%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT244-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:56:24 PM UTC 2026
% Result : Unsatisfiable 198.87s 29.69s
% Output : Proof 198.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 17
% Syntax : Number of formulae : 198 ( 194 unt; 0 def)
% Number of atoms : 206 ( 205 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 : 237 ( 28 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
sFlat0 = complement(b),
introduced(definition) ).
cnf(t92,plain,
complement(b) = sFlat0,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sFlat1 = complement(a),
introduced(definition) ).
cnf(t87,plain,
complement(a) = sFlat1,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sFlat2 = join(complement(b),complement(a)),
introduced(definition) ).
cnf(t44,plain,
join(complement(b),complement(a)) = sFlat2,
inference(orient,[status(thm)],[t16]) ).
cnf(t576260,plain,
join(complement(b),sFlat1) = sFlat2,
inference(step,[status(thm)],[t44,t87]) ).
cnf(t91,plain,
join(complement(b),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t576260]) ).
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(t27,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t576271,plain,
join(sFlat1,complement(b)) = sFlat2,
inference(step,[status(thm)],[t91,t27]) ).
cnf(t576272,plain,
join(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t576271,t92]) ).
cnf(t576273,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t576272,t27]) ).
cnf(t162,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t576273]) ).
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(t30,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(f1,axiom,
join(X,X) = X,
file('/export/starexec/sandbox2/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(t17,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t34,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t30,t17]) ).
cnf(t226,plain,
join(X1,join(X1,X2)) = join(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(f11,axiom,
meet(X,join(Y,Z)) = meet(X,join(Y,meet(join(X,Y),join(Z,meet(X,Y))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H58) ).
fof(f11_nnf,plain,
! [X,Y,Z] : meet(X,join(Y,Z)) = meet(X,join(Y,meet(join(X,Y),join(Z,meet(X,Y))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] : meet(X,join(Y,Z)) = meet(X,join(Y,meet(join(X,Y),join(Z,meet(X,Y))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,X2)) = meet(X0,join(X1,meet(join(X0,X1),join(X2,meet(X0,X1))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,meet(join(X1,X2),join(X3,meet(X1,X2))))) = meet(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t51,plain,
meet(X1,join(X2,meet(join(X1,X2),join(X3,meet(X1,X2))))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
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(t48,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t62,plain,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(join(X1,X2),join(X3,meet(X2,X1))))),
inference(cp,[status(thm)],[t51,t48]) ).
cnf(t60832,plain,
meet(X1,join(X2,meet(join(X1,X2),join(X3,meet(X2,X1))))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t62]) ).
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(t65,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
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(t77,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t93,plain,
zero = meet(b,sFlat0),
inference(cp,[status(thm)],[t77,t92]) ).
cnf(t576266,plain,
zero = meet(sFlat0,b),
inference(step,[status(thm)],[t93,t48]) ).
cnf(t120,plain,
meet(sFlat0,b) = zero,
inference(orient,[status(thm)],[t576266]) ).
cnf(t121,plain,
meet(sFlat0,meet(b,X1)) = meet(zero,X1),
inference(cp,[status(thm)],[t65,t120]) ).
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(t18,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t79,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t18,t77]) ).
cnf(t101,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t79]) ).
cnf(t102,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t101,t27]) ).
cnf(t139,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t102]) ).
cnf(t141,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t139,t18]) ).
cnf(t154,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t141]) ).
cnf(t576293,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(step,[status(thm)],[t121,t154]) ).
cnf(t298,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(orient,[status(thm)],[t576293]) ).
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(t82,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t299,plain,
zero = meet(sFlat0,a),
inference(cp,[status(thm)],[t298,t82]) ).
cnf(t304,plain,
meet(sFlat0,a) = zero,
inference(orient,[status(thm)],[t299]) ).
cnf(t61499,plain,
meet(a,join(sFlat0,X1)) = meet(a,join(sFlat0,meet(join(a,sFlat0),join(X1,zero)))),
inference(cp,[status(thm)],[t60832,t304]) ).
cnf(t578302,plain,
meet(a,join(sFlat0,X1)) = meet(a,join(sFlat0,meet(join(sFlat0,a),join(X1,zero)))),
inference(step,[status(thm)],[t61499,t27]) ).
cnf(t578303,plain,
meet(a,join(sFlat0,X1)) = meet(a,join(sFlat0,meet(join(sFlat0,a),X1))),
inference(step,[status(thm)],[t578302,t101]) ).
cnf(t574743,plain,
meet(a,join(sFlat0,meet(join(sFlat0,a),X1))) = meet(a,join(sFlat0,X1)),
inference(orient,[status(thm)],[t578303]) ).
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(t20,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t28,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t20,t27]) ).
cnf(t171,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t28]) ).
cnf(t173,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t171,t18]) ).
cnf(t576326,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t173,t65]) ).
cnf(t536,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t576326]) ).
cnf(t80,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t65,t77]) ).
cnf(t576397,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t80,t154]) ).
cnf(t1204,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t576397]) ).
cnf(t1208,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t536,t1204]) ).
cnf(t576399,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t1208,t65]) ).
cnf(t576400,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t576399,t65]) ).
cnf(t155,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t154,t48]) ).
cnf(t159,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t155]) ).
cnf(t576401,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t576400,t159]) ).
cnf(t576402,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t576401,t159]) ).
cnf(t1284,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t576402]) ).
cnf(t1291,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t1284,t171]) ).
cnf(t576404,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t1291,t48]) ).
cnf(t1333,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t576404]) ).
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(t39,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t42,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t20,t39]) ).
cnf(t96,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t42]) ).
cnf(t97,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t96,t48]) ).
cnf(t130,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t97]) ).
cnf(t132,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t130,t20]) ).
cnf(t149,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t132]) ).
cnf(t152,plain,
meet(one,join(X1,X2)) = meet(one,join(X1,meet(one,join(X2,meet(one,X1))))),
inference(cp,[status(thm)],[t51,t149]) ).
cnf(t576295,plain,
join(X1,X2) = meet(one,join(X1,meet(one,join(X2,meet(one,X1))))),
inference(step,[status(thm)],[t152,t130]) ).
cnf(t576296,plain,
join(X1,X2) = join(X1,meet(one,join(X2,meet(one,X1)))),
inference(step,[status(thm)],[t576295,t130]) ).
cnf(t576297,plain,
join(X1,X2) = join(X1,join(X2,meet(one,X1))),
inference(step,[status(thm)],[t576296,t130]) ).
cnf(t576298,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t576297,t130]) ).
cnf(t331,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t576298]) ).
cnf(t1335,plain,
zero = meet(join(X1,X2),complement(join(X2,X1))),
inference(cp,[status(thm)],[t1333,t331]) ).
cnf(t6831,plain,
meet(join(X1,X2),complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t1335]) ).
cnf(t574768,plain,
meet(a,join(sFlat0,complement(join(a,sFlat0)))) = meet(a,join(sFlat0,zero)),
inference(cp,[status(thm)],[t574743,t6831]) ).
cnf(t578304,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = meet(a,join(sFlat0,zero)),
inference(step,[status(thm)],[t574768,t27]) ).
cnf(t578305,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = meet(a,sFlat0),
inference(step,[status(thm)],[t578304,t101]) ).
cnf(t578306,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = meet(sFlat0,a),
inference(step,[status(thm)],[t578305,t48]) ).
cnf(t578307,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = zero,
inference(step,[status(thm)],[t578306,t304]) ).
cnf(t575136,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = zero,
inference(orient,[status(thm)],[t578307]) ).
cnf(t575140,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(zero,zero,ifeq(join(a,join(sFlat0,complement(join(sFlat0,a)))),one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),join(sFlat0,complement(join(sFlat0,a)))),
inference(cp,[status(thm)],[t22,t575136]) ).
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(t578308,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(join(a,join(sFlat0,complement(join(sFlat0,a)))),one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t575140,t21]) ).
cnf(t36,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t30,t27]) ).
cnf(t576560,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t36,t30]) ).
cnf(t7138,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t576560]) ).
cnf(t307,plain,
meet(sFlat0,join(a,X1)) = meet(sFlat0,join(a,meet(join(sFlat0,a),join(X1,zero)))),
inference(cp,[status(thm)],[t51,t304]) ).
cnf(t577926,plain,
meet(sFlat0,join(a,X1)) = meet(sFlat0,join(a,meet(join(sFlat0,a),X1))),
inference(step,[status(thm)],[t307,t101]) ).
cnf(t345470,plain,
meet(sFlat0,join(a,meet(join(sFlat0,a),X1))) = meet(sFlat0,join(a,X1)),
inference(orient,[status(thm)],[t577926]) ).
cnf(t345488,plain,
meet(sFlat0,join(a,complement(join(a,sFlat0)))) = meet(sFlat0,join(a,zero)),
inference(cp,[status(thm)],[t345470,t6831]) ).
cnf(t577927,plain,
meet(sFlat0,join(a,complement(join(sFlat0,a)))) = meet(sFlat0,join(a,zero)),
inference(step,[status(thm)],[t345488,t27]) ).
cnf(t577928,plain,
meet(sFlat0,join(a,complement(join(sFlat0,a)))) = meet(sFlat0,a),
inference(step,[status(thm)],[t577927,t101]) ).
cnf(t577929,plain,
meet(sFlat0,join(a,complement(join(sFlat0,a)))) = zero,
inference(step,[status(thm)],[t577928,t304]) ).
cnf(t345787,plain,
meet(sFlat0,join(a,complement(join(sFlat0,a)))) = zero,
inference(orient,[status(thm)],[t577929]) ).
cnf(t345792,plain,
join(a,complement(join(sFlat0,a))) = ifeq(zero,zero,ifeq(join(sFlat0,join(a,complement(join(sFlat0,a)))),one,complement(sFlat0),join(a,complement(join(sFlat0,a)))),join(a,complement(join(sFlat0,a)))),
inference(cp,[status(thm)],[t22,t345787]) ).
cnf(t577930,plain,
join(a,complement(join(sFlat0,a))) = ifeq(join(sFlat0,join(a,complement(join(sFlat0,a)))),one,complement(sFlat0),join(a,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t345792,t21]) ).
cnf(t40,plain,
one = join(X1,join(X2,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t39,t30]) ).
cnf(t4888,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(orient,[status(thm)],[t40]) ).
cnf(t577931,plain,
join(a,complement(join(sFlat0,a))) = ifeq(one,one,complement(sFlat0),join(a,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t577930,t4888]) ).
cnf(t577932,plain,
join(a,complement(join(sFlat0,a))) = complement(sFlat0),
inference(step,[status(thm)],[t577931,t21]) ).
cnf(t94,plain,
one = join(b,sFlat0),
inference(cp,[status(thm)],[t39,t92]) ).
cnf(t576267,plain,
one = join(sFlat0,b),
inference(step,[status(thm)],[t94,t27]) ).
cnf(t124,plain,
join(sFlat0,b) = one,
inference(orient,[status(thm)],[t576267]) ).
cnf(t126,plain,
b = ifeq(meet(sFlat0,b),zero,ifeq(one,one,complement(sFlat0),b),b),
inference(cp,[status(thm)],[t22,t124]) ).
cnf(t576268,plain,
b = ifeq(zero,zero,ifeq(one,one,complement(sFlat0),b),b),
inference(step,[status(thm)],[t126,t120]) ).
cnf(t576269,plain,
b = ifeq(one,one,complement(sFlat0),b),
inference(step,[status(thm)],[t576268,t21]) ).
cnf(t576270,plain,
b = complement(sFlat0),
inference(step,[status(thm)],[t576269,t21]) ).
cnf(t128,plain,
complement(sFlat0) = b,
inference(orient,[status(thm)],[t576270]) ).
cnf(t577933,plain,
join(a,complement(join(sFlat0,a))) = b,
inference(step,[status(thm)],[t577932,t128]) ).
cnf(t345916,plain,
join(a,complement(join(sFlat0,a))) = b,
inference(orient,[status(thm)],[t577933]) ).
cnf(t346129,plain,
join(a,join(X1,complement(join(sFlat0,a)))) = join(X1,b),
inference(cp,[status(thm)],[t7138,t345916]) ).
cnf(t347587,plain,
join(a,join(X1,complement(join(sFlat0,a)))) = join(X1,b),
inference(orient,[status(thm)],[t346129]) ).
cnf(t578309,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(join(sFlat0,b),one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t578308,t347587]) ).
cnf(t578310,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(one,one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t578309,t124]) ).
cnf(t578311,plain,
join(sFlat0,complement(join(sFlat0,a))) = complement(a),
inference(step,[status(thm)],[t578310,t21]) ).
cnf(t578312,plain,
join(sFlat0,complement(join(sFlat0,a))) = sFlat1,
inference(step,[status(thm)],[t578311,t87]) ).
cnf(t575272,plain,
join(sFlat0,complement(join(sFlat0,a))) = sFlat1,
inference(orient,[status(thm)],[t578312]) ).
cnf(t575277,plain,
join(sFlat0,complement(join(sFlat0,a))) = join(sFlat0,sFlat1),
inference(cp,[status(thm)],[t226,t575272]) ).
cnf(t578314,plain,
sFlat1 = join(sFlat0,sFlat1),
inference(step,[status(thm)],[t575277,t575272]) ).
cnf(t578315,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t578314,t162]) ).
cnf(t575586,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t578315]) ).
cnf(t578316,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t162,t575586]) ).
cnf(t575587,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t578316]) ).
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,t92]) ).
cnf(g0_1,plain,
join(sFlat0,sFlat1) != complement(a),
inference(rw,[status(thm)],[g0_0,t87]) ).
cnf(g0_2,plain,
sFlat1 != complement(a),
inference(rw,[status(thm)],[g0_1,t575587]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t87]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT244-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 20:42:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 198.87/29.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 198.87/29.69 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------