%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT194-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 01:55:51 PM UTC 2026
% Result : Unsatisfiable 26.72s 3.89s
% Output : Proof 26.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 85
% Number of leaves : 13
% Syntax : Number of formulae : 298 ( 294 unt; 0 def)
% Number of atoms : 306 ( 305 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 : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 642 ( 79 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t6,plain,
join(X1,meet(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t16,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t6]) ).
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(t7,plain,
meet(X1,X2) = meet(X2,X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t23,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t24,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t16,t23]) ).
cnf(t121,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t24]) ).
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(t10,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t125,plain,
X1 = join(X1,meet(X2,meet(X3,X1))),
inference(cp,[status(thm)],[t121,t26]) ).
cnf(t274,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(orient,[status(thm)],[t125]) ).
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(t8,plain,
meet(X1,join(X1,X2)) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t14,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t8]) ).
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(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t62,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t63,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t14,t62]) ).
cnf(t128,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t63]) ).
cnf(t123,plain,
join(X1,X2) = join(join(X1,X2),X1),
inference(cp,[status(thm)],[t121,t14]) ).
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(t9,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t66,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t98395,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(step,[status(thm)],[t123,t66]) ).
cnf(t151,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t98395]) ).
cnf(t155,plain,
join(X1,X2) = meet(join(X1,X2),join(X2,X1)),
inference(cp,[status(thm)],[t128,t151]) ).
cnf(t413,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t155]) ).
cnf(t437,plain,
join(X1,X2) = join(join(X1,X2),meet(X3,join(X2,X1))),
inference(cp,[status(thm)],[t274,t413]) ).
cnf(t98455,plain,
join(X1,X2) = join(X1,join(X2,meet(X3,join(X2,X1)))),
inference(step,[status(thm)],[t437,t66]) ).
cnf(t3140,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t98455]) ).
cnf(t130,plain,
meet(X1,X2) = meet(meet(X1,X2),X1),
inference(cp,[status(thm)],[t128,t16]) ).
cnf(t98396,plain,
meet(X1,X2) = meet(X1,meet(X2,X1)),
inference(step,[status(thm)],[t130,t26]) ).
cnf(t158,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t98396]) ).
cnf(t164,plain,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3),
inference(cp,[status(thm)],[t26,t158]) ).
cnf(t98446,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3),
inference(step,[status(thm)],[t164,t26]) ).
cnf(t98447,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(step,[status(thm)],[t98446,t26]) ).
cnf(t1353,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t98447]) ).
cnf(t1406,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X1,meet(X3,X2))),
inference(cp,[status(thm)],[t274,t1353]) ).
cnf(t3884,plain,
join(meet(X1,X2),meet(X1,meet(X3,X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t1406]) ).
cnf(t3941,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X1,X2)),
inference(cp,[status(thm)],[t3884,t14]) ).
cnf(t98594,plain,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(X2,X3))),
inference(step,[status(thm)],[t3941,t62]) ).
cnf(t30839,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t98594]) ).
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(t11,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t18,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X1,X2),one,complement(X1),X2),X2) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(f11,axiom,
meet(X,join(Y,meet(X,meet(Z,U)))) = meet(X,join(Y,meet(Z,join(meet(X,U),meet(Y,U))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H32) ).
fof(f11_nnf,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(X,meet(Z,U)))) = meet(X,join(Y,meet(Z,join(meet(X,U),meet(Y,U))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z,U] : meet(X,join(Y,meet(X,meet(Z,U)))) = meet(X,join(Y,meet(Z,join(meet(X,U),meet(Y,U))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
meet(X0,join(X1,meet(X0,meet(X2,X3)))) = meet(X0,join(X1,meet(X2,join(meet(X0,X3),meet(X1,X3))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
meet(X1,join(X2,meet(X3,join(meet(X1,X4),meet(X2,X4))))) = meet(X1,join(X2,meet(X1,meet(X3,X4)))),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t35,plain,
meet(X1,join(X2,meet(X3,join(meet(X1,X4),meet(X2,X4))))) = meet(X1,join(X2,meet(X1,meet(X3,X4)))),
inference(orient,[status(thm)],[t12]) ).
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(t2,plain,
join(X1,complement(X1)) = one,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t76,plain,
join(X1,complement(X1)) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t78,plain,
X1 = meet(X1,one),
inference(cp,[status(thm)],[t14,t76]) ).
cnf(t84,plain,
meet(X1,one) = X1,
inference(orient,[status(thm)],[t78]) ).
cnf(t88,plain,
meet(X1,join(X2,meet(X1,meet(X3,one)))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,one))))),
inference(cp,[status(thm)],[t35,t84]) ).
cnf(t98601,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,one))))),
inference(step,[status(thm)],[t88,t84]) ).
cnf(t98602,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,X2)))),
inference(step,[status(thm)],[t98601,t84]) ).
cnf(t33683,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(orient,[status(thm)],[t98602]) ).
cnf(t33759,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),meet(X2,one))),
inference(cp,[status(thm)],[t33683,t76]) ).
cnf(t98603,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t33759,t84]) ).
cnf(t33984,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(orient,[status(thm)],[t98603]) ).
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(t3,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t55,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t57,plain,
meet(X1,meet(complement(X1),X2)) = meet(zero,X2),
inference(cp,[status(thm)],[t26,t55]) ).
cnf(t58,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t16,t55]) ).
cnf(t80,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t58]) ).
cnf(t81,plain,
X1 = join(zero,X1),
inference(cp,[status(thm)],[t80,t62]) ).
cnf(t90,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t81]) ).
cnf(t92,plain,
meet(zero,X1) = zero,
inference(cp,[status(thm)],[t90,t16]) ).
cnf(t109,plain,
meet(zero,X1) = zero,
inference(orient,[status(thm)],[t92]) ).
cnf(t98401,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(step,[status(thm)],[t57,t109]) ).
cnf(t170,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(orient,[status(thm)],[t98401]) ).
cnf(t173,plain,
meet(meet(complement(X1),X2),X1) = meet(meet(complement(X1),X2),zero),
inference(cp,[status(thm)],[t158,t170]) ).
cnf(t98402,plain,
meet(complement(X1),meet(X2,X1)) = meet(meet(complement(X1),X2),zero),
inference(step,[status(thm)],[t173,t26]) ).
cnf(t98403,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),meet(X2,zero)),
inference(step,[status(thm)],[t98402,t26]) ).
cnf(t110,plain,
zero = meet(X1,zero),
inference(cp,[status(thm)],[t109,t23]) ).
cnf(t117,plain,
meet(X1,zero) = zero,
inference(orient,[status(thm)],[t110]) ).
cnf(t98404,plain,
meet(complement(X1),meet(X2,X1)) = meet(complement(X1),zero),
inference(step,[status(thm)],[t98403,t117]) ).
cnf(t98405,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t98404,t117]) ).
cnf(t185,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t98405]) ).
cnf(t190,plain,
zero = meet(complement(join(X1,X2)),X1),
inference(cp,[status(thm)],[t185,t14]) ).
cnf(t98406,plain,
zero = meet(X1,complement(join(X1,X2))),
inference(step,[status(thm)],[t190,t23]) ).
cnf(t200,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t98406]) ).
cnf(t34045,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t33984,t200]) ).
cnf(t98604,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t34045,t80]) ).
cnf(t98605,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(step,[status(thm)],[t98604,t55]) ).
cnf(t34231,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t98605]) ).
cnf(t34278,plain,
join(complement(X1),complement(join(X1,X2))) = ifeq(zero,zero,ifeq(join(X1,join(complement(X1),complement(join(X1,X2)))),one,complement(X1),join(complement(X1),complement(join(X1,X2)))),join(complement(X1),complement(join(X1,X2)))),
inference(cp,[status(thm)],[t18,t34231]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t98606,plain,
join(complement(X1),complement(join(X1,X2))) = ifeq(join(X1,join(complement(X1),complement(join(X1,X2)))),one,complement(X1),join(complement(X1),complement(join(X1,X2)))),
inference(step,[status(thm)],[t34278,t17]) ).
cnf(t79,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(cp,[status(thm)],[t66,t76]) ).
cnf(t85,plain,
X1 = meet(one,X1),
inference(cp,[status(thm)],[t84,t23]) ).
cnf(t98,plain,
meet(one,X1) = X1,
inference(orient,[status(thm)],[t85]) ).
cnf(t100,plain,
join(one,X1) = one,
inference(cp,[status(thm)],[t98,t14]) ).
cnf(t114,plain,
join(one,X1) = one,
inference(orient,[status(thm)],[t100]) ).
cnf(t98408,plain,
join(X1,join(complement(X1),X2)) = one,
inference(step,[status(thm)],[t79,t114]) ).
cnf(t228,plain,
join(X1,join(complement(X1),X2)) = one,
inference(orient,[status(thm)],[t98408]) ).
cnf(t98607,plain,
join(complement(X1),complement(join(X1,X2))) = ifeq(one,one,complement(X1),join(complement(X1),complement(join(X1,X2)))),
inference(step,[status(thm)],[t98606,t228]) ).
cnf(t98608,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(step,[status(thm)],[t98607,t17]) ).
cnf(t34387,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t98608]) ).
cnf(t68,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(cp,[status(thm)],[t66,t16]) ).
cnf(t2374,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(orient,[status(thm)],[t68]) ).
cnf(t72,plain,
join(X1,join(X2,X3)) = join(join(X2,X1),X3),
inference(cp,[status(thm)],[t66,t62]) ).
cnf(t98450,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(step,[status(thm)],[t72,t66]) ).
cnf(t1981,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(orient,[status(thm)],[t98450]) ).
cnf(t2376,plain,
join(X1,X2) = join(X2,join(X1,meet(join(X1,X2),X3))),
inference(cp,[status(thm)],[t2374,t1981]) ).
cnf(t4309,plain,
join(X1,join(X2,meet(join(X2,X1),X3))) = join(X2,X1),
inference(orient,[status(thm)],[t2376]) ).
cnf(t34389,plain,
complement(X1) = join(complement(X1),complement(join(X2,X1))),
inference(cp,[status(thm)],[t34387,t4309]) ).
cnf(t34790,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(orient,[status(thm)],[t34389]) ).
cnf(t34836,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X2)),
inference(cp,[status(thm)],[t128,t34790]) ).
cnf(t98614,plain,
complement(join(X1,X2)) = meet(complement(X2),complement(join(X1,X2))),
inference(step,[status(thm)],[t34836,t23]) ).
cnf(t35957,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(orient,[status(thm)],[t98614]) ).
cnf(t56,plain,
zero = meet(X1,meet(X2,complement(meet(X1,X2)))),
inference(cp,[status(thm)],[t55,t26]) ).
cnf(t565,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(orient,[status(thm)],[t56]) ).
cnf(t34039,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,join(complement(X1),zero)),
inference(cp,[status(thm)],[t33984,t565]) ).
cnf(t98692,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t34039,t80]) ).
cnf(t98693,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(step,[status(thm)],[t98692,t55]) ).
cnf(t67529,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = zero,
inference(orient,[status(thm)],[t98693]) ).
cnf(t67690,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = ifeq(zero,zero,ifeq(join(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))),one,complement(X1),join(complement(X1),meet(X2,complement(meet(X1,X2))))),join(complement(X1),meet(X2,complement(meet(X1,X2))))),
inference(cp,[status(thm)],[t18,t67529]) ).
cnf(t98694,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = ifeq(join(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))),one,complement(X1),join(complement(X1),meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t67690,t17]) ).
cnf(t98695,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = ifeq(one,one,complement(X1),join(complement(X1),meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t98694,t228]) ).
cnf(t98696,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(step,[status(thm)],[t98695,t17]) ).
cnf(t67815,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(orient,[status(thm)],[t98696]) ).
cnf(t67935,plain,
complement(join(complement(X1),meet(X2,complement(meet(X1,X2))))) = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(cp,[status(thm)],[t35957,t67815]) ).
cnf(t98698,plain,
complement(complement(X1)) = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t67935,t67815]) ).
cnf(t25,plain,
X1 = ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1),
inference(cp,[status(thm)],[t18,t23]) ).
cnf(t10379,plain,
ifeq(meet(X1,X2),zero,ifeq(join(X2,X1),one,complement(X2),X1),X1) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t10431,plain,
X1 = ifeq(zero,zero,ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),X1),
inference(cp,[status(thm)],[t10379,t55]) ).
cnf(t98560,plain,
X1 = ifeq(join(complement(X1),X1),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t10431,t17]) ).
cnf(t98561,plain,
X1 = ifeq(join(X1,complement(X1)),one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t98560,t62]) ).
cnf(t98562,plain,
X1 = ifeq(one,one,complement(complement(X1)),X1),
inference(step,[status(thm)],[t98561,t76]) ).
cnf(t98563,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t98562,t17]) ).
cnf(t18924,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t98563]) ).
cnf(t98699,plain,
X1 = meet(complement(meet(X2,complement(meet(X1,X2)))),complement(complement(X1))),
inference(step,[status(thm)],[t98698,t18924]) ).
cnf(t98700,plain,
X1 = meet(complement(complement(X1)),complement(meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t98699,t23]) ).
cnf(t98701,plain,
X1 = meet(X1,complement(meet(X2,complement(meet(X1,X2))))),
inference(step,[status(thm)],[t98700,t18924]) ).
cnf(t68366,plain,
meet(X1,complement(meet(X2,complement(meet(X1,X2))))) = X1,
inference(orient,[status(thm)],[t98701]) ).
cnf(t192,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t185,t128]) ).
cnf(t98407,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t192,t23]) ).
cnf(t209,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t98407]) ).
cnf(t212,plain,
zero = meet(X1,complement(join(X2,join(X3,X1)))),
inference(cp,[status(thm)],[t209,t66]) ).
cnf(t709,plain,
meet(X1,complement(join(X2,join(X3,X1)))) = zero,
inference(orient,[status(thm)],[t212]) ).
cnf(t163,plain,
meet(X1,X2) = join(meet(X1,X2),meet(X2,X1)),
inference(cp,[status(thm)],[t121,t158]) ).
cnf(t443,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(orient,[status(thm)],[t163]) ).
cnf(t721,plain,
zero = meet(meet(X1,X2),complement(join(X3,meet(X2,X1)))),
inference(cp,[status(thm)],[t709,t443]) ).
cnf(t98494,plain,
zero = meet(X1,meet(X2,complement(join(X3,meet(X2,X1))))),
inference(step,[status(thm)],[t721,t26]) ).
cnf(t8177,plain,
meet(X1,meet(X2,complement(join(X3,meet(X2,X1))))) = zero,
inference(orient,[status(thm)],[t98494]) ).
cnf(t34409,plain,
complement(join(X1,X2)) = meet(complement(join(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t128,t34387]) ).
cnf(t98610,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(join(X1,X2))),
inference(step,[status(thm)],[t34409,t23]) ).
cnf(t34943,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t98610]) ).
cnf(t35070,plain,
zero = meet(X1,complement(join(X2,meet(complement(X2),X1)))),
inference(cp,[status(thm)],[t8177,t34943]) ).
cnf(t38300,plain,
meet(X1,complement(join(X2,meet(complement(X2),X1)))) = zero,
inference(orient,[status(thm)],[t35070]) ).
cnf(t68377,plain,
X1 = meet(X1,complement(meet(complement(join(X2,meet(complement(X2),X1))),complement(zero)))),
inference(cp,[status(thm)],[t68366,t38300]) ).
cnf(t98702,plain,
X1 = meet(X1,complement(meet(complement(zero),complement(join(X2,meet(complement(X2),X1)))))),
inference(step,[status(thm)],[t68377,t23]) ).
cnf(t91,plain,
complement(zero) = one,
inference(cp,[status(thm)],[t90,t76]) ).
cnf(t96,plain,
complement(zero) = one,
inference(orient,[status(thm)],[t91]) ).
cnf(t98703,plain,
X1 = meet(X1,complement(meet(one,complement(join(X2,meet(complement(X2),X1)))))),
inference(step,[status(thm)],[t98702,t96]) ).
cnf(t98704,plain,
X1 = meet(X1,complement(complement(join(X2,meet(complement(X2),X1))))),
inference(step,[status(thm)],[t98703,t98]) ).
cnf(t98705,plain,
X1 = meet(X1,join(X2,meet(complement(X2),X1))),
inference(step,[status(thm)],[t98704,t18924]) ).
cnf(t68701,plain,
meet(X1,join(X2,meet(complement(X2),X1))) = X1,
inference(orient,[status(thm)],[t98705]) ).
cnf(t68838,plain,
meet(X1,join(join(X2,meet(complement(X2),X1)),X3)) = join(X1,meet(X1,join(join(X2,meet(complement(X2),X1)),X3))),
inference(cp,[status(thm)],[t30839,t68701]) ).
cnf(t98755,plain,
meet(X1,join(X2,join(meet(complement(X2),X1),X3))) = join(X1,meet(X1,join(join(X2,meet(complement(X2),X1)),X3))),
inference(step,[status(thm)],[t68838,t66]) ).
cnf(t98756,plain,
meet(X1,join(X2,join(meet(complement(X2),X1),X3))) = X1,
inference(step,[status(thm)],[t98755,t16]) ).
cnf(t73805,plain,
meet(X1,join(X2,join(meet(complement(X2),X1),X3))) = X1,
inference(orient,[status(thm)],[t98756]) ).
cnf(t74100,plain,
join(join(meet(complement(X1),X2),X3),X1) = join(join(meet(complement(X1),X2),X3),join(X1,X2)),
inference(cp,[status(thm)],[t3140,t73805]) ).
cnf(t98757,plain,
join(meet(complement(X1),X2),join(X3,X1)) = join(join(meet(complement(X1),X2),X3),join(X1,X2)),
inference(step,[status(thm)],[t74100,t66]) ).
cnf(t69,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t66,t62]) ).
cnf(t1814,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t69]) ).
cnf(t1835,plain,
join(join(X1,X2),join(X3,X2)) = join(X3,join(X2,X1)),
inference(cp,[status(thm)],[t1814,t151]) ).
cnf(t98453,plain,
join(X1,join(X2,join(X3,X2))) = join(X3,join(X2,X1)),
inference(step,[status(thm)],[t1835,t66]) ).
cnf(t98454,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(step,[status(thm)],[t98453,t151]) ).
cnf(t2161,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(orient,[status(thm)],[t98454]) ).
cnf(t98758,plain,
join(X1,join(X3,meet(complement(X1),X2))) = join(join(meet(complement(X1),X2),X3),join(X1,X2)),
inference(step,[status(thm)],[t98757,t2161]) ).
cnf(t98759,plain,
join(X1,join(X3,meet(complement(X1),X2))) = join(meet(complement(X1),X2),join(X3,join(X1,X2))),
inference(step,[status(thm)],[t98758,t66]) ).
cnf(t126,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t66,t121]) ).
cnf(t359,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t126]) ).
cnf(t1831,plain,
join(join(meet(X1,X2),X3),join(X4,X2)) = join(X4,join(X2,X3)),
inference(cp,[status(thm)],[t1814,t359]) ).
cnf(t98583,plain,
join(meet(X1,X2),join(X3,join(X4,X2))) = join(X4,join(X2,X3)),
inference(step,[status(thm)],[t1831,t66]) ).
cnf(t25895,plain,
join(meet(X1,X2),join(X3,join(X4,X2))) = join(X4,join(X2,X3)),
inference(orient,[status(thm)],[t98583]) ).
cnf(t98760,plain,
join(X1,join(X3,meet(complement(X1),X2))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t98759,t25895]) ).
cnf(t74142,plain,
join(X1,join(X2,meet(complement(X1),X3))) = join(X1,join(X3,X2)),
inference(orient,[status(thm)],[t98760]) ).
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(t15,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t70,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t66,t15]) ).
cnf(t146,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t70]) ).
cnf(t74143,plain,
join(X1,join(X2,X1)) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t74142,t146]) ).
cnf(t98762,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(step,[status(thm)],[t74143,t151]) ).
cnf(t74521,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t98762]) ).
cnf(t74570,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(complement(X1),meet(X2,X3))),
inference(cp,[status(thm)],[t74521,t1353]) ).
cnf(t98791,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t74570,t74521]) ).
cnf(t80764,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t98791]) ).
cnf(t67816,plain,
complement(complement(X1)) = join(X1,meet(X2,complement(meet(complement(X1),X2)))),
inference(cp,[status(thm)],[t67815,t18924]) ).
cnf(t98697,plain,
X1 = join(X1,meet(X2,complement(meet(complement(X1),X2)))),
inference(step,[status(thm)],[t67816,t18924]) ).
cnf(t68088,plain,
join(X1,meet(X2,complement(meet(complement(X1),X2)))) = X1,
inference(orient,[status(thm)],[t98697]) ).
cnf(t74160,plain,
join(X1,join(complement(meet(complement(X2),complement(X1))),X2)) = join(X1,X2),
inference(cp,[status(thm)],[t74142,t68088]) ).
cnf(t98818,plain,
join(X1,join(X2,complement(meet(complement(X2),complement(X1))))) = join(X1,X2),
inference(step,[status(thm)],[t74160,t62]) ).
cnf(t34810,plain,
complement(meet(X1,X2)) = join(complement(meet(X1,X2)),complement(X1)),
inference(cp,[status(thm)],[t34790,t16]) ).
cnf(t98611,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(meet(X1,X2))),
inference(step,[status(thm)],[t34810,t62]) ).
cnf(t35079,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t98611]) ).
cnf(t35080,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t35079,t18924]) ).
cnf(t36392,plain,
join(X1,complement(meet(complement(X1),X2))) = complement(meet(complement(X1),X2)),
inference(orient,[status(thm)],[t35080]) ).
cnf(t98819,plain,
join(X1,complement(meet(complement(X2),complement(X1)))) = join(X1,X2),
inference(step,[status(thm)],[t98818,t36392]) ).
cnf(t35100,plain,
complement(X1) = meet(complement(X1),complement(meet(X1,X2))),
inference(cp,[status(thm)],[t14,t35079]) ).
cnf(t35210,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(orient,[status(thm)],[t35100]) ).
cnf(t35211,plain,
complement(complement(X1)) = meet(X1,complement(meet(complement(X1),X2))),
inference(cp,[status(thm)],[t35210,t18924]) ).
cnf(t98612,plain,
X1 = meet(X1,complement(meet(complement(X1),X2))),
inference(step,[status(thm)],[t35211,t18924]) ).
cnf(t35345,plain,
meet(X1,complement(meet(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t98612]) ).
cnf(t28,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(cp,[status(thm)],[t26,t14]) ).
cnf(t2255,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(orient,[status(thm)],[t28]) ).
cnf(t32,plain,
meet(X1,meet(X2,X3)) = meet(meet(X2,X1),X3),
inference(cp,[status(thm)],[t26,t23]) ).
cnf(t98449,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(step,[status(thm)],[t32,t26]) ).
cnf(t1724,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(orient,[status(thm)],[t98449]) ).
cnf(t2257,plain,
meet(X1,X2) = meet(X2,meet(X1,join(meet(X1,X2),X3))),
inference(cp,[status(thm)],[t2255,t1724]) ).
cnf(t4156,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(orient,[status(thm)],[t2257]) ).
cnf(t35347,plain,
X1 = meet(X1,complement(meet(X2,complement(X1)))),
inference(cp,[status(thm)],[t35345,t4156]) ).
cnf(t35488,plain,
meet(X1,complement(meet(X2,complement(X1)))) = X1,
inference(orient,[status(thm)],[t35347]) ).
cnf(t35493,plain,
complement(meet(X1,complement(X2))) = join(complement(meet(X1,complement(X2))),X2),
inference(cp,[status(thm)],[t121,t35488]) ).
cnf(t98617,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(meet(X1,complement(X2)))),
inference(step,[status(thm)],[t35493,t62]) ).
cnf(t36524,plain,
join(X1,complement(meet(X2,complement(X1)))) = complement(meet(X2,complement(X1))),
inference(orient,[status(thm)],[t98617]) ).
cnf(t98820,plain,
complement(meet(complement(X2),complement(X1))) = join(X1,X2),
inference(step,[status(thm)],[t98819,t36524]) ).
cnf(t90905,plain,
complement(meet(complement(X1),complement(X2))) = join(X2,X1),
inference(orient,[status(thm)],[t98820]) ).
cnf(t90948,plain,
join(X1,complement(X2)) = complement(meet(X2,complement(X1))),
inference(cp,[status(thm)],[t90905,t18924]) ).
cnf(t91207,plain,
complement(meet(X1,complement(X2))) = join(X2,complement(X1)),
inference(orient,[status(thm)],[t90948]) ).
cnf(t91242,plain,
meet(X1,complement(X2)) = complement(join(X2,complement(X1))),
inference(cp,[status(thm)],[t18924,t91207]) ).
cnf(t91931,plain,
complement(join(X1,complement(X2))) = meet(X2,complement(X1)),
inference(orient,[status(thm)],[t91242]) ).
cnf(t91948,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t91931,t62]) ).
cnf(t92122,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t91948]) ).
cnf(t74172,plain,
join(X1,join(X2,meet(X2,complement(X1)))) = join(X1,meet(X2,complement(X1))),
inference(cp,[status(thm)],[t74142,t443]) ).
cnf(t98764,plain,
join(X1,X2) = join(X1,meet(X2,complement(X1))),
inference(step,[status(thm)],[t74172,t16]) ).
cnf(t74787,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t98764]) ).
cnf(t74812,plain,
join(complement(X1),X2) = join(complement(X1),meet(X2,X1)),
inference(cp,[status(thm)],[t74787,t18924]) ).
cnf(t75276,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t74812]) ).
cnf(t92135,plain,
meet(X1,complement(meet(X2,X1))) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t92122,t75276]) ).
cnf(t98885,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t92135,t92122]) ).
cnf(t92604,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t98885]) ).
cnf(t91236,plain,
join(X1,complement(X2)) = complement(meet(complement(X1),X2)),
inference(cp,[status(thm)],[t91207,t23]) ).
cnf(t91468,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t91236]) ).
cnf(t92608,plain,
meet(X1,complement(complement(X2))) = meet(X1,join(X2,complement(X1))),
inference(cp,[status(thm)],[t92604,t91468]) ).
cnf(t98886,plain,
meet(X1,X2) = meet(X1,join(X2,complement(X1))),
inference(step,[status(thm)],[t92608,t18924]) ).
cnf(t92890,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t98886]) ).
cnf(t92990,plain,
join(X1,meet(X2,join(X3,complement(complement(X1))))) = join(X1,meet(X2,meet(complement(X1),X3))),
inference(cp,[status(thm)],[t80764,t92890]) ).
cnf(t98901,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,meet(complement(X1),X3))),
inference(step,[status(thm)],[t92990,t18924]) ).
cnf(t98902,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(step,[status(thm)],[t98901,t80764]) ).
cnf(t94605,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X2,X3)),
inference(orient,[status(thm)],[t98902]) ).
cnf(t92906,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t92890,t62]) ).
cnf(t93062,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t92906]) ).
cnf(t74315,plain,
join(complement(X1),join(X2,X3)) = join(complement(X1),join(X3,meet(X1,X2))),
inference(cp,[status(thm)],[t74142,t18924]) ).
cnf(t81874,plain,
join(complement(X1),join(X2,meet(X1,X3))) = join(complement(X1),join(X3,X2)),
inference(orient,[status(thm)],[t74315]) ).
cnf(t93073,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(complement(X1),join(X3,X2))),
inference(cp,[status(thm)],[t93062,t81874]) ).
cnf(t98908,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,X2)),
inference(step,[status(thm)],[t93073,t93062]) ).
cnf(t96428,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,X2)),
inference(orient,[status(thm)],[t98908]) ).
cnf(t96630,plain,
join(meet(X1,X2),meet(X1,X3)) = join(meet(X1,X2),meet(X1,join(X2,X3))),
inference(cp,[status(thm)],[t94605,t96428]) ).
cnf(t98925,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)),
inference(step,[status(thm)],[t96630,t30839]) ).
cnf(t97897,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)),
inference(orient,[status(thm)],[t98925]) ).
cnf(f12,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f12_nnf,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
join(meet(a,b),meet(a,c)) != meet(a,join(b,c)),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
meet(a,join(b,c)) != meet(a,join(b,c)),
inference(rw,[status(thm)],[goal_0,t97897]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT194-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 20:35:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.72/3.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.72/3.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------