFlat2,X2)),meet(sFlat0,X1)),
inference(cp,[status(thm)],[t182,t4215]) ).
cnf(t651910,plain,
meet(X1,join(sFlat2,X2)) = join(meet(sFlat0,X1),meet(X1,join(sFlat2,X2))),
inference(step,[status(thm)],[t4222,t71]) ).
cnf(t434481,plain,
join(meet(sFlat0,X1),meet(X1,join(sFlat2,X2))) = meet(X1,join(sFlat2,X2)),
inference(orient,[status(thm)],[t651910]) ).
cnf(f0,axiom,
meet(X,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
fof(f0_nnf,plain,
! [X] : meet(X,X) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : meet(X,X) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
meet(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
meet(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t17,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t34,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(cp,[status(thm)],[t30,t17]) ).
cnf(t216,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t34]) ).
cnf(f10,axiom,
( complement(X) = Y
| join(X,Y) != one
| meet(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
fof(f10_nnf,plain,
! [X,Y] :
( complement(X) = Y
| join(X,Y) != one
| meet(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] :
( complement(X) = Y
| join(X,Y) != one
| meet(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( complement(X0) = X1
| join(X0,X1) != one
| meet(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t12,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t22,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t187,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t182,t30]) ).
cnf(t1507,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t187]) ).
cnf(t1512,plain,
join(X1,X2) = join(join(X1,X2),meet(X3,X1)),
inference(cp,[status(thm)],[t1507,t18]) ).
cnf(t650428,plain,
join(X1,X2) = join(X1,join(X2,meet(X3,X1))),
inference(step,[status(thm)],[t1512,t75]) ).
cnf(t3458,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(orient,[status(thm)],[t650428]) ).
cnf(f11,axiom,
join(meet(X,Y),meet(X,Z)) = meet(X,join(meet(X,Y),join(meet(X,Z),meet(Y,join(X,Z))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H18) ).
fof(f11_nnf,plain,
! [X,Y,Z] : join(meet(X,Y),meet(X,Z)) = meet(X,join(meet(X,Y),join(meet(X,Z),meet(Y,join(X,Z))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] : join(meet(X,Y),meet(X,Z)) = meet(X,join(meet(X,Y),join(meet(X,Z),meet(Y,join(X,Z))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
join(meet(X0,X1),meet(X0,X2)) = meet(X0,join(meet(X0,X1),join(meet(X0,X2),meet(X1,join(X0,X2))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(meet(X1,X2),join(meet(X1,X3),meet(X2,join(X1,X3))))) = join(meet(X1,X2),meet(X1,X3)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
meet(X1,join(meet(X1,X2),join(meet(X1,X3),meet(X2,join(X1,X3))))) = join(meet(X1,X2),meet(X1,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(f12,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
fof(f12_nnf,plain,
meet(b,a) = a,
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
meet(b,a) = a,
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t2,plain,
meet(b,a) = a,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t65,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t67,plain,
b = join(b,a),
inference(cp,[status(thm)],[t20,t65]) ).
cnf(t109,plain,
join(b,a) = b,
inference(orient,[status(thm)],[t67]) ).
cnf(t110,plain,
join(b,join(a,X1)) = join(b,X1),
inference(cp,[status(thm)],[t75,t109]) ).
cnf(t251,plain,
join(b,join(a,X1)) = join(b,X1),
inference(orient,[status(thm)],[t110]) ).
cnf(f8,axiom,
join(X,complement(X)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
fof(f8_nnf,plain,
! [X] : join(X,complement(X)) = one,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : join(X,complement(X)) = one,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
join(X0,complement(X0)) = one,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t3,plain,
join(X1,complement(X1)) = one,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t85,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t252,plain,
join(b,complement(a)) = join(b,one),
inference(cp,[status(thm)],[t251,t85]) ).
cnf(t650246,plain,
join(b,sFlat1) = join(b,one),
inference(step,[status(thm)],[t252,t95]) ).
cnf(t650247,plain,
join(sFlat1,b) = join(b,one),
inference(step,[status(thm)],[t650246,t71]) ).
cnf(t87,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t18,t85]) ).
cnf(t113,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t87]) ).
cnf(t114,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t113,t27]) ).
cnf(t148,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t114]) ).
cnf(t150,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t148,t18]) ).
cnf(t162,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t150]) ).
cnf(t163,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t162,t71]) ).
cnf(t170,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t163]) ).
cnf(t650248,plain,
join(sFlat1,b) = one,
inference(step,[status(thm)],[t650247,t170]) ).
cnf(t257,plain,
join(sFlat1,b) = one,
inference(orient,[status(thm)],[t650248]) ).
cnf(t260,plain,
join(meet(sFlat1,X1),meet(sFlat1,b)) = meet(sFlat1,join(meet(sFlat1,X1),join(meet(sFlat1,b),meet(X1,one)))),
inference(cp,[status(thm)],[t39,t257]) ).
cnf(t652021,plain,
join(meet(sFlat1,X1),meet(sFlat1,b)) = meet(sFlat1,join(meet(sFlat1,X1),join(meet(sFlat1,b),X1))),
inference(step,[status(thm)],[t260,t113]) ).
cnf(t78,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t75,t71]) ).
cnf(t28919,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t78]) ).
cnf(t165,plain,
join(meet(one,X1),meet(one,X2)) = meet(one,join(meet(one,X1),join(meet(one,X2),meet(X1,one)))),
inference(cp,[status(thm)],[t39,t162]) ).
cnf(t650255,plain,
join(X1,meet(one,X2)) = meet(one,join(meet(one,X1),join(meet(one,X2),meet(X1,one)))),
inference(step,[status(thm)],[t165,t148]) ).
cnf(t650256,plain,
join(X1,X2) = meet(one,join(meet(one,X1),join(meet(one,X2),meet(X1,one)))),
inference(step,[status(thm)],[t650255,t148]) ).
cnf(t650257,plain,
join(X1,X2) = join(meet(one,X1),join(meet(one,X2),meet(X1,one))),
inference(step,[status(thm)],[t650256,t148]) ).
cnf(t650258,plain,
join(X1,X2) = join(X1,join(meet(one,X2),meet(X1,one))),
inference(step,[status(thm)],[t650257,t148]) ).
cnf(t650259,plain,
join(X1,X2) = join(X1,join(X2,meet(X1,one))),
inference(step,[status(thm)],[t650258,t148]) ).
cnf(t650260,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t650259,t113]) ).
cnf(t336,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t650260]) ).
cnf(t28962,plain,
join(join(X1,X2),join(X3,X2)) = join(X3,join(X2,X1)),
inference(cp,[status(thm)],[t28919,t336]) ).
cnf(t650846,plain,
join(X1,join(X2,join(X3,X2))) = join(X3,join(X2,X1)),
inference(step,[status(thm)],[t28962,t75]) ).
cnf(t650847,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(step,[status(thm)],[t650846,t336]) ).
cnf(t31007,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(orient,[status(thm)],[t650847]) ).
cnf(t652022,plain,
join(meet(sFlat1,X1),meet(sFlat1,b)) = meet(sFlat1,join(X1,join(meet(sFlat1,b),meet(sFlat1,X1)))),
inference(step,[status(thm)],[t652021,t31007]) ).
cnf(t652023,plain,
join(meet(sFlat1,X1),meet(sFlat1,b)) = meet(sFlat1,join(X1,meet(sFlat1,b))),
inference(step,[status(thm)],[t652022,t3458]) ).
cnf(t536317,plain,
join(meet(sFlat1,X1),meet(sFlat1,b)) = meet(sFlat1,join(X1,meet(sFlat1,b))),
inference(orient,[status(thm)],[t652023]) ).
cnf(t536717,plain,
join(b,meet(sFlat1,X1)) = join(b,meet(sFlat1,join(X1,meet(sFlat1,b)))),
inference(cp,[status(thm)],[t3458,t536317]) ).
cnf(t647230,plain,
join(b,meet(sFlat1,join(X1,meet(sFlat1,b)))) = join(b,meet(sFlat1,X1)),
inference(orient,[status(thm)],[t536717]) ).
cnf(t647232,plain,
join(b,meet(sFlat1,X1)) = join(b,meet(sFlat1,join(meet(sFlat1,b),X1))),
inference(cp,[status(thm)],[t647230,t71]) ).
cnf(t648283,plain,
join(b,meet(sFlat1,join(meet(sFlat1,b),X1))) = join(b,meet(sFlat1,X1)),
inference(orient,[status(thm)],[t647232]) ).
cnf(t88,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t75,t85]) ).
cnf(t650361,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t88,t162]) ).
cnf(t1290,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t650361]) ).
cnf(t1293,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t336,t1290]) ).
cnf(t650363,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t1293,t75]) ).
cnf(t650364,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t650363,t75]) ).
cnf(t650365,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t650364,t170]) ).
cnf(t650366,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t650365,t170]) ).
cnf(t1368,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t650366]) ).
cnf(t1374,plain,
one = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t1368,t182]) ).
cnf(t650368,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t1374,t71]) ).
cnf(t1421,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t650368]) ).
cnf(t1423,plain,
one = join(meet(X1,X2),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t1421,t561]) ).
cnf(t6881,plain,
join(meet(X1,X2),complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t1423]) ).
cnf(t648307,plain,
join(b,meet(sFlat1,complement(meet(b,sFlat1)))) = join(b,meet(sFlat1,one)),
inference(cp,[status(thm)],[t648283,t6881]) ).
cnf(t652317,plain,
join(b,meet(sFlat1,complement(meet(sFlat1,b)))) = join(b,meet(sFlat1,one)),
inference(step,[status(thm)],[t648307,t27]) ).
cnf(t652318,plain,
join(b,meet(sFlat1,complement(meet(sFlat1,b)))) = join(b,sFlat1),
inference(step,[status(thm)],[t652317,t113]) ).
cnf(t652319,plain,
join(b,meet(sFlat1,complement(meet(sFlat1,b)))) = join(sFlat1,b),
inference(step,[status(thm)],[t652318,t71]) ).
cnf(t652320,plain,
join(b,meet(sFlat1,complement(meet(sFlat1,b)))) = one,
inference(step,[status(thm)],[t652319,t257]) ).
cnf(t648630,plain,
join(b,meet(sFlat1,complement(meet(sFlat1,b)))) = one,
inference(orient,[status(thm)],[t652320]) ).
cnf(t648635,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = ifeq(meet(b,meet(sFlat1,complement(meet(sFlat1,b)))),zero,ifeq(one,one,complement(b),meet(sFlat1,complement(meet(sFlat1,b)))),meet(sFlat1,complement(meet(sFlat1,b)))),
inference(cp,[status(thm)],[t22,t648630]) ).
cnf(f9,axiom,
meet(X,complement(X)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
fof(f9_nnf,plain,
! [X] : meet(X,complement(X)) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : meet(X,complement(X)) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
meet(X0,complement(X0)) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t4,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t58,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t60,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t30,t58]) ).
cnf(t61,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t20,t58]) ).
cnf(t104,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t61]) ).
cnf(t105,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t104,t71]) ).
cnf(t140,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t105]) ).
cnf(t142,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t140,t20]) ).
cnf(t158,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t142]) ).
cnf(t650348,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t60,t158]) ).
cnf(t1127,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t650348]) ).
cnf(t1132,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t561,t1127]) ).
cnf(t650349,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t1132,t30]) ).
cnf(t650350,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t650349,t30]) ).
cnf(t159,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t158,t27]) ).
cnf(t166,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t159]) ).
cnf(t650351,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t650350,t166]) ).
cnf(t650352,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t650351,t166]) ).
cnf(t1145,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t650352]) ).
cnf(t1150,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t1145,t195]) ).
cnf(t650353,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t1150,t27]) ).
cnf(t1176,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t650353]) ).
cnf(t580,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,X1)),
inference(cp,[status(thm)],[t182,t561]) ).
cnf(t2845,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t580]) ).
cnf(t2924,plain,
zero = meet(meet(X1,X2),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t1176,t2845]) ).
cnf(t650533,plain,
zero = meet(X1,meet(X2,complement(meet(X2,X1)))),
inference(step,[status(thm)],[t2924,t30]) ).
cnf(t8548,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(orient,[status(thm)],[t650533]) ).
cnf(t652321,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = ifeq(zero,zero,ifeq(one,one,complement(b),meet(sFlat1,complement(meet(sFlat1,b)))),meet(sFlat1,complement(meet(sFlat1,b)))),
inference(step,[status(thm)],[t648635,t8548]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t652322,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = ifeq(one,one,complement(b),meet(sFlat1,complement(meet(sFlat1,b)))),
inference(step,[status(thm)],[t652321,t21]) ).
cnf(t652323,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = complement(b),
inference(step,[status(thm)],[t652322,t21]) ).
cnf(t652324,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = sFlat0,
inference(step,[status(thm)],[t652323,t100]) ).
cnf(t648780,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = sFlat0,
inference(orient,[status(thm)],[t652324]) ).
cnf(t648790,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = meet(sFlat1,sFlat0),
inference(cp,[status(thm)],[t216,t648780]) ).
cnf(t652326,plain,
sFlat0 = meet(sFlat1,sFlat0),
inference(step,[status(thm)],[t648790,t648780]) ).
cnf(t652327,plain,
sFlat0 = meet(sFlat0,sFlat1),
inference(step,[status(thm)],[t652326,t27]) ).
cnf(t649166,plain,
meet(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t652327]) ).
cnf(t649240,plain,
meet(sFlat1,join(sFlat2,X1)) = join(sFlat0,meet(sFlat1,join(sFlat2,X1))),
inference(cp,[status(thm)],[t434481,t649166]) ).
cnf(t198,plain,
sFlat1 = meet(sFlat1,sFlat2),
inference(cp,[status(thm)],[t195,t173]) ).
cnf(t205,plain,
meet(sFlat1,sFlat2) = sFlat1,
inference(orient,[status(thm)],[t198]) ).
cnf(t207,plain,
meet(sFlat1,meet(sFlat2,X1)) = meet(sFlat1,X1),
inference(cp,[status(thm)],[t30,t205]) ).
cnf(t653,plain,
meet(sFlat1,meet(sFlat2,X1)) = meet(sFlat1,X1),
inference(orient,[status(thm)],[t207]) ).
cnf(t657,plain,
meet(sFlat1,join(sFlat2,X1)) = meet(sFlat1,sFlat2),
inference(cp,[status(thm)],[t653,t18]) ).
cnf(t650303,plain,
meet(sFlat1,join(sFlat2,X1)) = sFlat1,
inference(step,[status(thm)],[t657,t205]) ).
cnf(t680,plain,
meet(sFlat1,join(sFlat2,X1)) = sFlat1,
inference(orient,[status(thm)],[t650303]) ).
cnf(t652329,plain,
sFlat1 = join(sFlat0,meet(sFlat1,join(sFlat2,X1))),
inference(step,[status(thm)],[t649240,t680]) ).
cnf(t652330,plain,
sFlat1 = join(sFlat0,sFlat1),
inference(step,[status(thm)],[t652329,t680]) ).
cnf(t652331,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t652330,t173]) ).
cnf(t649511,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t652331]) ).
cnf(t652332,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t173,t649511]) ).
cnf(t649512,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t652332]) ).
cnf(f13,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f13_nnf,plain,
join(complement(b),complement(a)) != complement(a),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
join(complement(b),complement(a)) != complement(a),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
join(complement(b),complement(a)) != complement(a),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
join(sFlat0,complement(a)) != complement(a),
inference(rw,[status(thm)],[goal_0,t100]) ).
cnf(g0_1,plain,
join(sFlat0,sFlat1) != complement(a),
inference(rw,[status(thm)],[g0_0,t95]) ).
cnf(g0_2,plain,
sFlat1 != complement(a),
inference(rw,[status(thm)],[g0_1,t649512]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t95]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT230-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 20:38:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 231.32/34.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 231.32/34.54 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------