%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT236-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 01:56:22 PM UTC 2026
% Result : Unsatisfiable 22.08s 3.24s
% Output : Proof 22.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 95
% Number of leaves : 15
% Syntax : Number of formulae : 233 ( 229 unt; 0 def)
% Number of atoms : 241 ( 240 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 : 7 ( 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 : 480 ( 78 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Z))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H39) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Z))))),
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,meet(Z,join(U,meet(X,Z))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(X1,meet(X2,join(X3,meet(X0,X2))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X1,X3))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t47,plain,
meet(X1,join(X2,meet(X3,join(X4,meet(X1,X3))))) = meet(X1,join(X2,meet(X3,join(X1,X4)))),
inference(orient,[status(thm)],[t13]) ).
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(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(t24,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t11121,plain,
meet(X3,meet(X1,X2)) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t11,t24]) ).
cnf(t27,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(orient,[status(thm)],[t11121]) ).
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(t60,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t64,plain,
meet(X1,meet(complement(X1),X2)) = meet(X2,zero),
inference(cp,[status(thm)],[t27,t60]) ).
cnf(t11133,plain,
meet(X1,meet(X2,complement(X1))) = meet(X2,zero),
inference(step,[status(thm)],[t64,t24]) ).
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(t14,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t30,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(cp,[status(thm)],[t27,t14]) ).
cnf(t11123,plain,
meet(X1,meet(X1,X2)) = meet(X2,X1),
inference(step,[status(thm)],[t30,t27]) ).
cnf(t11124,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(step,[status(thm)],[t11123,t24]) ).
cnf(t116,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t11124]) ).
cnf(t119,plain,
meet(X1,complement(X1)) = meet(X1,zero),
inference(cp,[status(thm)],[t116,t60]) ).
cnf(t11125,plain,
zero = meet(X1,zero),
inference(step,[status(thm)],[t119,t60]) ).
cnf(t127,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t11125]) ).
cnf(t11134,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(step,[status(thm)],[t11133,t127]) ).
cnf(t160,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(orient,[status(thm)],[t11134]) ).
cnf(t165,plain,
meet(X1,join(X2,meet(meet(X3,complement(X1)),join(X1,X4)))) = meet(X1,join(X2,meet(meet(X3,complement(X1)),join(X4,zero)))),
inference(cp,[status(thm)],[t47,t160]) ).
cnf(t11300,plain,
meet(X1,join(X2,meet(join(X1,X4),meet(X3,complement(X1))))) = meet(X1,join(X2,meet(meet(X3,complement(X1)),join(X4,zero)))),
inference(step,[status(thm)],[t165,t24]) ).
cnf(t11301,plain,
meet(X1,join(X2,meet(complement(X1),meet(join(X1,X4),X3)))) = meet(X1,join(X2,meet(meet(X3,complement(X1)),join(X4,zero)))),
inference(step,[status(thm)],[t11300,t27]) ).
cnf(t11302,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),join(X1,X4))))) = meet(X1,join(X2,meet(meet(X3,complement(X1)),join(X4,zero)))),
inference(step,[status(thm)],[t11301,t27]) ).
cnf(t11303,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),join(X1,X4))))) = meet(X1,join(X2,meet(join(X4,zero),meet(X3,complement(X1))))),
inference(step,[status(thm)],[t11302,t24]) ).
cnf(t11304,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),join(X1,X4))))) = meet(X1,join(X2,meet(complement(X1),meet(join(X4,zero),X3)))),
inference(step,[status(thm)],[t11303,t27]) ).
cnf(t11305,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),join(X1,X4))))) = meet(X1,join(X2,meet(X3,meet(complement(X1),join(X4,zero))))),
inference(step,[status(thm)],[t11304,t27]) ).
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(t17,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t61,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t60]) ).
cnf(t101,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t61]) ).
cnf(t11306,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),join(X1,X4))))) = meet(X1,join(X2,meet(X3,meet(complement(X1),X4)))),
inference(step,[status(thm)],[t11305,t101]) ).
cnf(t11307,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),join(X1,X4))))) = meet(X1,join(X2,meet(X3,meet(X4,complement(X1))))),
inference(step,[status(thm)],[t11306,t24]) ).
cnf(t805,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),join(X1,X4))))) = meet(X1,join(X2,meet(X3,meet(X4,complement(X1))))),
inference(orient,[status(thm)],[t11307]) ).
cnf(t810,plain,
meet(X1,join(X2,meet(complement(X1),meet(X3,complement(X1))))) = meet(X1,join(X2,meet(complement(X1),join(X1,X3)))),
inference(cp,[status(thm)],[t805,t116]) ).
cnf(t11333,plain,
meet(X1,join(X2,meet(X3,meet(complement(X1),complement(X1))))) = meet(X1,join(X2,meet(complement(X1),join(X1,X3)))),
inference(step,[status(thm)],[t810,t27]) ).
cnf(t11334,plain,
meet(X1,join(X2,meet(X3,complement(X1)))) = meet(X1,join(X2,meet(complement(X1),join(X1,X3)))),
inference(step,[status(thm)],[t11333,t14]) ).
cnf(t1061,plain,
meet(X1,join(X2,meet(complement(X1),join(X1,X3)))) = meet(X1,join(X2,meet(X3,complement(X1)))),
inference(orient,[status(thm)],[t11334]) ).
cnf(t1062,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = meet(X1,complement(X1)),
inference(cp,[status(thm)],[t1061,t17]) ).
cnf(t11335,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(step,[status(thm)],[t1062,t60]) ).
cnf(t1102,plain,
meet(X1,join(complement(X1),meet(X2,complement(X1)))) = zero,
inference(orient,[status(thm)],[t11335]) ).
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(t16,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t48,plain,
meet(X1,join(meet(X2,join(X3,meet(X1,X2))),meet(X2,join(X1,X3)))) = meet(X1,meet(X2,join(X3,meet(X1,X2)))),
inference(cp,[status(thm)],[t47,t16]) ).
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(t72,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t11588,plain,
meet(X1,join(meet(X2,join(X1,X3)),meet(X2,join(X3,meet(X1,X2))))) = meet(X1,meet(X2,join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t48,t72]) ).
cnf(t11589,plain,
meet(X1,join(meet(X2,join(X1,X3)),meet(X2,join(X1,X3)))) = meet(X1,meet(X2,join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t11588,t47]) ).
cnf(t11590,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,meet(X2,join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t11589,t16]) ).
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(t15,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t31,plain,
meet(join(X1,X2),meet(X3,X1)) = meet(X3,X1),
inference(cp,[status(thm)],[t27,t15]) ).
cnf(t11137,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X3,X1),
inference(step,[status(thm)],[t31,t27]) ).
cnf(t11138,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X3,X1),
inference(step,[status(thm)],[t11137,t24]) ).
cnf(t11139,plain,
meet(X1,meet(X3,join(X1,X2))) = meet(X1,X3),
inference(step,[status(thm)],[t11138,t24]) ).
cnf(t175,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t11139]) ).
cnf(t11591,plain,
meet(X1,X2) = meet(X1,meet(X2,join(X3,meet(X1,X2)))),
inference(step,[status(thm)],[t11590,t175]) ).
cnf(t3465,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(orient,[status(thm)],[t11591]) ).
cnf(t3516,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,meet(meet(X2,join(X1,X3)),join(X4,meet(X1,X2)))),
inference(cp,[status(thm)],[t3465,t175]) ).
cnf(t11650,plain,
meet(X1,X2) = meet(X1,meet(meet(X2,join(X1,X3)),join(X4,meet(X1,X2)))),
inference(step,[status(thm)],[t3516,t175]) ).
cnf(t4267,plain,
meet(X1,meet(meet(X2,join(X1,X3)),join(X4,meet(X1,X2)))) = meet(X1,X2),
inference(orient,[status(thm)],[t11650]) ).
cnf(t4337,plain,
meet(X1,meet(X1,X2)) = meet(X1,meet(meet(meet(X1,X2),join(X1,X3)),join(X4,meet(X1,X2)))),
inference(cp,[status(thm)],[t4267,t116]) ).
cnf(t11891,plain,
meet(X1,X2) = meet(X1,meet(meet(meet(X1,X2),join(X1,X3)),join(X4,meet(X1,X2)))),
inference(step,[status(thm)],[t4337,t116]) ).
cnf(t11892,plain,
meet(X1,X2) = meet(X1,meet(join(X4,meet(X1,X2)),meet(meet(X1,X2),join(X1,X3)))),
inference(step,[status(thm)],[t11891,t24]) ).
cnf(t11893,plain,
meet(X1,X2) = meet(X1,meet(join(X1,X3),meet(join(X4,meet(X1,X2)),meet(X1,X2)))),
inference(step,[status(thm)],[t11892,t27]) ).
cnf(t11894,plain,
meet(X1,X2) = meet(X1,meet(meet(X1,X2),meet(join(X1,X3),join(X4,meet(X1,X2))))),
inference(step,[status(thm)],[t11893,t27]) ).
cnf(t8302,plain,
meet(X1,meet(meet(X1,X2),meet(join(X1,X3),join(X4,meet(X1,X2))))) = meet(X1,X2),
inference(orient,[status(thm)],[t11894]) ).
cnf(t8372,plain,
meet(X1,complement(join(X1,X2))) = meet(X1,meet(meet(X1,complement(join(X1,X2))),zero)),
inference(cp,[status(thm)],[t8302,t1102]) ).
cnf(t11895,plain,
meet(X1,complement(join(X1,X2))) = meet(X1,zero),
inference(step,[status(thm)],[t8372,t127]) ).
cnf(t11896,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(step,[status(thm)],[t11895,t127]) ).
cnf(t8491,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t11896]) ).
cnf(t8506,plain,
meet(X1,join(X2,meet(complement(join(X1,X3)),join(X1,X4)))) = meet(X1,join(X2,meet(complement(join(X1,X3)),join(X4,zero)))),
inference(cp,[status(thm)],[t47,t8491]) ).
cnf(t11932,plain,
meet(X1,join(X2,meet(join(X1,X4),complement(join(X1,X3))))) = meet(X1,join(X2,meet(complement(join(X1,X3)),join(X4,zero)))),
inference(step,[status(thm)],[t8506,t24]) ).
cnf(t11933,plain,
meet(X1,join(X2,meet(join(X1,X4),complement(join(X1,X3))))) = meet(X1,join(X2,meet(join(X4,zero),complement(join(X1,X3))))),
inference(step,[status(thm)],[t11932,t24]) ).
cnf(t11934,plain,
meet(X1,join(X2,meet(join(X1,X4),complement(join(X1,X3))))) = meet(X1,join(X2,meet(X4,complement(join(X1,X3))))),
inference(step,[status(thm)],[t11933,t101]) ).
cnf(t8761,plain,
meet(X1,join(X2,meet(join(X1,X3),complement(join(X1,X4))))) = meet(X1,join(X2,meet(X3,complement(join(X1,X4))))),
inference(orient,[status(thm)],[t11934]) ).
cnf(t8762,plain,
meet(X1,join(join(X1,X2),meet(X2,complement(join(X1,X3))))) = meet(X1,join(X1,X2)),
inference(cp,[status(thm)],[t8761,t17]) ).
cnf(t11942,plain,
meet(X1,join(join(X1,X2),meet(X2,complement(join(X1,X3))))) = X1,
inference(step,[status(thm)],[t8762,t15]) ).
cnf(t9006,plain,
meet(X1,join(join(X1,X2),meet(X2,complement(join(X1,X3))))) = X1,
inference(orient,[status(thm)],[t11942]) ).
cnf(t9015,plain,
X1 = meet(X1,join(join(X1,X2),meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t9006,t16]) ).
cnf(t9075,plain,
meet(X1,join(join(X1,X2),meet(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t9015]) ).
cnf(t26,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1),
inference(cp,[status(thm)],[t19,t24]) ).
cnf(t11236,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1),
inference(step,[status(thm)],[t26,t72]) ).
cnf(t478,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t11236]) ).
cnf(t490,plain,
X1 = ifeq(zero,zero,ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t478,t60]) ).
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(t11237,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t490,t18]) ).
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(t97,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t11238,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t11237,t97]) ).
cnf(t11239,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t11238,t18]) ).
cnf(t513,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t11239]) ).
cnf(t9083,plain,
complement(X1) = meet(complement(X1),join(join(complement(X1),X2),meet(X2,X1))),
inference(cp,[status(thm)],[t9075,t513]) ).
cnf(t11943,plain,
complement(X1) = meet(complement(X1),join(meet(X2,X1),join(complement(X1),X2))),
inference(step,[status(thm)],[t9083,t72]) ).
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(t11122,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t10,t72]) ).
cnf(t77,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t11122]) ).
cnf(t11944,plain,
complement(X1) = meet(complement(X1),join(X2,join(meet(X2,X1),complement(X1)))),
inference(step,[status(thm)],[t11943,t77]) ).
cnf(t11945,plain,
complement(X1) = meet(complement(X1),join(X2,join(complement(X1),meet(X2,X1)))),
inference(step,[status(thm)],[t11944,t72]) ).
cnf(t81,plain,
join(meet(X1,X2),join(X3,X1)) = join(X3,X1),
inference(cp,[status(thm)],[t77,t17]) ).
cnf(t11140,plain,
join(X1,join(meet(X1,X2),X3)) = join(X3,X1),
inference(step,[status(thm)],[t81,t77]) ).
cnf(t11141,plain,
join(X1,join(X3,meet(X1,X2))) = join(X3,X1),
inference(step,[status(thm)],[t11140,t72]) ).
cnf(t11142,plain,
join(X1,join(X3,meet(X1,X2))) = join(X1,X3),
inference(step,[status(thm)],[t11141,t72]) ).
cnf(t189,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(orient,[status(thm)],[t11142]) ).
cnf(t11946,plain,
complement(X1) = meet(complement(X1),join(X2,complement(X1))),
inference(step,[status(thm)],[t11945,t189]) ).
cnf(t9136,plain,
meet(complement(X1),join(X2,complement(X1))) = complement(X1),
inference(orient,[status(thm)],[t11946]) ).
cnf(t99,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t77,t97]) ).
cnf(t11135,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t99,t72]) ).
cnf(t80,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t77,t16]) ).
cnf(t11126,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t80,t77]) ).
cnf(t11127,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t11126,t72]) ).
cnf(t133,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t11127]) ).
cnf(t136,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t133,t97]) ).
cnf(t11128,plain,
one = join(X1,one),
inference(step,[status(thm)],[t136,t97]) ).
cnf(t143,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t11128]) ).
cnf(t11136,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t11135,t143]) ).
cnf(t168,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t11136]) ).
cnf(t505,plain,
X1 = ifeq(meet(X1,join(X2,complement(X1))),zero,ifeq(one,one,complement(join(X2,complement(X1))),X1),X1),
inference(cp,[status(thm)],[t478,t168]) ).
cnf(t11265,plain,
X1 = ifeq(meet(X1,join(X2,complement(X1))),zero,complement(join(X2,complement(X1))),X1),
inference(step,[status(thm)],[t505,t18]) ).
cnf(t603,plain,
ifeq(meet(X1,join(X2,complement(X1))),zero,complement(join(X2,complement(X1))),X1) = X1,
inference(orient,[status(thm)],[t11265]) ).
cnf(t605,plain,
complement(X1) = ifeq(meet(complement(X1),join(X2,X1)),zero,complement(join(X2,complement(complement(X1)))),complement(X1)),
inference(cp,[status(thm)],[t603,t513]) ).
cnf(t11271,plain,
complement(X1) = ifeq(meet(complement(X1),join(X1,X2)),zero,complement(join(X2,complement(complement(X1)))),complement(X1)),
inference(step,[status(thm)],[t605,t72]) ).
cnf(t11272,plain,
complement(X1) = ifeq(meet(complement(X1),join(X1,X2)),zero,complement(join(X2,X1)),complement(X1)),
inference(step,[status(thm)],[t11271,t513]) ).
cnf(t11273,plain,
complement(X1) = ifeq(meet(complement(X1),join(X1,X2)),zero,complement(join(X1,X2)),complement(X1)),
inference(step,[status(thm)],[t11272,t72]) ).
cnf(t635,plain,
ifeq(meet(complement(X1),join(X1,X2)),zero,complement(join(X1,X2)),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t11273]) ).
cnf(t8777,plain,
meet(X1,join(X2,meet(complement(X1),complement(join(X1,X3))))) = meet(X1,join(X2,meet(one,complement(join(X1,X3))))),
inference(cp,[status(thm)],[t8761,t97]) ).
cnf(t9146,plain,
meet(complement(X1),join(X2,complement(X1))) = meet(complement(X1),meet(join(X2,complement(X1)),join(X3,complement(X1)))),
inference(cp,[status(thm)],[t3465,t9136]) ).
cnf(t11952,plain,
complement(X1) = meet(complement(X1),meet(join(X2,complement(X1)),join(X3,complement(X1)))),
inference(step,[status(thm)],[t9146,t9136]) ).
cnf(t9232,plain,
meet(complement(X1),meet(join(X2,complement(X1)),join(X3,complement(X1)))) = complement(X1),
inference(orient,[status(thm)],[t11952]) ).
cnf(t9235,plain,
complement(X1) = meet(complement(X1),meet(one,join(X2,complement(X1)))),
inference(cp,[status(thm)],[t9232,t97]) ).
cnf(t11953,plain,
complement(X1) = meet(one,meet(join(X2,complement(X1)),complement(X1))),
inference(step,[status(thm)],[t9235,t27]) ).
cnf(t11954,plain,
complement(X1) = meet(one,meet(complement(X1),join(X2,complement(X1)))),
inference(step,[status(thm)],[t11953,t24]) ).
cnf(t11955,plain,
complement(X1) = meet(one,complement(X1)),
inference(step,[status(thm)],[t11954,t9136]) ).
cnf(t9276,plain,
meet(one,complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t11955]) ).
cnf(t12042,plain,
meet(X1,join(X2,meet(complement(X1),complement(join(X1,X3))))) = meet(X1,join(X2,complement(join(X1,X3)))),
inference(step,[status(thm)],[t8777,t9276]) ).
cnf(t10460,plain,
meet(X1,join(X2,meet(complement(X1),complement(join(X1,X3))))) = meet(X1,join(X2,complement(join(X1,X3)))),
inference(orient,[status(thm)],[t12042]) ).
cnf(t10461,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = meet(X1,complement(X1)),
inference(cp,[status(thm)],[t10460,t17]) ).
cnf(t12043,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(step,[status(thm)],[t10461,t60]) ).
cnf(t10505,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t12043]) ).
cnf(t10506,plain,
zero = meet(complement(X1),join(X1,complement(join(complement(X1),X2)))),
inference(cp,[status(thm)],[t10505,t513]) ).
cnf(t12044,plain,
zero = meet(complement(X1),join(X1,complement(join(X2,complement(X1))))),
inference(step,[status(thm)],[t10506,t72]) ).
cnf(t10547,plain,
meet(complement(X1),join(X1,complement(join(X2,complement(X1))))) = zero,
inference(orient,[status(thm)],[t12044]) ).
cnf(t10555,plain,
complement(X1) = ifeq(zero,zero,complement(join(X1,complement(join(X2,complement(X1))))),complement(X1)),
inference(cp,[status(thm)],[t635,t10547]) ).
cnf(t12045,plain,
complement(X1) = complement(join(X1,complement(join(X2,complement(X1))))),
inference(step,[status(thm)],[t10555,t18]) ).
cnf(t10592,plain,
complement(join(X1,complement(join(X2,complement(X1))))) = complement(X1),
inference(orient,[status(thm)],[t12045]) ).
cnf(t10597,plain,
join(X1,complement(join(X2,complement(X1)))) = complement(complement(X1)),
inference(cp,[status(thm)],[t513,t10592]) ).
cnf(t12046,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(step,[status(thm)],[t10597,t513]) ).
cnf(t10691,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t12046]) ).
cnf(t10696,plain,
complement(join(X1,complement(X2))) = meet(complement(join(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t9136,t10691]) ).
cnf(t12050,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(join(X1,complement(X2)))),
inference(step,[status(thm)],[t10696,t24]) ).
cnf(t10849,plain,
meet(X1,complement(join(X2,complement(X1)))) = complement(join(X2,complement(X1))),
inference(orient,[status(thm)],[t12050]) ).
cnf(t10853,plain,
complement(join(X1,complement(complement(X2)))) = meet(complement(X2),complement(join(X1,X2))),
inference(cp,[status(thm)],[t10849,t513]) ).
cnf(t12051,plain,
complement(join(X1,X2)) = meet(complement(X2),complement(join(X1,X2))),
inference(step,[status(thm)],[t10853,t513]) ).
cnf(t10903,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(orient,[status(thm)],[t12051]) ).
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(t66,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t67,plain,
b = join(b,a),
inference(cp,[status(thm)],[t17,t66]) ).
cnf(t106,plain,
join(b,a) = b,
inference(orient,[status(thm)],[t67]) ).
cnf(t10911,plain,
complement(join(b,a)) = meet(complement(a),complement(b)),
inference(cp,[status(thm)],[t10903,t106]) ).
cnf(t12052,plain,
complement(b) = meet(complement(a),complement(b)),
inference(step,[status(thm)],[t10911,t106]) ).
cnf(t12053,plain,
complement(b) = meet(complement(b),complement(a)),
inference(step,[status(thm)],[t12052,t24]) ).
cnf(t10966,plain,
meet(complement(b),complement(a)) = complement(b),
inference(orient,[status(thm)],[t12053]) ).
cnf(t10979,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(cp,[status(thm)],[t1102,t10966]) ).
cnf(t12063,plain,
zero = meet(a,join(complement(b),complement(a))),
inference(step,[status(thm)],[t10979,t72]) ).
cnf(t11043,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t12063]) ).
cnf(t11044,plain,
join(complement(b),complement(a)) = ifeq(zero,zero,ifeq(join(a,join(complement(b),complement(a))),one,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(cp,[status(thm)],[t19,t11043]) ).
cnf(t12064,plain,
join(complement(b),complement(a)) = ifeq(join(a,join(complement(b),complement(a))),one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t11044,t18]) ).
cnf(t12065,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t12064,t168]) ).
cnf(t12066,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t12065,t18]) ).
cnf(t11079,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t12066]) ).
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,
complement(a) != complement(a),
inference(rw,[status(thm)],[goal_0,t11079]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT236-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 20:42:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 22.08/3.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.08/3.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------