%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT248-1 : 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 01:56:24 PM UTC 2026
% Result : Unsatisfiable 81.75s 12.61s
% Output : Proof 81.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 18
% Syntax : Number of formulae : 200 ( 196 unt; 0 def)
% Number of atoms : 208 ( 207 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 : 285 ( 42 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
sFlat0 = complement(b),
introduced(definition) ).
cnf(t96,plain,
complement(b) = sFlat0,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sFlat1 = complement(a),
introduced(definition) ).
cnf(t91,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(t197106,plain,
join(complement(b),sFlat1) = sFlat2,
inference(step,[status(thm)],[t44,t91]) ).
cnf(t95,plain,
join(complement(b),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t197106]) ).
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(t197117,plain,
join(sFlat1,complement(b)) = sFlat2,
inference(step,[status(thm)],[t95,t27]) ).
cnf(t197118,plain,
join(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t197117,t96]) ).
cnf(t197119,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t197118,t27]) ).
cnf(t163,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t197119]) ).
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(t206,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(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(t70,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(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(t172,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t28]) ).
cnf(t179,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t70,t172]) ).
cnf(t2198,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t179]) ).
cnf(f11,axiom,
meet(X,meet(join(Y,Z),join(Y,U))) = meet(X,join(Y,meet(join(Y,Z),join(U,meet(Y,Z))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H63) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,meet(join(Y,Z),join(Y,U))) = meet(X,join(Y,meet(join(Y,Z),join(U,meet(Y,Z))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z,U] : meet(X,meet(join(Y,Z),join(Y,U))) = meet(X,join(Y,meet(join(Y,Z),join(U,meet(Y,Z))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,meet(join(X1,X2),join(X1,X3))) = meet(X0,join(X1,meet(join(X1,X2),join(X3,meet(X1,X2))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,meet(join(X2,X3),join(X4,meet(X2,X3))))) = meet(X1,meet(join(X2,X3),join(X2,X4))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t51,plain,
meet(X1,join(X2,meet(join(X2,X3),join(X4,meet(X2,X3))))) = meet(X1,meet(join(X2,X3),join(X2,X4))),
inference(orient,[status(thm)],[t13]) ).
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(t19,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t53,plain,
meet(join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))),meet(join(X1,X2),join(X1,X3))) = join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))),
inference(cp,[status(thm)],[t51,t19]) ).
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(t197596,plain,
meet(meet(join(X1,X2),join(X1,X3)),join(X1,meet(join(X1,X2),join(X3,meet(X1,X2))))) = join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t53,t48]) ).
cnf(t197597,plain,
meet(join(X1,X2),meet(join(X1,X3),join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))))) = join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t197596,t70]) ).
cnf(t197598,plain,
meet(join(X1,X2),meet(join(X1,X3),meet(join(X1,X2),join(X1,X3)))) = join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t197597,t51]) ).
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(t175,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t172,t18]) ).
cnf(t197145,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t175,t70]) ).
cnf(t395,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t197145]) ).
cnf(t197599,plain,
meet(join(X1,X2),meet(join(X1,X3),join(X1,X2))) = join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t197598,t395]) ).
cnf(t197600,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t197599,t395]) ).
cnf(t18424,plain,
join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))) = meet(join(X1,X2),join(X1,X3)),
inference(orient,[status(thm)],[t197600]) ).
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(t81,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t97,plain,
zero = meet(b,sFlat0),
inference(cp,[status(thm)],[t81,t96]) ).
cnf(t197112,plain,
zero = meet(sFlat0,b),
inference(step,[status(thm)],[t97,t48]) ).
cnf(t122,plain,
meet(sFlat0,b) = zero,
inference(orient,[status(thm)],[t197112]) ).
cnf(t123,plain,
meet(sFlat0,meet(b,X1)) = meet(zero,X1),
inference(cp,[status(thm)],[t70,t122]) ).
cnf(t83,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t18,t81]) ).
cnf(t105,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t83]) ).
cnf(t106,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t105,t27]) ).
cnf(t141,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t106]) ).
cnf(t143,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t141,t18]) ).
cnf(t155,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t143]) ).
cnf(t197135,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(step,[status(thm)],[t123,t155]) ).
cnf(t276,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(orient,[status(thm)],[t197135]) ).
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(t86,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t277,plain,
zero = meet(sFlat0,a),
inference(cp,[status(thm)],[t276,t86]) ).
cnf(t282,plain,
meet(sFlat0,a) = zero,
inference(orient,[status(thm)],[t277]) ).
cnf(t18754,plain,
meet(join(sFlat0,a),join(sFlat0,X1)) = join(sFlat0,meet(join(sFlat0,a),join(X1,zero))),
inference(cp,[status(thm)],[t18424,t282]) ).
cnf(t197687,plain,
meet(join(sFlat0,a),join(sFlat0,X1)) = join(sFlat0,meet(join(sFlat0,a),X1)),
inference(step,[status(thm)],[t18754,t105]) ).
cnf(t26141,plain,
join(sFlat0,meet(join(sFlat0,a),X1)) = meet(join(sFlat0,a),join(sFlat0,X1)),
inference(orient,[status(thm)],[t197687]) ).
cnf(t84,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t70,t81]) ).
cnf(t197239,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t84,t155]) ).
cnf(t1215,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t197239]) ).
cnf(t1219,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t395,t1215]) ).
cnf(t197241,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t1219,t70]) ).
cnf(t197242,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t197241,t70]) ).
cnf(t156,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t155,t48]) ).
cnf(t161,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t156]) ).
cnf(t197243,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t197242,t161]) ).
cnf(t197244,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t197243,t161]) ).
cnf(t1295,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t197244]) ).
cnf(t1302,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t1295,t172]) ).
cnf(t197246,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t1302,t48]) ).
cnf(t1344,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t197246]) ).
cnf(t49,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t18,t48]) ).
cnf(t186,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t49]) ).
cnf(t188,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t186,t20]) ).
cnf(t197161,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t188,t30]) ).
cnf(t507,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t197161]) ).
cnf(t1346,plain,
zero = meet(join(X1,X2),complement(join(X2,X1))),
inference(cp,[status(thm)],[t1344,t507]) ).
cnf(t6818,plain,
meet(join(X1,X2),complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t1346]) ).
cnf(t26151,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(a,sFlat0)))) = join(sFlat0,zero),
inference(cp,[status(thm)],[t26141,t6818]) ).
cnf(t198426,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(sFlat0,a)))) = join(sFlat0,zero),
inference(step,[status(thm)],[t26151,t27]) ).
cnf(t198427,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(sFlat0,a)))) = sFlat0,
inference(step,[status(thm)],[t198426,t105]) ).
cnf(t196287,plain,
meet(join(sFlat0,a),join(sFlat0,complement(join(sFlat0,a)))) = sFlat0,
inference(orient,[status(thm)],[t198427]) ).
cnf(t196340,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = meet(a,sFlat0),
inference(cp,[status(thm)],[t2198,t196287]) ).
cnf(t198428,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = meet(sFlat0,a),
inference(step,[status(thm)],[t196340,t48]) ).
cnf(t198429,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = zero,
inference(step,[status(thm)],[t198428,t282]) ).
cnf(t196398,plain,
meet(a,join(sFlat0,complement(join(sFlat0,a)))) = zero,
inference(orient,[status(thm)],[t198429]) ).
cnf(t196402,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,t196398]) ).
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(t198432,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)],[t196402,t21]) ).
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(t41,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t30,t39]) ).
cnf(t42,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t20,t39]) ).
cnf(t100,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t42]) ).
cnf(t101,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t100,t48]) ).
cnf(t132,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t101]) ).
cnf(t134,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t132,t20]) ).
cnf(t151,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t134]) ).
cnf(t197226,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t41,t151]) ).
cnf(t1067,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t197226]) ).
cnf(t1070,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t507,t1067]) ).
cnf(t197227,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t1070,t30]) ).
cnf(t197228,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t197227,t30]) ).
cnf(t152,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t151,t27]) ).
cnf(t158,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t152]) ).
cnf(t197229,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t197228,t158]) ).
cnf(t197230,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t197229,t158]) ).
cnf(t1080,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t197230]) ).
cnf(t1086,plain,
one = join(complement(meet(X1,X2)),X2),
inference(cp,[status(thm)],[t1080,t186]) ).
cnf(t197232,plain,
one = join(X2,complement(meet(X1,X2))),
inference(step,[status(thm)],[t1086,t27]) ).
cnf(t1132,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(orient,[status(thm)],[t197232]) ).
cnf(t533,plain,
join(X1,X2) = meet(join(X1,X2),join(X2,X1)),
inference(cp,[status(thm)],[t172,t507]) ).
cnf(t2830,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t533]) ).
cnf(t2915,plain,
one = join(join(X1,X2),complement(join(X2,X1))),
inference(cp,[status(thm)],[t1132,t2830]) ).
cnf(t197431,plain,
one = join(X1,join(X2,complement(join(X2,X1)))),
inference(step,[status(thm)],[t2915,t30]) ).
cnf(t8436,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(orient,[status(thm)],[t197431]) ).
cnf(t198433,plain,
join(sFlat0,complement(join(sFlat0,a))) = ifeq(one,one,complement(a),join(sFlat0,complement(join(sFlat0,a)))),
inference(step,[status(thm)],[t198432,t8436]) ).
cnf(t198434,plain,
join(sFlat0,complement(join(sFlat0,a))) = complement(a),
inference(step,[status(thm)],[t198433,t21]) ).
cnf(t198435,plain,
join(sFlat0,complement(join(sFlat0,a))) = sFlat1,
inference(step,[status(thm)],[t198434,t91]) ).
cnf(t196466,plain,
join(sFlat0,complement(join(sFlat0,a))) = sFlat1,
inference(orient,[status(thm)],[t198435]) ).
cnf(t196471,plain,
join(sFlat0,complement(join(sFlat0,a))) = join(sFlat0,sFlat1),
inference(cp,[status(thm)],[t206,t196466]) ).
cnf(t198438,plain,
sFlat1 = join(sFlat0,sFlat1),
inference(step,[status(thm)],[t196471,t196466]) ).
cnf(t198439,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t198438,t163]) ).
cnf(t196677,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t198439]) ).
cnf(t198440,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t163,t196677]) ).
cnf(t196678,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t198440]) ).
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,t96]) ).
cnf(g0_1,plain,
join(sFlat0,sFlat1) != complement(a),
inference(rw,[status(thm)],[g0_0,t91]) ).
cnf(g0_2,plain,
sFlat1 != complement(a),
inference(rw,[status(thm)],[g0_1,t196678]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t91]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT248-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 20:41:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 81.75/12.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.75/12.61 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------