%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT241-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 01:56:23 PM UTC 2026
% Result : Unsatisfiable 51.59s 7.93s
% Output : Proof 51.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 18
% Syntax : Number of formulae : 247 ( 243 unt; 0 def)
% Number of atoms : 255 ( 254 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 : 295 ( 37 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
sFlat0 = complement(b),
introduced(definition) ).
cnf(t94,plain,
complement(b) = sFlat0,
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
sFlat1 = complement(a),
introduced(definition) ).
cnf(t89,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(t65263,plain,
join(complement(b),sFlat1) = sFlat2,
inference(step,[status(thm)],[t85,t89]) ).
cnf(t93,plain,
join(complement(b),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t65263]) ).
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(t66,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t65274,plain,
join(sFlat1,complement(b)) = sFlat2,
inference(step,[status(thm)],[t93,t66]) ).
cnf(t65275,plain,
join(sFlat1,sFlat0) = sFlat2,
inference(step,[status(thm)],[t65274,t94]) ).
cnf(t65276,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t65275,t66]) ).
cnf(t160,plain,
join(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t65276]) ).
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(t68,plain,
X1 = ifeq(meet(X2,X1),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1),
inference(cp,[status(thm)],[t22,t66]) ).
cnf(t27996,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t68]) ).
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(t71,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t162,plain,
join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
inference(cp,[status(thm)],[t71,t160]) ).
cnf(t305,plain,
join(sFlat0,join(sFlat1,X1)) = join(sFlat2,X1),
inference(orient,[status(thm)],[t162]) ).
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(t81,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t90,plain,
one = join(a,sFlat1),
inference(cp,[status(thm)],[t81,t89]) ).
cnf(t65264,plain,
one = join(sFlat1,a),
inference(step,[status(thm)],[t90,t66]) ).
cnf(t111,plain,
join(sFlat1,a) = one,
inference(orient,[status(thm)],[t65264]) ).
cnf(t312,plain,
join(sFlat2,a) = join(sFlat0,one),
inference(cp,[status(thm)],[t305,t111]) ).
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(t83,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t18,t81]) ).
cnf(t105,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t83]) ).
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(t106,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t105,t27]) ).
cnf(t139,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t106]) ).
cnf(t141,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t139,t18]) ).
cnf(t152,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t141]) ).
cnf(t153,plain,
one = join(X1,one),
inference(cp,[status(thm)],[t152,t66]) ).
cnf(t158,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t153]) ).
cnf(t65294,plain,
join(sFlat2,a) = one,
inference(step,[status(thm)],[t312,t158]) ).
cnf(t326,plain,
join(sFlat2,a) = one,
inference(orient,[status(thm)],[t65294]) ).
cnf(t28485,plain,
sFlat2 = ifeq(meet(a,sFlat2),zero,ifeq(one,one,complement(a),sFlat2),sFlat2),
inference(cp,[status(thm)],[t27996,t326]) ).
cnf(t65885,plain,
sFlat2 = ifeq(meet(sFlat2,a),zero,ifeq(one,one,complement(a),sFlat2),sFlat2),
inference(step,[status(thm)],[t28485,t27]) ).
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(t65886,plain,
sFlat2 = ifeq(meet(sFlat2,a),zero,complement(a),sFlat2),
inference(step,[status(thm)],[t65885,t21]) ).
cnf(t65887,plain,
sFlat2 = ifeq(meet(sFlat2,a),zero,sFlat1,sFlat2),
inference(step,[status(thm)],[t65886,t89]) ).
cnf(t28602,plain,
ifeq(meet(sFlat2,a),zero,sFlat1,sFlat2) = sFlat2,
inference(orient,[status(thm)],[t65887]) ).
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(t53,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
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(t28,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t20,t27]) ).
cnf(t169,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t28]) ).
cnf(f11,axiom,
meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H51) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(X1,join(meet(X0,X2),meet(X2,X3)))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X3,X4)))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
meet(X1,join(X2,join(meet(X1,X3),meet(X3,X4)))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t13]) ).
cnf(t59,plain,
meet(X1,join(X2,meet(X3,join(X1,complement(X3))))) = meet(X1,join(X2,join(meet(X1,X3),zero))),
inference(cp,[status(thm)],[t39,t53]) ).
cnf(t56,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t20,t53]) ).
cnf(t98,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t56]) ).
cnf(t65753,plain,
meet(X1,join(X2,meet(X3,join(X1,complement(X3))))) = meet(X1,join(X2,meet(X1,X3))),
inference(step,[status(thm)],[t59,t98]) ).
cnf(t21540,plain,
meet(X1,join(X2,meet(X3,join(X1,complement(X3))))) = meet(X1,join(X2,meet(X1,X3))),
inference(orient,[status(thm)],[t65753]) ).
cnf(t91,plain,
zero = meet(a,sFlat1),
inference(cp,[status(thm)],[t53,t89]) ).
cnf(t65265,plain,
zero = meet(sFlat1,a),
inference(step,[status(thm)],[t91,t27]) ).
cnf(t114,plain,
meet(sFlat1,a) = zero,
inference(orient,[status(thm)],[t65265]) ).
cnf(t117,plain,
meet(sFlat1,join(X1,meet(a,join(sFlat1,X2)))) = meet(sFlat1,join(X1,join(zero,meet(a,X2)))),
inference(cp,[status(thm)],[t39,t114]) ).
cnf(t99,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t98,t66]) ).
cnf(t131,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t99]) ).
cnf(t66128,plain,
meet(sFlat1,join(X1,meet(a,join(sFlat1,X2)))) = meet(sFlat1,join(X1,meet(a,X2))),
inference(step,[status(thm)],[t117,t131]) ).
cnf(t64086,plain,
meet(sFlat1,join(X1,meet(a,join(sFlat1,X2)))) = meet(sFlat1,join(X1,meet(a,X2))),
inference(orient,[status(thm)],[t66128]) ).
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(t174,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t169,t30]) ).
cnf(t1422,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t174]) ).
cnf(t1428,plain,
join(X1,X2) = join(join(X1,X2),meet(X3,X1)),
inference(cp,[status(thm)],[t1422,t18]) ).
cnf(t65442,plain,
join(X1,X2) = join(X1,join(X2,meet(X3,X1))),
inference(step,[status(thm)],[t1428,t71]) ).
cnf(t3176,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(orient,[status(thm)],[t65442]) ).
cnf(t161,plain,
sFlat0 = meet(sFlat0,sFlat2),
inference(cp,[status(thm)],[t18,t160]) ).
cnf(t164,plain,
meet(sFlat0,sFlat2) = sFlat0,
inference(orient,[status(thm)],[t161]) ).
cnf(t165,plain,
meet(sFlat0,meet(sFlat2,X1)) = meet(sFlat0,X1),
inference(cp,[status(thm)],[t30,t164]) ).
cnf(t373,plain,
meet(sFlat0,meet(sFlat2,X1)) = meet(sFlat0,X1),
inference(orient,[status(thm)],[t165]) ).
cnf(t377,plain,
meet(sFlat2,X1) = join(meet(sFlat2,X1),meet(sFlat0,X1)),
inference(cp,[status(thm)],[t169,t373]) ).
cnf(t65440,plain,
meet(sFlat2,X1) = join(meet(sFlat0,X1),meet(sFlat2,X1)),
inference(step,[status(thm)],[t377,t66]) ).
cnf(t2639,plain,
join(meet(sFlat0,X1),meet(sFlat2,X1)) = meet(sFlat2,X1),
inference(orient,[status(thm)],[t65440]) ).
cnf(t67,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t18,t66]) ).
cnf(t181,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t67]) ).
cnf(t2650,plain,
meet(sFlat2,join(X1,sFlat0)) = join(sFlat0,meet(sFlat2,join(X1,sFlat0))),
inference(cp,[status(thm)],[t2639,t181]) ).
cnf(t17468,plain,
join(sFlat0,meet(sFlat2,join(X1,sFlat0))) = meet(sFlat2,join(X1,sFlat0)),
inference(orient,[status(thm)],[t2650]) ).
cnf(t17488,plain,
join(join(X1,sFlat0),sFlat0) = join(join(X1,sFlat0),meet(sFlat2,join(X1,sFlat0))),
inference(cp,[status(thm)],[t3176,t17468]) ).
cnf(t65679,plain,
join(X1,join(sFlat0,sFlat0)) = join(join(X1,sFlat0),meet(sFlat2,join(X1,sFlat0))),
inference(step,[status(thm)],[t17488,t71]) ).
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(t19,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t65680,plain,
join(X1,sFlat0) = join(join(X1,sFlat0),meet(sFlat2,join(X1,sFlat0))),
inference(step,[status(thm)],[t65679,t19]) ).
cnf(t65681,plain,
join(X1,sFlat0) = join(X1,join(sFlat0,meet(sFlat2,join(X1,sFlat0)))),
inference(step,[status(thm)],[t65680,t71]) ).
cnf(t65682,plain,
join(X1,sFlat0) = join(X1,meet(sFlat2,join(X1,sFlat0))),
inference(step,[status(thm)],[t65681,t17468]) ).
cnf(t17502,plain,
join(X1,meet(sFlat2,join(X1,sFlat0))) = join(X1,sFlat0),
inference(orient,[status(thm)],[t65682]) ).
cnf(t17513,plain,
join(X1,sFlat0) = join(X1,meet(sFlat2,join(sFlat0,X1))),
inference(cp,[status(thm)],[t17502,t66]) ).
cnf(t17585,plain,
join(X1,meet(sFlat2,join(sFlat0,X1))) = join(X1,sFlat0),
inference(orient,[status(thm)],[t17513]) ).
cnf(t64134,plain,
meet(sFlat1,join(X1,meet(a,meet(sFlat2,join(sFlat0,sFlat1))))) = meet(sFlat1,join(X1,meet(a,join(sFlat1,sFlat0)))),
inference(cp,[status(thm)],[t64086,t17585]) ).
cnf(t36,plain,
meet(X1,meet(X2,X3)) = meet(meet(X2,X1),X3),
inference(cp,[status(thm)],[t30,t27]) ).
cnf(t65451,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t36,t30]) ).
cnf(t3525,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t65451]) ).
cnf(t66129,plain,
meet(sFlat1,join(X1,meet(sFlat2,meet(a,join(sFlat0,sFlat1))))) = meet(sFlat1,join(X1,meet(a,join(sFlat1,sFlat0)))),
inference(step,[status(thm)],[t64134,t3525]) ).
cnf(t66130,plain,
meet(sFlat1,join(X1,meet(sFlat2,meet(a,sFlat2)))) = meet(sFlat1,join(X1,meet(a,join(sFlat1,sFlat0)))),
inference(step,[status(thm)],[t66129,t160]) ).
cnf(t66131,plain,
meet(sFlat1,join(X1,meet(sFlat2,meet(sFlat2,a)))) = meet(sFlat1,join(X1,meet(a,join(sFlat1,sFlat0)))),
inference(step,[status(thm)],[t66130,t27]) ).
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(t202,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t34]) ).
cnf(t66132,plain,
meet(sFlat1,join(X1,meet(sFlat2,a))) = meet(sFlat1,join(X1,meet(a,join(sFlat1,sFlat0)))),
inference(step,[status(thm)],[t66131,t202]) ).
cnf(t66133,plain,
meet(sFlat1,join(X1,meet(sFlat2,a))) = meet(sFlat1,join(X1,meet(a,sFlat0))),
inference(step,[status(thm)],[t66132,t64086]) ).
cnf(t66134,plain,
meet(sFlat1,join(X1,meet(sFlat2,a))) = meet(sFlat1,join(X1,meet(sFlat0,a))),
inference(step,[status(thm)],[t66133,t27]) ).
cnf(t96,plain,
zero = meet(b,sFlat0),
inference(cp,[status(thm)],[t53,t94]) ).
cnf(t65270,plain,
zero = meet(sFlat0,b),
inference(step,[status(thm)],[t96,t27]) ).
cnf(t124,plain,
meet(sFlat0,b) = zero,
inference(orient,[status(thm)],[t65270]) ).
cnf(t125,plain,
meet(sFlat0,meet(b,X1)) = meet(zero,X1),
inference(cp,[status(thm)],[t30,t124]) ).
cnf(t133,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t131,t20]) ).
cnf(t148,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t133]) ).
cnf(t65293,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(step,[status(thm)],[t125,t148]) ).
cnf(t276,plain,
meet(sFlat0,meet(b,X1)) = zero,
inference(orient,[status(thm)],[t65293]) ).
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(t60,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t277,plain,
zero = meet(sFlat0,a),
inference(cp,[status(thm)],[t276,t60]) ).
cnf(t283,plain,
meet(sFlat0,a) = zero,
inference(orient,[status(thm)],[t277]) ).
cnf(t66135,plain,
meet(sFlat1,join(X1,meet(sFlat2,a))) = meet(sFlat1,join(X1,zero)),
inference(step,[status(thm)],[t66134,t283]) ).
cnf(t66136,plain,
meet(sFlat1,join(X1,meet(sFlat2,a))) = meet(sFlat1,X1),
inference(step,[status(thm)],[t66135,t98]) ).
cnf(t64252,plain,
meet(sFlat1,join(X1,meet(sFlat2,a))) = meet(sFlat1,X1),
inference(orient,[status(thm)],[t66136]) ).
cnf(t64254,plain,
meet(sFlat1,X1) = meet(sFlat1,join(meet(sFlat2,a),X1)),
inference(cp,[status(thm)],[t64252,t66]) ).
cnf(t64337,plain,
meet(sFlat1,join(meet(sFlat2,a),X1)) = meet(sFlat1,X1),
inference(orient,[status(thm)],[t64254]) ).
cnf(t171,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t169,t18]) ).
cnf(t65302,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t171,t71]) ).
cnf(t386,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t65302]) ).
cnf(t84,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t71,t81]) ).
cnf(t65379,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t84,t152]) ).
cnf(t1212,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t65379]) ).
cnf(t1215,plain,
join(join(complement(X1),X2),X1) = join(join(complement(X1),X2),one),
inference(cp,[status(thm)],[t386,t1212]) ).
cnf(t65380,plain,
join(complement(X1),join(X2,X1)) = join(join(complement(X1),X2),one),
inference(step,[status(thm)],[t1215,t71]) ).
cnf(t65381,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),join(X2,one)),
inference(step,[status(thm)],[t65380,t71]) ).
cnf(t65382,plain,
join(complement(X1),join(X2,X1)) = join(complement(X1),one),
inference(step,[status(thm)],[t65381,t158]) ).
cnf(t65383,plain,
join(complement(X1),join(X2,X1)) = one,
inference(step,[status(thm)],[t65382,t158]) ).
cnf(t1284,plain,
join(complement(X1),join(X2,X1)) = one,
inference(orient,[status(thm)],[t65383]) ).
cnf(t2656,plain,
meet(sFlat2,X1) = join(meet(sFlat0,X1),meet(X1,sFlat2)),
inference(cp,[status(thm)],[t2639,t27]) ).
cnf(t4097,plain,
join(meet(sFlat0,X1),meet(X1,sFlat2)) = meet(sFlat2,X1),
inference(orient,[status(thm)],[t2656]) ).
cnf(t4148,plain,
one = join(complement(meet(X1,sFlat2)),meet(sFlat2,X1)),
inference(cp,[status(thm)],[t1284,t4097]) ).
cnf(t65569,plain,
one = join(meet(sFlat2,X1),complement(meet(X1,sFlat2))),
inference(step,[status(thm)],[t4148,t66]) ).
cnf(t8945,plain,
join(meet(sFlat2,X1),complement(meet(X1,sFlat2))) = one,
inference(orient,[status(thm)],[t65569]) ).
cnf(t64341,plain,
meet(sFlat1,complement(meet(a,sFlat2))) = meet(sFlat1,one),
inference(cp,[status(thm)],[t64337,t8945]) ).
cnf(t66137,plain,
meet(sFlat1,complement(meet(sFlat2,a))) = meet(sFlat1,one),
inference(step,[status(thm)],[t64341,t27]) ).
cnf(t66138,plain,
meet(sFlat1,complement(meet(sFlat2,a))) = sFlat1,
inference(step,[status(thm)],[t66137,t105]) ).
cnf(t64452,plain,
meet(sFlat1,complement(meet(sFlat2,a))) = sFlat1,
inference(orient,[status(thm)],[t66138]) ).
cnf(t64459,plain,
complement(meet(sFlat2,a)) = join(complement(meet(sFlat2,a)),sFlat1),
inference(cp,[status(thm)],[t169,t64452]) ).
cnf(t66139,plain,
complement(meet(sFlat2,a)) = join(sFlat1,complement(meet(sFlat2,a))),
inference(step,[status(thm)],[t64459,t66]) ).
cnf(t64525,plain,
join(sFlat1,complement(meet(sFlat2,a))) = complement(meet(sFlat2,a)),
inference(orient,[status(thm)],[t66139]) ).
cnf(t64528,plain,
join(sFlat2,complement(meet(sFlat2,a))) = join(sFlat0,complement(meet(sFlat2,a))),
inference(cp,[status(thm)],[t305,t64525]) ).
cnf(t1289,plain,
one = join(complement(meet(X1,X2)),X1),
inference(cp,[status(thm)],[t1284,t20]) ).
cnf(t65384,plain,
one = join(X1,complement(meet(X1,X2))),
inference(step,[status(thm)],[t1289,t66]) ).
cnf(t1321,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(orient,[status(thm)],[t65384]) ).
cnf(t66140,plain,
one = join(sFlat0,complement(meet(sFlat2,a))),
inference(step,[status(thm)],[t64528,t1321]) ).
cnf(t64573,plain,
join(sFlat0,complement(meet(sFlat2,a))) = one,
inference(orient,[status(thm)],[t66140]) ).
cnf(t64599,plain,
meet(sFlat0,join(X1,meet(sFlat0,meet(sFlat2,a)))) = meet(sFlat0,join(X1,meet(meet(sFlat2,a),one))),
inference(cp,[status(thm)],[t21540,t64573]) ).
cnf(t66141,plain,
meet(sFlat0,join(X1,meet(sFlat0,a))) = meet(sFlat0,join(X1,meet(meet(sFlat2,a),one))),
inference(step,[status(thm)],[t64599,t373]) ).
cnf(t66142,plain,
meet(sFlat0,join(X1,zero)) = meet(sFlat0,join(X1,meet(meet(sFlat2,a),one))),
inference(step,[status(thm)],[t66141,t283]) ).
cnf(t66143,plain,
meet(sFlat0,X1) = meet(sFlat0,join(X1,meet(meet(sFlat2,a),one))),
inference(step,[status(thm)],[t66142,t98]) ).
cnf(t66144,plain,
meet(sFlat0,X1) = meet(sFlat0,join(X1,meet(sFlat2,meet(a,one)))),
inference(step,[status(thm)],[t66143,t30]) ).
cnf(t66145,plain,
meet(sFlat0,X1) = meet(sFlat0,join(X1,meet(sFlat2,a))),
inference(step,[status(thm)],[t66144,t105]) ).
cnf(t64656,plain,
meet(sFlat0,join(X1,meet(sFlat2,a))) = meet(sFlat0,X1),
inference(orient,[status(thm)],[t66145]) ).
cnf(t64658,plain,
meet(sFlat0,X1) = meet(sFlat0,join(meet(sFlat2,a),X1)),
inference(cp,[status(thm)],[t64656,t66]) ).
cnf(t64739,plain,
meet(sFlat0,join(meet(sFlat2,a),X1)) = meet(sFlat0,X1),
inference(orient,[status(thm)],[t64658]) ).
cnf(t64743,plain,
meet(sFlat0,complement(meet(a,sFlat2))) = meet(sFlat0,one),
inference(cp,[status(thm)],[t64739,t8945]) ).
cnf(t66146,plain,
meet(sFlat0,complement(meet(sFlat2,a))) = meet(sFlat0,one),
inference(step,[status(thm)],[t64743,t27]) ).
cnf(t66147,plain,
meet(sFlat0,complement(meet(sFlat2,a))) = sFlat0,
inference(step,[status(thm)],[t66146,t105]) ).
cnf(t64851,plain,
meet(sFlat0,complement(meet(sFlat2,a))) = sFlat0,
inference(orient,[status(thm)],[t66147]) ).
cnf(t64858,plain,
complement(meet(sFlat2,a)) = join(complement(meet(sFlat2,a)),sFlat0),
inference(cp,[status(thm)],[t169,t64851]) ).
cnf(t66148,plain,
complement(meet(sFlat2,a)) = join(sFlat0,complement(meet(sFlat2,a))),
inference(step,[status(thm)],[t64858,t66]) ).
cnf(t66149,plain,
complement(meet(sFlat2,a)) = one,
inference(step,[status(thm)],[t66148,t64573]) ).
cnf(t64926,plain,
complement(meet(sFlat2,a)) = one,
inference(orient,[status(thm)],[t66149]) ).
cnf(t64929,plain,
zero = meet(meet(sFlat2,a),one),
inference(cp,[status(thm)],[t53,t64926]) ).
cnf(t66150,plain,
zero = meet(sFlat2,meet(a,one)),
inference(step,[status(thm)],[t64929,t30]) ).
cnf(t66151,plain,
zero = meet(sFlat2,a),
inference(step,[status(thm)],[t66150,t105]) ).
cnf(t64946,plain,
meet(sFlat2,a) = zero,
inference(orient,[status(thm)],[t66151]) ).
cnf(t66164,plain,
ifeq(zero,zero,sFlat1,sFlat2) = sFlat2,
inference(step,[status(thm)],[t28602,t64946]) ).
cnf(t66165,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t66164,t21]) ).
cnf(t65036,plain,
sFlat1 = sFlat2,
inference(rw,[status(thm)],[t66165]) ).
cnf(t65038,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t65036]) ).
cnf(t66168,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t160,t65038]) ).
cnf(t65039,plain,
join(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t66168]) ).
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,t94]) ).
cnf(g0_1,plain,
join(sFlat0,sFlat1) != complement(a),
inference(rw,[status(thm)],[g0_0,t89]) ).
cnf(g0_2,plain,
sFlat1 != complement(a),
inference(rw,[status(thm)],[g0_1,t65039]) ).
cnf(g0_3,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_2,t89]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT241-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.40 % Computer : n001.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Wed Sep 23 20:45:51 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 51.59/7.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.59/7.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------