%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT251-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:56:25 PM UTC 2026
% Result : Unsatisfiable 39.25s 5.46s
% Output : Proof 39.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 12
% Syntax : Number of formulae : 131 ( 127 unt; 0 def)
% Number of atoms : 139 ( 138 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 : 6 ( 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 : 189 ( 10 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,Z)) = join(meet(X,join(Z,meet(X,Y))),meet(X,join(Y,meet(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H69) ).
fof(f11_nnf,plain,
! [X,Y,Z] : meet(X,join(Y,Z)) = join(meet(X,join(Z,meet(X,Y))),meet(X,join(Y,meet(X,Z)))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] : meet(X,join(Y,Z)) = join(meet(X,join(Z,meet(X,Y))),meet(X,join(Y,meet(X,Z)))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,X2)) = join(meet(X0,join(X2,meet(X0,X1))),meet(X0,join(X1,meet(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t13,plain,
join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(X3,meet(X1,X2)))) = meet(X1,join(X3,X2)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t47,plain,
join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(X3,meet(X1,X2)))) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t13]) ).
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(t69,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t72,plain,
meet(X1,join(complement(X1),X2)) = join(meet(X1,join(X2,zero)),meet(X1,join(complement(X1),meet(X1,X2)))),
inference(cp,[status(thm)],[t47,t69]) ).
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(t83,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t18044,plain,
meet(X1,join(X2,complement(X1))) = join(meet(X1,join(X2,zero)),meet(X1,join(complement(X1),meet(X1,X2)))),
inference(step,[status(thm)],[t72,t83]) ).
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(t70,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t17,t69]) ).
cnf(t117,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t70]) ).
cnf(t18045,plain,
meet(X1,join(X2,complement(X1))) = join(meet(X1,X2),meet(X1,join(complement(X1),meet(X1,X2)))),
inference(step,[status(thm)],[t18044,t117]) ).
cnf(t16488,plain,
join(meet(X1,X2),meet(X1,join(complement(X1),meet(X1,X2)))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t18045]) ).
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(t17007,plain,
join(X3,join(X1,X2)) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t10,t83]) ).
cnf(t91,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(orient,[status(thm)],[t17007]) ).
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(t94,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(cp,[status(thm)],[t91,t16]) ).
cnf(t17011,plain,
join(X1,join(X1,X2)) = join(X2,X1),
inference(step,[status(thm)],[t94,t91]) ).
cnf(t17012,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(step,[status(thm)],[t17011,t83]) ).
cnf(t152,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t17012]) ).
cnf(t17005,plain,
join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(X3,meet(X1,X2)))) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t47,t83]) ).
cnf(t84,plain,
join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(X3,meet(X1,X2)))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t17005]) ).
cnf(t156,plain,
join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(X3,meet(X1,X2)))) = join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(X2,X3))),
inference(cp,[status(thm)],[t152,t84]) ).
cnf(t17262,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t156,t84]) ).
cnf(t17263,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X1,join(X2,meet(X1,X3)))),
inference(step,[status(thm)],[t17262,t83]) ).
cnf(t1480,plain,
join(meet(X1,join(X2,X3)),meet(X1,join(X2,meet(X1,X3)))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t17263]) ).
cnf(t1532,plain,
meet(X1,join(X2,complement(X1))) = join(meet(X1,join(X2,complement(X1))),meet(X1,join(X2,zero))),
inference(cp,[status(thm)],[t1480,t69]) ).
cnf(t17275,plain,
meet(X1,join(X2,complement(X1))) = join(meet(X1,join(X2,zero)),meet(X1,join(X2,complement(X1)))),
inference(step,[status(thm)],[t1532,t83]) ).
cnf(t17276,plain,
meet(X1,join(X2,complement(X1))) = join(meet(X1,X2),meet(X1,join(X2,complement(X1)))),
inference(step,[status(thm)],[t17275,t117]) ).
cnf(t1621,plain,
join(meet(X1,X2),meet(X1,join(X2,complement(X1)))) = meet(X1,join(X2,complement(X1))),
inference(orient,[status(thm)],[t17276]) ).
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(t26,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1),
inference(cp,[status(thm)],[t19,t24]) ).
cnf(t17171,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1),
inference(step,[status(thm)],[t26,t83]) ).
cnf(t811,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t17171]) ).
cnf(t829,plain,
X1 = ifeq(zero,zero,ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t811,t69]) ).
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(t17172,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t829,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(t113,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t17173,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t17172,t113]) ).
cnf(t17174,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t17173,t18]) ).
cnf(t857,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t17174]) ).
cnf(t1667,plain,
meet(complement(X1),join(X2,complement(complement(X1)))) = join(meet(complement(X1),X2),meet(complement(X1),join(X2,X1))),
inference(cp,[status(thm)],[t1621,t857]) ).
cnf(t17318,plain,
meet(complement(X1),join(X2,X1)) = join(meet(complement(X1),X2),meet(complement(X1),join(X2,X1))),
inference(step,[status(thm)],[t1667,t857]) ).
cnf(t17319,plain,
meet(complement(X1),join(X1,X2)) = join(meet(complement(X1),X2),meet(complement(X1),join(X2,X1))),
inference(step,[status(thm)],[t17318,t83]) ).
cnf(t17320,plain,
meet(complement(X1),join(X1,X2)) = join(meet(X2,complement(X1)),meet(complement(X1),join(X2,X1))),
inference(step,[status(thm)],[t17319,t24]) ).
cnf(t17321,plain,
meet(complement(X1),join(X1,X2)) = join(meet(X2,complement(X1)),meet(complement(X1),join(X1,X2))),
inference(step,[status(thm)],[t17320,t83]) ).
cnf(t2059,plain,
join(meet(X1,complement(X2)),meet(complement(X2),join(X2,X1))) = meet(complement(X2),join(X2,X1)),
inference(orient,[status(thm)],[t17321]) ).
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(t76,plain,
meet(b,a) = a,
inference(orient,[status(thm)],[t2]) ).
cnf(t77,plain,
b = join(b,a),
inference(cp,[status(thm)],[t17,t76]) ).
cnf(t122,plain,
join(b,a) = b,
inference(orient,[status(thm)],[t77]) ).
cnf(t2088,plain,
meet(complement(b),join(b,a)) = join(meet(a,complement(b)),meet(complement(b),b)),
inference(cp,[status(thm)],[t2059,t122]) ).
cnf(t17339,plain,
meet(complement(b),b) = join(meet(a,complement(b)),meet(complement(b),b)),
inference(step,[status(thm)],[t2088,t122]) ).
cnf(t17340,plain,
meet(b,complement(b)) = join(meet(a,complement(b)),meet(complement(b),b)),
inference(step,[status(thm)],[t17339,t24]) ).
cnf(t17341,plain,
zero = join(meet(a,complement(b)),meet(complement(b),b)),
inference(step,[status(thm)],[t17340,t69]) ).
cnf(t17342,plain,
zero = join(meet(a,complement(b)),meet(b,complement(b))),
inference(step,[status(thm)],[t17341,t24]) ).
cnf(t17343,plain,
zero = join(meet(a,complement(b)),zero),
inference(step,[status(thm)],[t17342,t69]) ).
cnf(t17344,plain,
zero = meet(a,complement(b)),
inference(step,[status(thm)],[t17343,t117]) ).
cnf(t2219,plain,
meet(a,complement(b)) = zero,
inference(orient,[status(thm)],[t17344]) ).
cnf(t16637,plain,
meet(a,join(complement(b),complement(a))) = join(zero,meet(a,join(complement(a),meet(a,complement(b))))),
inference(cp,[status(thm)],[t16488,t2219]) ).
cnf(t18046,plain,
meet(a,join(complement(b),complement(a))) = join(zero,meet(a,join(complement(a),zero))),
inference(step,[status(thm)],[t16637,t2219]) ).
cnf(t18047,plain,
meet(a,join(complement(b),complement(a))) = join(zero,meet(a,complement(a))),
inference(step,[status(thm)],[t18046,t117]) ).
cnf(t18048,plain,
meet(a,join(complement(b),complement(a))) = join(zero,zero),
inference(step,[status(thm)],[t18047,t69]) ).
cnf(t18049,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(step,[status(thm)],[t18048,t117]) ).
cnf(t16907,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(orient,[status(thm)],[t18049]) ).
cnf(t16910,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,t16907]) ).
cnf(t18052,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)],[t16910,t18]) ).
cnf(t115,plain,
join(X1,join(complement(X1),X2)) = join(X2,one),
inference(cp,[status(thm)],[t91,t113]) ).
cnf(t17020,plain,
join(X1,join(X2,complement(X1))) = join(X2,one),
inference(step,[status(thm)],[t115,t83]) ).
cnf(t155,plain,
join(X1,complement(X1)) = join(X1,one),
inference(cp,[status(thm)],[t152,t113]) ).
cnf(t17013,plain,
one = join(X1,one),
inference(step,[status(thm)],[t155,t113]) ).
cnf(t163,plain,
join(X1,one) = one,
inference(orient,[status(thm)],[t17013]) ).
cnf(t17021,plain,
join(X1,join(X2,complement(X1))) = one,
inference(step,[status(thm)],[t17020,t163]) ).
cnf(t189,plain,
join(X1,join(X2,complement(X1))) = one,
inference(orient,[status(thm)],[t17021]) ).
cnf(t18053,plain,
join(complement(b),complement(a)) = ifeq(one,one,complement(a),join(complement(b),complement(a))),
inference(step,[status(thm)],[t18052,t189]) ).
cnf(t18054,plain,
join(complement(b),complement(a)) = complement(a),
inference(step,[status(thm)],[t18053,t18]) ).
cnf(t16955,plain,
join(complement(b),complement(a)) = complement(a),
inference(orient,[status(thm)],[t18054]) ).
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,t16955]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT251-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.43 % Computer : n015.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Wed Sep 23 20:44:55 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 39.25/5.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.25/5.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------