%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT243-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 225.31s 33.57s
% Output : Proof 225.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 14
% Syntax : Number of formulae : 202 ( 198 unt; 0 def)
% Number of atoms : 210 ( 209 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 384 ( 73 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t64,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/sandbox/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(t16,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t68,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t64,t16]) ).
cnf(t169,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t68]) ).
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(t19,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,meet(X,join(Y,Z)))) = meet(X,join(Y,meet(join(X,Y),join(Z,meet(X,Y))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H57) ).
fof(f11_nnf,plain,
! [X,Y,Z] : meet(X,join(Y,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,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,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,meet(X1,join(X2,X3)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t36,plain,
meet(X1,join(X2,meet(join(X1,X2),join(X3,meet(X1,X2))))) = meet(X1,join(X2,meet(X1,join(X2,X3)))),
inference(orient,[status(thm)],[t13]) ).
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(t15,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
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(t59,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t60,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t15,t59]) ).
cnf(t134,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t60]) ).
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(t17,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
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(t27,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
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(t54,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t55,plain,
meet(b,meet(a,X1)) = meet(a,X1),
inference(cp,[status(thm)],[t27,t54]) ).
cnf(t150,plain,
meet(b,meet(a,X1)) = meet(a,X1),
inference(orient,[status(thm)],[t55]) ).
cnf(t152,plain,
b = join(b,meet(a,X1)),
inference(cp,[status(thm)],[t17,t150]) ).
cnf(t155,plain,
join(b,meet(a,X1)) = b,
inference(orient,[status(thm)],[t152]) ).
cnf(t157,plain,
meet(a,X1) = meet(meet(a,X1),b),
inference(cp,[status(thm)],[t134,t155]) ).
cnf(t659314,plain,
meet(a,X1) = meet(a,meet(X1,b)),
inference(step,[status(thm)],[t157,t27]) ).
cnf(t215,plain,
meet(a,meet(X1,b)) = meet(a,X1),
inference(orient,[status(thm)],[t659314]) ).
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(t24,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t219,plain,
meet(a,X1) = meet(a,meet(b,X1)),
inference(cp,[status(thm)],[t215,t24]) ).
cnf(t231,plain,
meet(a,meet(b,X1)) = meet(a,X1),
inference(orient,[status(thm)],[t219]) ).
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(t48,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t234,plain,
meet(a,complement(b)) = meet(a,zero),
inference(cp,[status(thm)],[t231,t48]) ).
cnf(t51,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t48]) ).
cnf(t81,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t51]) ).
cnf(t82,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t81,t59]) ).
cnf(t95,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t82]) ).
cnf(t97,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t95,t17]) ).
cnf(t114,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t97]) ).
cnf(t115,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t114,t24]) ).
cnf(t122,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t115]) ).
cnf(t659315,plain,
meet(a,complement(b)) = zero,
inference(step,[status(thm)],[t234,t122]) ).
cnf(t241,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t659315]) ).
cnf(t245,plain,
meet(a,join(complement(b),meet(a,join(complement(b),X1)))) = meet(a,join(complement(b),meet(join(a,complement(b)),join(X1,zero)))),
inference(cp,[status(thm)],[t36,t241]) ).
cnf(t29,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t7252,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t29]) ).
cnf(t33,plain,
meet(X1,meet(X2,X3)) = meet(meet(X2,X1),X3),
inference(cp,[status(thm)],[t27,t24]) ).
cnf(t659458,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t33,t27]) ).
cnf(t6097,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t659458]) ).
cnf(t7254,plain,
meet(X1,X2) = meet(X2,meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t7252,t6097]) ).
cnf(t13459,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t7254]) ).
cnf(t69,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t64,t17]) ).
cnf(t619,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t69]) ).
cnf(t635,plain,
join(meet(X1,X2),X3) = meet(join(meet(X1,X2),X3),join(X1,X3)),
inference(cp,[status(thm)],[t134,t619]) ).
cnf(t659844,plain,
join(meet(X1,X2),X3) = meet(join(X1,X3),join(meet(X1,X2),X3)),
inference(step,[status(thm)],[t635,t24]) ).
cnf(t84143,plain,
meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2),
inference(orient,[status(thm)],[t659844]) ).
cnf(t84169,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))),
inference(cp,[status(thm)],[t84143,t17]) ).
cnf(t222156,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(orient,[status(thm)],[t84169]) ).
cnf(t222759,plain,
meet(X1,X2) = meet(X2,join(meet(X1,X2),meet(X1,X3))),
inference(cp,[status(thm)],[t13459,t222156]) ).
cnf(t223418,plain,
meet(X1,join(meet(X2,X1),meet(X2,X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t222759]) ).
cnf(t223882,plain,
meet(X1,X2) = meet(X2,join(meet(X2,X1),meet(X1,X3))),
inference(cp,[status(thm)],[t223418,t24]) ).
cnf(t228651,plain,
meet(X1,join(meet(X1,X2),meet(X2,X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t223882]) ).
cnf(t25,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t17,t24]) ).
cnf(t126,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t129,plain,
join(X1,meet(join(X2,X1),join(X3,meet(X2,X1)))) = join(join(X1,meet(join(X2,X1),join(X3,meet(X2,X1)))),meet(X2,join(X1,meet(X2,join(X1,X3))))),
inference(cp,[status(thm)],[t126,t36]) ).
cnf(t660061,plain,
join(X1,meet(join(X2,X1),join(X3,meet(X2,X1)))) = join(X1,join(meet(join(X2,X1),join(X3,meet(X2,X1))),meet(X2,join(X1,meet(X2,join(X1,X3)))))),
inference(step,[status(thm)],[t129,t64]) ).
cnf(t660062,plain,
join(X1,meet(join(X2,X1),join(X3,meet(X2,X1)))) = join(X1,join(meet(X2,join(X1,meet(X2,join(X1,X3)))),meet(join(X2,X1),join(X3,meet(X2,X1))))),
inference(step,[status(thm)],[t660061,t59]) ).
cnf(t183874,plain,
join(X1,join(meet(X2,join(X1,meet(X2,join(X1,X3)))),meet(join(X2,X1),join(X3,meet(X2,X1))))) = join(X1,meet(join(X2,X1),join(X3,meet(X2,X1)))),
inference(orient,[status(thm)],[t660062]) ).
cnf(t138,plain,
X1 = meet(X1,join(X2,join(X3,X1))),
inference(cp,[status(thm)],[t134,t64]) ).
cnf(t508,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(orient,[status(thm)],[t138]) ).
cnf(t511,plain,
X1 = meet(X1,join(join(X2,X1),X3)),
inference(cp,[status(thm)],[t508,t59]) ).
cnf(t659352,plain,
X1 = meet(X1,join(X2,join(X1,X3))),
inference(step,[status(thm)],[t511,t64]) ).
cnf(t567,plain,
meet(X1,join(X2,join(X1,X3))) = X1,
inference(orient,[status(thm)],[t659352]) ).
cnf(t183962,plain,
join(X1,meet(join(X2,X1),join(join(X2,X3),meet(X2,X1)))) = join(X1,join(meet(X2,join(X1,X2)),meet(join(X2,X1),join(join(X2,X3),meet(X2,X1))))),
inference(cp,[status(thm)],[t183874,t567]) ).
cnf(t660067,plain,
join(X1,meet(join(X2,X1),join(X2,join(X3,meet(X2,X1))))) = join(X1,join(meet(X2,join(X1,X2)),meet(join(X2,X1),join(join(X2,X3),meet(X2,X1))))),
inference(step,[status(thm)],[t183962,t64]) ).
cnf(t130,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t126,t27]) ).
cnf(t486,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t130]) ).
cnf(t489,plain,
X1 = join(X1,meet(meet(X2,X1),X3)),
inference(cp,[status(thm)],[t486,t24]) ).
cnf(t659351,plain,
X1 = join(X1,meet(X2,meet(X1,X3))),
inference(step,[status(thm)],[t489,t27]) ).
cnf(t551,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(orient,[status(thm)],[t659351]) ).
cnf(t32,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t597,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t32]) ).
cnf(t615,plain,
join(X1,X2) = join(join(X1,X2),meet(X1,X3)),
inference(cp,[status(thm)],[t551,t597]) ).
cnf(t659362,plain,
join(X1,X2) = join(X1,join(X2,meet(X1,X3))),
inference(step,[status(thm)],[t615,t64]) ).
cnf(t1179,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(orient,[status(thm)],[t659362]) ).
cnf(t660068,plain,
join(X1,meet(join(X2,X1),join(X2,X3))) = join(X1,join(meet(X2,join(X1,X2)),meet(join(X2,X1),join(join(X2,X3),meet(X2,X1))))),
inference(step,[status(thm)],[t660067,t1179]) ).
cnf(t660069,plain,
join(X1,meet(join(X2,X1),join(X2,X3))) = join(X1,join(X2,meet(join(X2,X1),join(join(X2,X3),meet(X2,X1))))),
inference(step,[status(thm)],[t660068,t134]) ).
cnf(t66,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(cp,[status(thm)],[t64,t17]) ).
cnf(t7468,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(orient,[status(thm)],[t66]) ).
cnf(t70,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t64,t59]) ).
cnf(t659459,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t70,t64]) ).
cnf(t6671,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t659459]) ).
cnf(t7470,plain,
join(X1,X2) = join(X2,join(X1,meet(join(X1,X2),X3))),
inference(cp,[status(thm)],[t7468,t6671]) ).
cnf(t13890,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(orient,[status(thm)],[t7470]) ).
cnf(t660070,plain,
join(X1,meet(join(X2,X1),join(X2,X3))) = join(X2,X1),
inference(step,[status(thm)],[t660069,t13890]) ).
cnf(t187056,plain,
join(X1,meet(join(X2,X1),join(X2,X3))) = join(X2,X1),
inference(orient,[status(thm)],[t660070]) ).
cnf(t187138,plain,
join(X1,X2) = join(X2,meet(join(X1,X3),join(X1,X2))),
inference(cp,[status(thm)],[t187056,t24]) ).
cnf(t191073,plain,
join(X1,meet(join(X2,X3),join(X2,X1))) = join(X2,X1),
inference(orient,[status(thm)],[t187138]) ).
cnf(t191911,plain,
join(X1,X2) = join(X2,meet(join(X1,X3),join(X2,X1))),
inference(cp,[status(thm)],[t191073,t59]) ).
cnf(t195754,plain,
join(X1,meet(join(X2,X3),join(X1,X2))) = join(X2,X1),
inference(orient,[status(thm)],[t191911]) ).
cnf(t228718,plain,
meet(join(X1,X2),X3) = meet(X3,join(X1,meet(X3,join(X1,X2)))),
inference(cp,[status(thm)],[t228651,t195754]) ).
cnf(t240760,plain,
meet(X1,join(X2,meet(X1,join(X2,X3)))) = meet(join(X2,X3),X1),
inference(orient,[status(thm)],[t228718]) ).
cnf(t660543,plain,
meet(join(complement(b),X1),a) = meet(a,join(complement(b),meet(join(a,complement(b)),join(X1,zero)))),
inference(step,[status(thm)],[t245,t240760]) ).
cnf(t660544,plain,
meet(a,join(complement(b),X1)) = meet(a,join(complement(b),meet(join(a,complement(b)),join(X1,zero)))),
inference(step,[status(thm)],[t660543,t24]) ).
cnf(t660545,plain,
meet(a,join(complement(b),X1)) = meet(a,join(complement(b),meet(join(a,complement(b)),X1))),
inference(step,[status(thm)],[t660544,t81]) ).
cnf(t657426,plain,
meet(a,join(complement(b),meet(join(a,complement(b)),X1))) = meet(a,join(complement(b),X1)),
inference(orient,[status(thm)],[t660545]) ).
cnf(t136,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t134,t17]) ).
cnf(t659313,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t136,t27]) ).
cnf(t194,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t659313]) ).
cnf(t50,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t27,t48]) ).
cnf(t659333,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t50,t114]) ).
cnf(t329,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t659333]) ).
cnf(t332,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t194,t329]) ).
cnf(t659334,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t332,t27]) ).
cnf(t659335,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t659334,t27]) ).
cnf(t659336,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t659335,t122]) ).
cnf(t659337,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t659336,t122]) ).
cnf(t342,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t659337]) ).
cnf(t349,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t342,t134]) ).
cnf(t659339,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t349,t24]) ).
cnf(t372,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t659339]) ).
cnf(t128,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t126,t15]) ).
cnf(t659312,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t128,t64]) ).
cnf(t184,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t659312]) ).
cnf(t374,plain,
zero = meet(join(X1,X2),complement(join(X2,X1))),
inference(cp,[status(thm)],[t372,t184]) ).
cnf(t1794,plain,
meet(join(X1,X2),complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t374]) ).
cnf(t657456,plain,
meet(a,join(complement(b),complement(join(complement(b),a)))) = meet(a,join(complement(b),zero)),
inference(cp,[status(thm)],[t657426,t1794]) ).
cnf(t660546,plain,
meet(a,join(complement(b),complement(join(a,complement(b))))) = meet(a,join(complement(b),zero)),
inference(step,[status(thm)],[t657456,t59]) ).
cnf(t660547,plain,
meet(a,join(complement(b),complement(join(a,complement(b))))) = meet(a,complement(b)),
inference(step,[status(thm)],[t660546,t81]) ).
cnf(t660548,plain,
meet(a,join(complement(b),complement(join(a,complement(b))))) = zero,
inference(step,[status(thm)],[t660547,t241]) ).
cnf(t658047,plain,
meet(a,join(complement(b),complement(join(a,complement(b))))) = zero,
inference(orient,[status(thm)],[t660548]) ).
cnf(t658051,plain,
join(complement(b),complement(join(a,complement(b)))) = ifeq(zero,zero,ifeq(join(a,join(complement(b),complement(join(a,complement(b))))),one,complement(a),join(complement(b),complement(join(a,complement(b))))),join(complement(b),complement(join(a,complement(b))))),
inference(cp,[status(thm)],[t19,t658047]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t660549,plain,
join(complement(b),complement(join(a,complement(b)))) = ifeq(join(a,join(complement(b),complement(join(a,complement(b))))),one,complement(a),join(complement(b),complement(join(a,complement(b))))),
inference(step,[status(thm)],[t658051,t18]) ).
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(t76,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t77,plain,
one = join(X1,join(X2,complement(join(X1,X2)))),
inference(cp,[status(thm)],[t76,t64]) ).
cnf(t1547,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(orient,[status(thm)],[t77]) ).
cnf(t660550,plain,
join(complement(b),complement(join(a,complement(b)))) = ifeq(one,one,complement(a),join(complement(b),complement(join(a,complement(b))))),
inference(step,[status(thm)],[t660549,t1547]) ).
cnf(t660551,plain,
join(complement(b),complement(join(a,complement(b)))) = complement(a),
inference(step,[status(thm)],[t660550,t18]) ).
cnf(t658312,plain,
join(complement(b),complement(join(a,complement(b)))) = complement(a),
inference(orient,[status(thm)],[t660551]) ).
cnf(t658317,plain,
join(complement(b),complement(join(a,complement(b)))) = join(complement(b),complement(a)),
inference(cp,[status(thm)],[t169,t658312]) ).
cnf(t660552,plain,
complement(a) = join(complement(b),complement(a)),
inference(step,[status(thm)],[t658317,t658312]) ).
cnf(t659024,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t660552]) ).
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,
complement(a) != complement(a),
inference(rw,[status(thm)],[goal_0,t659024]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT243-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 20:40:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 225.31/33.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 225.31/33.57 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------