%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT223-1 : 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 01:56:21 PM UTC 2026
% Result : Unsatisfiable 223.64s 28.99s
% Output : Proof 223.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 17
% Syntax : Number of formulae : 226 ( 222 unt; 0 def)
% Number of atoms : 234 ( 233 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 : 7 ( 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 : 272 ( 48 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
sFlat0 = complement(b),
introduced(definition) ).
cnf(t95,plain,
complement(b) = sFlat0,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sFlat1 = complement(a),
introduced(definition) ).
cnf(t90,plain,
complement(a) = sFlat1,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat2 = join(complement(b),complement(a)),
introduced(definition) ).
cnf(t85,plain,
join(complement(b),complement(a)) = sFlat2,
inference(orient,[status(thm)],[t16]) ).
cnf(t389671,plain,
join(complement(b),sFlat1) = sFlat2,
inference(step,[status(thm)],[t85,t90]) ).
cnf(t94,plain,
join(complement(b),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t389671]) ).
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(t65,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t389682,plain,
join(sFlat1,complement(b)) = sFlat2,
inference(step,[status(thm)],[t94,t65]) ).
cnf(t389683,plain,
join(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t389682,t95]) ).
cnf(t389684,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t389683,t65]) ).
cnf(t166,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t389684]) ).
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(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/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(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(t175,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/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(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/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(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/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(t69,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t168,plain,
join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
inference(cp,[status(thm)],[t69,t166]) ).
cnf(t311,plain,
join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
inference(orient,[status(thm)],[t168]) ).
cnf(t325,plain,
sFlat0 = meet(sFlat0,join(sFlat2,X1)),
inference(cp,[status(thm)],[t18,t311]) ).
cnf(t374,plain,
meet(sFlat0,join(sFlat2,X1)) = sFlat0,
inference(orient,[status(thm)],[t325]) ).
cnf(t377,plain,
meet(sFlat0,meet(join(sFlat2,X1),X2)) = meet(sFlat0,X2),
inference(cp,[status(thm)],[t30,t374]) ).
cnf(t2509,plain,
meet(sFlat0,meet(join(sFlat2,X1),X2)) = meet(sFlat0,X2),
inference(orient,[status(thm)],[t377]) ).
cnf(t66,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t18,t65]) ).
cnf(t188,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t66]) ).
cnf(t190,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t188,t20]) ).
cnf(t389731,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t190,t30]) ).
cnf(t538,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t389731]) ).
cnf(t2513,plain,
meet(sFlat0,meet(X1,join(sFlat2,X2))) = meet(sFlat0,meet(join(sFlat2,X2),X1)),
inference(cp,[status(thm)],[t2509,t538]) ).
cnf(t389885,plain,
meet(sFlat0,meet(X1,join(sFlat2,X2))) = meet(sFlat0,X1),
inference(step,[status(thm)],[t2513,t2509]) ).
cnf(t4058,plain,
meet(sFlat0,meet(X1,join(sFlat2,X2))) = meet(sFlat0,X1),
inference(orient,[status(thm)],[t389885]) ).
cnf(t4065,plain,
meet(X1,join(sFlat2,X2)) = join(meet(X1,join(sFlat2,X2)),meet(sFlat0,X1)),
inference(cp,[status(thm)],[t175,t4058]) ).
cnf(t391307,plain,
meet(X1,join(sFlat2,X2)) = join(meet(sFlat0,X1),meet(X1,join(sFlat2,X2))),
inference(step,[status(thm)],[t4065,t65]) ).
cnf(t376332,plain,
join(meet(sFlat0,X1),meet(X1,join(sFlat2,X2))) = meet(X1,join(sFlat2,X2)),
inference(orient,[status(thm)],[t391307]) ).
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(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(t208,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/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(t22,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t177,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t175,t18]) ).
cnf(t389710,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t177,t69]) ).
cnf(t398,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t389710]) ).
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(t80,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t83,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t69,t80]) ).
cnf(t82,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t18,t80]) ).
cnf(t108,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t82]) ).
cnf(t109,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t108,t27]) ).
cnf(t142,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t109]) ).
cnf(t144,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t142,t18]) ).
cnf(t157,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t144]) ).
cnf(t389804,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t83,t157]) ).
cnf(t1217,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t389804]) ).
cnf(t1220,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t398,t1217]) ).
cnf(t389806,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t1220,t69]) ).
cnf(t389807,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t389806,t69]) ).
cnf(t158,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t157,t65]) ).
cnf(t164,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t158]) ).
cnf(t389808,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t389807,t164]) ).
cnf(t389809,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t389808,t164]) ).
cnf(t1295,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t389809]) ).
cnf(t1301,plain,
one = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t1295,t175]) ).
cnf(t389811,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t1301,t65]) ).
cnf(t1347,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t389811]) ).
cnf(f11,axiom,
meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H7) ).
fof(f11_nnf,plain,
! [X,Y,Z] : meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] : meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X0,X2))) = meet(X0,join(X1,meet(X0,join(meet(X0,X1),meet(X2,join(X0,X1)))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))) = meet(X1,join(X2,meet(X1,X3))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))) = meet(X1,join(X2,meet(X1,X3))),
inference(orient,[status(thm)],[t13]) ).
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(t60,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t62,plain,
b = join(b,a),
inference(cp,[status(thm)],[t20,t60]) ).
cnf(t104,plain,
join(b,a) = b,
inference(orient,[status(thm)],[t62]) ).
cnf(t105,plain,
join(b,join(a,X1)) = join(b,X1),
inference(cp,[status(thm)],[t69,t104]) ).
cnf(t236,plain,
join(b,join(a,X1)) = join(b,X1),
inference(orient,[status(thm)],[t105]) ).
cnf(t237,plain,
join(b,complement(a)) = join(b,one),
inference(cp,[status(thm)],[t236,t80]) ).
cnf(t389693,plain,
join(b,sFlat1) = join(b,one),
inference(step,[status(thm)],[t237,t90]) ).
cnf(t389694,plain,
join(sFlat1,b) = join(b,one),
inference(step,[status(thm)],[t389693,t65]) ).
cnf(t389695,plain,
join(sFlat1,b) = one,
inference(step,[status(thm)],[t389694,t164]) ).
cnf(t242,plain,
join(sFlat1,b) = one,
inference(orient,[status(thm)],[t389695]) ).
cnf(t245,plain,
meet(sFlat1,join(b,meet(sFlat1,X1))) = meet(sFlat1,join(b,meet(sFlat1,join(meet(sFlat1,b),meet(X1,one))))),
inference(cp,[status(thm)],[t39,t242]) ).
cnf(t391313,plain,
meet(sFlat1,join(b,meet(sFlat1,X1))) = meet(sFlat1,join(b,meet(sFlat1,join(meet(sFlat1,b),X1)))),
inference(step,[status(thm)],[t245,t108]) ).
cnf(t387867,plain,
meet(sFlat1,join(b,meet(sFlat1,join(meet(sFlat1,b),X1)))) = meet(sFlat1,join(b,meet(sFlat1,X1))),
inference(orient,[status(thm)],[t391313]) ).
cnf(t1349,plain,
one = join(meet(X1,X2),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t1347,t538]) ).
cnf(t6632,plain,
join(meet(X1,X2),complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t1349]) ).
cnf(t387884,plain,
meet(sFlat1,join(b,meet(sFlat1,complement(meet(b,sFlat1))))) = meet(sFlat1,join(b,meet(sFlat1,one))),
inference(cp,[status(thm)],[t387867,t6632]) ).
cnf(t391314,plain,
meet(sFlat1,join(b,meet(sFlat1,complement(meet(sFlat1,b))))) = meet(sFlat1,join(b,meet(sFlat1,one))),
inference(step,[status(thm)],[t387884,t27]) ).
cnf(t391315,plain,
meet(sFlat1,join(b,meet(sFlat1,complement(meet(sFlat1,b))))) = meet(sFlat1,join(b,sFlat1)),
inference(step,[status(thm)],[t391314,t108]) ).
cnf(t391316,plain,
meet(sFlat1,join(b,meet(sFlat1,complement(meet(sFlat1,b))))) = meet(sFlat1,join(sFlat1,b)),
inference(step,[status(thm)],[t391315,t65]) ).
cnf(t391317,plain,
meet(sFlat1,join(b,meet(sFlat1,complement(meet(sFlat1,b))))) = meet(sFlat1,one),
inference(step,[status(thm)],[t391316,t242]) ).
cnf(t391318,plain,
meet(sFlat1,join(b,meet(sFlat1,complement(meet(sFlat1,b))))) = sFlat1,
inference(step,[status(thm)],[t391317,t108]) ).
cnf(t388190,plain,
meet(sFlat1,join(b,meet(sFlat1,complement(meet(sFlat1,b))))) = sFlat1,
inference(orient,[status(thm)],[t391318]) ).
cnf(t388329,plain,
one = join(join(b,meet(sFlat1,complement(meet(sFlat1,b)))),complement(sFlat1)),
inference(cp,[status(thm)],[t1347,t388190]) ).
cnf(t391319,plain,
one = join(b,join(meet(sFlat1,complement(meet(sFlat1,b))),complement(sFlat1))),
inference(step,[status(thm)],[t388329,t69]) ).
cnf(t391320,plain,
one = join(b,join(complement(sFlat1),meet(sFlat1,complement(meet(sFlat1,b))))),
inference(step,[status(thm)],[t391319,t65]) ).
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(t54,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t92,plain,
zero = meet(a,sFlat1),
inference(cp,[status(thm)],[t54,t90]) ).
cnf(t389673,plain,
zero = meet(sFlat1,a),
inference(step,[status(thm)],[t92,t27]) ).
cnf(t117,plain,
meet(sFlat1,a) = zero,
inference(orient,[status(thm)],[t389673]) ).
cnf(t119,plain,
a = ifeq(zero,zero,ifeq(join(sFlat1,a),one,complement(sFlat1),a),a),
inference(cp,[status(thm)],[t22,t117]) ).
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(t389674,plain,
a = ifeq(join(sFlat1,a),one,complement(sFlat1),a),
inference(step,[status(thm)],[t119,t21]) ).
cnf(t91,plain,
one = join(a,sFlat1),
inference(cp,[status(thm)],[t80,t90]) ).
cnf(t389672,plain,
one = join(sFlat1,a),
inference(step,[status(thm)],[t91,t65]) ).
cnf(t113,plain,
join(sFlat1,a) = one,
inference(orient,[status(thm)],[t389672]) ).
cnf(t389675,plain,
a = ifeq(one,one,complement(sFlat1),a),
inference(step,[status(thm)],[t389674,t113]) ).
cnf(t389676,plain,
a = complement(sFlat1),
inference(step,[status(thm)],[t389675,t21]) ).
cnf(t121,plain,
complement(sFlat1) = a,
inference(orient,[status(thm)],[t389676]) ).
cnf(t391321,plain,
one = join(b,join(a,meet(sFlat1,complement(meet(sFlat1,b))))),
inference(step,[status(thm)],[t391320,t121]) ).
cnf(t391322,plain,
one = join(b,meet(sFlat1,complement(meet(sFlat1,b)))),
inference(step,[status(thm)],[t391321,t236]) ).
cnf(t388424,plain,
join(b,meet(sFlat1,complement(meet(sFlat1,b)))) = one,
inference(orient,[status(thm)],[t391322]) ).
cnf(t388429,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,t388424]) ).
cnf(t56,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t30,t54]) ).
cnf(t57,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t20,t54]) ).
cnf(t99,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t57]) ).
cnf(t100,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t99,t65]) ).
cnf(t133,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t100]) ).
cnf(t135,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t133,t20]) ).
cnf(t153,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t135]) ).
cnf(t389791,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t56,t153]) ).
cnf(t1068,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t389791]) ).
cnf(t1072,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t538,t1068]) ).
cnf(t389792,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t1072,t30]) ).
cnf(t389793,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t389792,t30]) ).
cnf(t154,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t153,t27]) ).
cnf(t161,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t154]) ).
cnf(t389794,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t389793,t161]) ).
cnf(t389795,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t389794,t161]) ).
cnf(t1083,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t389795]) ).
cnf(t1090,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t1083,t188]) ).
cnf(t389797,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t1090,t27]) ).
cnf(t1132,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t389797]) ).
cnf(t557,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,X1)),
inference(cp,[status(thm)],[t175,t538]) ).
cnf(t2713,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t557]) ).
cnf(t2791,plain,
zero = meet(meet(X1,X2),complement(meet(X2,X1))),
inference(cp,[status(thm)],[t1132,t2713]) ).
cnf(t389976,plain,
zero = meet(X1,meet(X2,complement(meet(X2,X1)))),
inference(step,[status(thm)],[t2791,t30]) ).
cnf(t8274,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(orient,[status(thm)],[t389976]) ).
cnf(t391323,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)],[t388429,t8274]) ).
cnf(t391324,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = ifeq(one,one,complement(b),meet(sFlat1,complement(meet(sFlat1,b)))),
inference(step,[status(thm)],[t391323,t21]) ).
cnf(t391325,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = complement(b),
inference(step,[status(thm)],[t391324,t21]) ).
cnf(t391326,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = sFlat0,
inference(step,[status(thm)],[t391325,t95]) ).
cnf(t388543,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = sFlat0,
inference(orient,[status(thm)],[t391326]) ).
cnf(t388551,plain,
meet(sFlat1,complement(meet(sFlat1,b))) = meet(sFlat1,sFlat0),
inference(cp,[status(thm)],[t208,t388543]) ).
cnf(t391328,plain,
sFlat0 = meet(sFlat1,sFlat0),
inference(step,[status(thm)],[t388551,t388543]) ).
cnf(t391329,plain,
sFlat0 = meet(sFlat0,sFlat1),
inference(step,[status(thm)],[t391328,t27]) ).
cnf(t388833,plain,
meet(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t391329]) ).
cnf(t388848,plain,
meet(sFlat1,join(sFlat2,X1)) = join(sFlat0,meet(sFlat1,join(sFlat2,X1))),
inference(cp,[status(thm)],[t376332,t388833]) ).
cnf(t191,plain,
sFlat1 = meet(sFlat1,sFlat2),
inference(cp,[status(thm)],[t188,t166]) ).
cnf(t197,plain,
meet(sFlat1,sFlat2) = sFlat1,
inference(orient,[status(thm)],[t191]) ).
cnf(t199,plain,
meet(sFlat1,meet(sFlat2,X1)) = meet(sFlat1,X1),
inference(cp,[status(thm)],[t30,t197]) ).
cnf(t620,plain,
meet(sFlat1,meet(sFlat2,X1)) = meet(sFlat1,X1),
inference(orient,[status(thm)],[t199]) ).
cnf(t623,plain,
meet(sFlat1,join(sFlat2,X1)) = meet(sFlat1,sFlat2),
inference(cp,[status(thm)],[t620,t18]) ).
cnf(t389745,plain,
meet(sFlat1,join(sFlat2,X1)) = sFlat1,
inference(step,[status(thm)],[t623,t197]) ).
cnf(t635,plain,
meet(sFlat1,join(sFlat2,X1)) = sFlat1,
inference(orient,[status(thm)],[t389745]) ).
cnf(t391334,plain,
sFlat1 = join(sFlat0,meet(sFlat1,join(sFlat2,X1))),
inference(step,[status(thm)],[t388848,t635]) ).
cnf(t391335,plain,
sFlat1 = join(sFlat0,sFlat1),
inference(step,[status(thm)],[t391334,t635]) ).
cnf(t391336,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t391335,t166]) ).
cnf(t389100,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t391336]) ).
cnf(t391337,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t166,t389100]) ).
cnf(t389101,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t391337]) ).
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,
join(sFlat0,complement(a)) != complement(a),
inference(rw,[status(thm)],[goal_0,t95]) ).
cnf(g0_1,plain,
join(sFlat0,sFlat1) != complement(a),
inference(rw,[status(thm)],[g0_0,t90]) ).
cnf(g0_2,plain,
sFlat1 != complement(a),
inference(rw,[status(thm)],[g0_1,t389101]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t90]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT223-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.65 % Computer : n006.cluster.edu
% 0.20/0.65 % Model : x86_64 x86_64
% 0.20/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.65 % Memory : 8046.5625MB
% 0.20/0.65 % OS : Linux 6.8.0-71-generic
% 0.20/0.65 % CPULimit : 300
% 0.20/0.65 % WCLimit : 300
% 0.20/0.65 % DateTime : Wed Sep 23 20:36:44 UTC 2026
% 0.20/0.65 % CPUTime :
% 0.20/0.65 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 223.64/28.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 223.64/28.99 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------