%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL027+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:35:06 PM UTC 2026
% Result : Theorem 45.01s 6.23s
% Output : Proof 45.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 148
% Number of leaves : 14
% Syntax : Number of formulae : 676 ( 672 unt; 0 def)
% Number of atoms : 680 ( 679 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 858 ( 97 sgn 77 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f3_nnf,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t41,plain,
complement(join(complement(X1),complement(X2))) = meet(X1,X2),
inference(orient,[status(thm)],[t6]) ).
fof(f0,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f0_nnf,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t5,plain,
join(X1,X2) = join(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t19,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t43,plain,
meet(X1,X2) = complement(join(complement(X2),complement(X1))),
inference(cp,[status(thm)],[t41,t19]) ).
cnf(t112120,plain,
meet(X1,X2) = meet(X2,X1),
inference(step,[status(thm)],[t43,t41]) ).
cnf(t71,plain,
meet(X1,X2) = meet(X2,X1),
inference(orient,[status(thm)],[t112120]) ).
fof(f1,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f1_nnf,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t10,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
fof(f10,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f10_nnf,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t12,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t112117,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t12,t19]) ).
cnf(t30,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t112117]) ).
fof(f9,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f9_nnf,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t7,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t53,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t7]) ).
fof(f7,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f7_nnf,plain,
! [X0] : converse(converse(X0)) = X0,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X0] : converse(converse(X0)) = X0,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
converse(converse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t1,plain,
converse(converse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t18,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t55,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t53,t18]) ).
cnf(t148,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t55]) ).
fof(f5,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
fof(f5_nnf,plain,
! [X0] : composition(X0,one) = X0,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X0] : composition(X0,one) = X0,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
composition(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t0,plain,
composition(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t17,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t149,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t148,t17]) ).
cnf(t112124,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t149,t18]) ).
cnf(t163,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t112124]) ).
cnf(t164,plain,
one = converse(one),
inference(cp,[status(thm)],[t163,t17]) ).
cnf(t170,plain,
converse(one) = one,
inference(orient,[status(thm)],[t164]) ).
cnf(t112125,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t163,t170]) ).
cnf(t180,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t112125]) ).
cnf(t181,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t180]) ).
cnf(t184,plain,
complement(X1) = join(complement(X1),composition(converse(one),complement(X1))),
inference(cp,[status(thm)],[t30,t181]) ).
cnf(t112128,plain,
complement(X1) = join(complement(X1),composition(one,complement(X1))),
inference(step,[status(thm)],[t184,t170]) ).
cnf(t112129,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t112128,t181]) ).
cnf(t213,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t112129]) ).
cnf(t223,plain,
meet(X1,X1) = complement(complement(X1)),
inference(cp,[status(thm)],[t41,t213]) ).
cnf(t237,plain,
meet(X1,X1) = complement(complement(X1)),
inference(orient,[status(thm)],[t223]) ).
fof(f2,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f2_nnf,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t13,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t14,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t20,plain,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[t14]) ).
cnf(t112136,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t20,t19]) ).
cnf(t112137,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(step,[status(thm)],[t112136,t41]) ).
cnf(t112138,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(step,[status(thm)],[t112137,t19]) ).
cnf(t263,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(orient,[status(thm)],[t112138]) ).
fof(f12,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
fof(f12_nnf,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t4,plain,
meet(X1,complement(X1)) = zero,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t60,plain,
meet(X1,complement(X1)) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t264,plain,
X1 = join(zero,complement(join(complement(X1),complement(X1)))),
inference(cp,[status(thm)],[t263,t60]) ).
cnf(t112139,plain,
X1 = join(zero,meet(X1,X1)),
inference(step,[status(thm)],[t264,t41]) ).
cnf(t281,plain,
join(zero,meet(X1,X1)) = X1,
inference(orient,[status(thm)],[t112139]) ).
fof(f11,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
fof(f11_nnf,plain,
! [X0] : top = join(X0,complement(X0)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X0] : top = join(X0,complement(X0)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t3,plain,
join(X1,complement(X1)) = top,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t24,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t3]) ).
cnf(t42,plain,
meet(X1,complement(X1)) = complement(top),
inference(cp,[status(thm)],[t41,t24]) ).
cnf(t112118,plain,
zero = complement(top),
inference(step,[status(thm)],[t42,t60]) ).
cnf(t62,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t112118]) ).
cnf(t217,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t213,t62]) ).
cnf(t112130,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t217,t62]) ).
cnf(t112131,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t112130,t62]) ).
cnf(t224,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t112131]) ).
cnf(t225,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t21,t224]) ).
cnf(t247,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t225]) ).
cnf(t283,plain,
join(zero,meet(X1,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t247,t281]) ).
cnf(t112140,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t283,t281]) ).
cnf(t285,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t112140]) ).
cnf(t112141,plain,
meet(X1,X1) = X1,
inference(step,[status(thm)],[t281,t285]) ).
cnf(t292,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[t112141]) ).
cnf(t312,plain,
meet(X1,X1) = X1,
inference(orient,[status(thm)],[t292]) ).
cnf(t112148,plain,
X1 = complement(complement(X1)),
inference(step,[status(thm)],[t237,t312]) ).
cnf(t314,plain,
X1 = complement(complement(X1)),
inference(rw,[status(thm)],[t112148]) ).
cnf(t321,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t314]) ).
cnf(t323,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t213,t321]) ).
cnf(t112155,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t323,t321]) ).
cnf(t112156,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t112155,t321]) ).
cnf(t331,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t112156]) ).
cnf(t333,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t21,t331]) ).
cnf(t425,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t333]) ).
cnf(t429,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = join(meet(X1,X2),X1),
inference(cp,[status(thm)],[t425,t263]) ).
cnf(t112175,plain,
X1 = join(meet(X1,X2),X1),
inference(step,[status(thm)],[t429,t263]) ).
cnf(t112176,plain,
X1 = join(X1,meet(X1,X2)),
inference(step,[status(thm)],[t112175,t19]) ).
cnf(t467,plain,
join(X1,meet(X1,X2)) = X1,
inference(orient,[status(thm)],[t112176]) ).
cnf(t469,plain,
X1 = join(X1,meet(X2,X1)),
inference(cp,[status(thm)],[t467,t71]) ).
cnf(t474,plain,
join(X1,meet(X2,X1)) = X1,
inference(orient,[status(thm)],[t469]) ).
cnf(t477,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(cp,[status(thm)],[t21,t474]) ).
cnf(t1950,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(orient,[status(thm)],[t477]) ).
cnf(t322,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(cp,[status(thm)],[t321,t41]) ).
cnf(t757,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(orient,[status(thm)],[t322]) ).
cnf(t760,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(cp,[status(thm)],[t757,t321]) ).
cnf(t836,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(orient,[status(thm)],[t760]) ).
cnf(t842,plain,
meet(X1,complement(X2)) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t321,t836]) ).
cnf(t988,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t842]) ).
cnf(t112214,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(step,[status(thm)],[t263,t988]) ).
cnf(t1013,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[t112214]) ).
cnf(t4444,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(orient,[status(thm)],[t1013]) ).
cnf(t4506,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(cp,[status(thm)],[t1950,t4444]) ).
cnf(t4551,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(orient,[status(thm)],[t4506]) ).
cnf(t4560,plain,
join(X1,X2) = join(X1,meet(complement(X1),X2)),
inference(cp,[status(thm)],[t4551,t71]) ).
cnf(t4636,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(orient,[status(thm)],[t4560]) ).
cnf(t4647,plain,
join(complement(X1),X2) = join(complement(X1),meet(X1,X2)),
inference(cp,[status(thm)],[t4636,t321]) ).
cnf(t5739,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(orient,[status(thm)],[t4647]) ).
cnf(t759,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(cp,[status(thm)],[t757,t321]) ).
cnf(t820,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t759]) ).
cnf(t827,plain,
meet(complement(X1),X2) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t321,t820]) ).
cnf(t852,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t827]) ).
cnf(t865,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(cp,[status(thm)],[t852,t321]) ).
cnf(t1014,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(orient,[status(thm)],[t865]) ).
cnf(t4554,plain,
join(X1,complement(X2)) = join(X1,complement(join(X2,X1))),
inference(cp,[status(thm)],[t4551,t1014]) ).
cnf(t4787,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(orient,[status(thm)],[t4554]) ).
cnf(t4884,plain,
meet(X1,complement(complement(join(X2,complement(X1))))) = complement(join(complement(X1),complement(X2))),
inference(cp,[status(thm)],[t988,t4787]) ).
cnf(t112302,plain,
meet(X1,join(X2,complement(X1))) = complement(join(complement(X1),complement(X2))),
inference(step,[status(thm)],[t4884,t321]) ).
cnf(t112303,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(step,[status(thm)],[t112302,t41]) ).
cnf(t5152,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t112303]) ).
cnf(t5174,plain,
meet(X1,X2) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t5152,t19]) ).
cnf(t5192,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(orient,[status(thm)],[t5174]) ).
fof(f8,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
fof(f8_nnf,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t8,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t34,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t36,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t34,t18]) ).
cnf(t117,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t36]) ).
cnf(t118,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(cp,[status(thm)],[t117,t24]) ).
cnf(t428,plain,
join(X1,complement(X1)) = join(X1,top),
inference(cp,[status(thm)],[t425,t24]) ).
cnf(t112167,plain,
top = join(X1,top),
inference(step,[status(thm)],[t428,t24]) ).
cnf(t435,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t112167]) ).
cnf(t439,plain,
join(X1,converse(top)) = converse(top),
inference(cp,[status(thm)],[t117,t435]) ).
cnf(t454,plain,
join(X1,converse(top)) = converse(top),
inference(orient,[status(thm)],[t439]) ).
cnf(t436,plain,
top = join(top,X1),
inference(cp,[status(thm)],[t435,t19]) ).
cnf(t441,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t436]) ).
cnf(t455,plain,
converse(top) = top,
inference(cp,[status(thm)],[t454,t441]) ).
cnf(t459,plain,
converse(top) = top,
inference(orient,[status(thm)],[t455]) ).
cnf(t112215,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(step,[status(thm)],[t118,t459]) ).
cnf(t1028,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(orient,[status(thm)],[t112215]) ).
cnf(t5211,plain,
meet(X1,converse(complement(converse(complement(X1))))) = meet(X1,top),
inference(cp,[status(thm)],[t5192,t1028]) ).
cnf(t65,plain,
meet(top,X1) = complement(join(zero,complement(X1))),
inference(cp,[status(thm)],[t41,t62]) ).
cnf(t81,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(orient,[status(thm)],[t65]) ).
cnf(t112145,plain,
complement(complement(X1)) = meet(top,X1),
inference(step,[status(thm)],[t81,t285]) ).
cnf(t295,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[t112145]) ).
cnf(t112157,plain,
X1 = meet(top,X1),
inference(step,[status(thm)],[t295,t321]) ).
cnf(t334,plain,
meet(top,X1) = X1,
inference(orient,[status(thm)],[t112157]) ).
cnf(t335,plain,
X1 = meet(X1,top),
inference(cp,[status(thm)],[t334,t71]) ).
cnf(t336,plain,
meet(X1,top) = X1,
inference(orient,[status(thm)],[t335]) ).
cnf(t112305,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t5211,t336]) ).
cnf(t5260,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t112305]) ).
cnf(t5291,plain,
join(X1,complement(converse(complement(converse(complement(complement(X1))))))) = complement(complement(X1)),
inference(cp,[status(thm)],[t820,t5260]) ).
cnf(t112306,plain,
join(X1,complement(converse(complement(converse(X1))))) = complement(complement(X1)),
inference(step,[status(thm)],[t5291,t321]) ).
cnf(t112307,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(step,[status(thm)],[t112306,t321]) ).
cnf(t5297,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(orient,[status(thm)],[t112307]) ).
cnf(t5343,plain,
join(X1,converse(complement(converse(complement(converse(converse(X1))))))) = converse(converse(X1)),
inference(cp,[status(thm)],[t117,t5297]) ).
cnf(t112308,plain,
join(X1,converse(complement(converse(complement(X1))))) = converse(converse(X1)),
inference(step,[status(thm)],[t5343,t18]) ).
cnf(t112309,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(step,[status(thm)],[t112308,t18]) ).
cnf(t5351,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(orient,[status(thm)],[t112309]) ).
cnf(t5373,plain,
meet(X1,converse(complement(converse(complement(complement(X1)))))) = meet(X1,complement(X1)),
inference(cp,[status(thm)],[t5192,t5351]) ).
cnf(t112310,plain,
meet(X1,converse(complement(converse(X1)))) = meet(X1,complement(X1)),
inference(step,[status(thm)],[t5373,t321]) ).
cnf(t112311,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(step,[status(thm)],[t112310,t60]) ).
cnf(t5392,plain,
meet(X1,converse(complement(converse(X1)))) = zero,
inference(orient,[status(thm)],[t112311]) ).
cnf(t5405,plain,
zero = meet(converse(X1),converse(complement(X1))),
inference(cp,[status(thm)],[t5392,t18]) ).
cnf(t5415,plain,
meet(converse(X1),converse(complement(X1))) = zero,
inference(orient,[status(thm)],[t5405]) ).
cnf(t5766,plain,
join(complement(converse(X1)),converse(complement(X1))) = join(complement(converse(X1)),zero),
inference(cp,[status(thm)],[t5739,t5415]) ).
cnf(t112354,plain,
join(converse(complement(X1)),complement(converse(X1))) = join(complement(converse(X1)),zero),
inference(step,[status(thm)],[t5766,t19]) ).
cnf(t287,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t285,t19]) ).
cnf(t308,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t287]) ).
cnf(t112355,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(step,[status(thm)],[t112354,t308]) ).
cnf(t6756,plain,
join(converse(complement(X1)),complement(converse(X1))) = complement(converse(X1)),
inference(orient,[status(thm)],[t112355]) ).
cnf(t6761,plain,
complement(converse(complement(X1))) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t6756,t321]) ).
cnf(t5310,plain,
converse(X1) = join(converse(X1),complement(converse(complement(X1)))),
inference(cp,[status(thm)],[t5297,t18]) ).
cnf(t6175,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(orient,[status(thm)],[t5310]) ).
cnf(t112356,plain,
complement(converse(complement(X1))) = converse(X1),
inference(step,[status(thm)],[t6761,t6175]) ).
cnf(t6795,plain,
complement(converse(complement(X1))) = converse(X1),
inference(orient,[status(thm)],[t112356]) ).
cnf(t6800,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(cp,[status(thm)],[t6795,t321]) ).
cnf(t6840,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(orient,[status(thm)],[t6800]) ).
cnf(t22,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(cp,[status(thm)],[t21,t19]) ).
cnf(t563,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(orient,[status(thm)],[t22]) ).
cnf(t575,plain,
join(complement(X1),join(X2,X1)) = join(X2,top),
inference(cp,[status(thm)],[t563,t24]) ).
cnf(t112190,plain,
join(X1,join(complement(X1),X2)) = join(X2,top),
inference(step,[status(thm)],[t575,t563]) ).
cnf(t112191,plain,
join(X1,join(complement(X1),X2)) = top,
inference(step,[status(thm)],[t112190,t435]) ).
cnf(t652,plain,
join(X1,join(complement(X1),X2)) = top,
inference(orient,[status(thm)],[t112191]) ).
cnf(t654,plain,
top = join(X1,join(X2,complement(X1))),
inference(cp,[status(thm)],[t652,t19]) ).
cnf(t744,plain,
join(X1,join(X2,complement(X1))) = top,
inference(orient,[status(thm)],[t654]) ).
cnf(t765,plain,
top = join(X1,complement(meet(X2,X1))),
inference(cp,[status(thm)],[t744,t757]) ).
cnf(t772,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(orient,[status(thm)],[t765]) ).
cnf(t854,plain,
meet(complement(X1),meet(X2,X1)) = complement(top),
inference(cp,[status(thm)],[t852,t772]) ).
cnf(t112206,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(step,[status(thm)],[t854,t62]) ).
cnf(t883,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(orient,[status(thm)],[t112206]) ).
cnf(t662,plain,
X1 = join(meet(X1,join(complement(complement(X1)),X2)),complement(top)),
inference(cp,[status(thm)],[t263,t652]) ).
cnf(t112192,plain,
X1 = join(complement(top),meet(X1,join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t662,t19]) ).
cnf(t112193,plain,
X1 = join(zero,meet(X1,join(complement(complement(X1)),X2))),
inference(step,[status(thm)],[t112192,t62]) ).
cnf(t112194,plain,
X1 = meet(X1,join(complement(complement(X1)),X2)),
inference(step,[status(thm)],[t112193,t285]) ).
cnf(t112195,plain,
X1 = meet(X1,join(X1,X2)),
inference(step,[status(thm)],[t112194,t321]) ).
cnf(t664,plain,
meet(X1,join(X1,X2)) = X1,
inference(orient,[status(thm)],[t112195]) ).
cnf(t892,plain,
zero = meet(complement(join(X1,X2)),X1),
inference(cp,[status(thm)],[t883,t664]) ).
cnf(t112210,plain,
zero = meet(X1,complement(join(X1,X2))),
inference(step,[status(thm)],[t892,t71]) ).
cnf(t935,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(orient,[status(thm)],[t112210]) ).
cnf(t940,plain,
zero = meet(converse(X1),complement(converse(join(X1,X2)))),
inference(cp,[status(thm)],[t935,t34]) ).
cnf(t4145,plain,
meet(converse(X1),complement(converse(join(X1,X2)))) = zero,
inference(orient,[status(thm)],[t940]) ).
cnf(t173,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(cp,[status(thm)],[t34,t170]) ).
cnf(t185,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(orient,[status(thm)],[t173]) ).
cnf(t186,plain,
join(one,converse(complement(one))) = converse(top),
inference(cp,[status(thm)],[t185,t24]) ).
cnf(t228,plain,
join(one,converse(complement(one))) = converse(top),
inference(orient,[status(thm)],[t186]) ).
cnf(t112173,plain,
join(one,converse(complement(one))) = top,
inference(step,[status(thm)],[t228,t459]) ).
cnf(t460,plain,
join(one,converse(complement(one))) = top,
inference(orient,[status(thm)],[t112173]) ).
cnf(t4845,plain,
join(converse(complement(one)),complement(one)) = join(converse(complement(one)),complement(top)),
inference(cp,[status(thm)],[t4787,t460]) ).
cnf(t112288,plain,
join(complement(one),converse(complement(one))) = join(converse(complement(one)),complement(top)),
inference(step,[status(thm)],[t4845,t19]) ).
cnf(t112289,plain,
join(complement(one),converse(complement(one))) = join(complement(top),converse(complement(one))),
inference(step,[status(thm)],[t112288,t19]) ).
cnf(t112290,plain,
join(complement(one),converse(complement(one))) = join(zero,converse(complement(one))),
inference(step,[status(thm)],[t112289,t62]) ).
cnf(t112291,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(step,[status(thm)],[t112290,t285]) ).
cnf(t4893,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(orient,[status(thm)],[t112291]) ).
cnf(t4911,plain,
zero = meet(converse(complement(one)),complement(converse(converse(complement(one))))),
inference(cp,[status(thm)],[t4145,t4893]) ).
cnf(t112292,plain,
zero = meet(converse(complement(one)),complement(complement(one))),
inference(step,[status(thm)],[t4911,t18]) ).
cnf(t112293,plain,
zero = meet(converse(complement(one)),one),
inference(step,[status(thm)],[t112292,t321]) ).
cnf(t112294,plain,
zero = meet(one,converse(complement(one))),
inference(step,[status(thm)],[t112293,t71]) ).
cnf(t4915,plain,
meet(one,converse(complement(one))) = zero,
inference(orient,[status(thm)],[t112294]) ).
cnf(t4917,plain,
one = join(zero,meet(one,complement(converse(complement(one))))),
inference(cp,[status(thm)],[t4444,t4915]) ).
cnf(t112295,plain,
one = meet(one,complement(converse(complement(one)))),
inference(step,[status(thm)],[t4917,t285]) ).
cnf(t4920,plain,
meet(one,complement(converse(complement(one)))) = one,
inference(orient,[status(thm)],[t112295]) ).
cnf(t4938,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(cp,[status(thm)],[t836,t4920]) ).
cnf(t112296,plain,
converse(complement(one)) = complement(one),
inference(step,[status(thm)],[t4938,t4893]) ).
cnf(t4941,plain,
converse(complement(one)) = complement(one),
inference(orient,[status(thm)],[t112296]) ).
cnf(t4945,plain,
converse(join(X1,complement(one))) = join(converse(X1),complement(one)),
inference(cp,[status(thm)],[t34,t4941]) ).
cnf(t5056,plain,
converse(join(X1,complement(one))) = join(converse(X1),complement(one)),
inference(orient,[status(thm)],[t4945]) ).
cnf(t6841,plain,
converse(complement(join(X1,complement(one)))) = complement(join(converse(X1),complement(one))),
inference(cp,[status(thm)],[t6840,t5056]) ).
cnf(t112368,plain,
converse(meet(complement(X1),one)) = complement(join(converse(X1),complement(one))),
inference(step,[status(thm)],[t6841,t852]) ).
cnf(t112369,plain,
converse(meet(one,complement(X1))) = complement(join(converse(X1),complement(one))),
inference(step,[status(thm)],[t112368,t71]) ).
cnf(t112370,plain,
converse(meet(one,complement(X1))) = meet(complement(converse(X1)),one),
inference(step,[status(thm)],[t112369,t852]) ).
cnf(t112371,plain,
converse(meet(one,complement(X1))) = meet(one,complement(converse(X1))),
inference(step,[status(thm)],[t112370,t71]) ).
cnf(t112372,plain,
converse(meet(one,complement(X1))) = meet(one,converse(complement(X1))),
inference(step,[status(thm)],[t112371,t6840]) ).
cnf(t6887,plain,
converse(meet(one,complement(X1))) = meet(one,converse(complement(X1))),
inference(orient,[status(thm)],[t112372]) ).
cnf(t6899,plain,
meet(one,converse(complement(complement(X1)))) = converse(meet(one,X1)),
inference(cp,[status(thm)],[t6887,t321]) ).
cnf(t112373,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(step,[status(thm)],[t6899,t321]) ).
cnf(t6921,plain,
converse(meet(one,X1)) = meet(one,converse(X1)),
inference(orient,[status(thm)],[t112373]) ).
cnf(t4676,plain,
meet(X1,complement(meet(complement(complement(X1)),X2))) = complement(join(complement(X1),X2)),
inference(cp,[status(thm)],[t988,t4636]) ).
cnf(t112319,plain,
meet(X1,join(complement(X1),complement(X2))) = complement(join(complement(X1),X2)),
inference(step,[status(thm)],[t4676,t820]) ).
cnf(t112320,plain,
meet(X1,complement(meet(X1,X2))) = complement(join(complement(X1),X2)),
inference(step,[status(thm)],[t112319,t757]) ).
cnf(t112321,plain,
meet(X1,complement(meet(X1,X2))) = meet(X1,complement(X2)),
inference(step,[status(thm)],[t112320,t988]) ).
cnf(t5808,plain,
meet(X1,complement(meet(X1,X2))) = meet(X1,complement(X2)),
inference(orient,[status(thm)],[t112321]) ).
cnf(t6927,plain,
meet(one,converse(complement(meet(one,X1)))) = converse(meet(one,complement(X1))),
inference(cp,[status(thm)],[t6921,t5808]) ).
cnf(t112565,plain,
meet(one,converse(complement(meet(one,X1)))) = meet(one,converse(complement(X1))),
inference(step,[status(thm)],[t6927,t6887]) ).
cnf(t20913,plain,
meet(one,converse(complement(meet(one,X1)))) = meet(one,converse(complement(X1))),
inference(orient,[status(thm)],[t112565]) ).
cnf(t5225,plain,
meet(complement(X1),X2) = meet(complement(X1),join(X1,X2)),
inference(cp,[status(thm)],[t5192,t321]) ).
cnf(t5986,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t5225]) ).
cnf(t432,plain,
join(X1,X2) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t425,t19]) ).
cnf(t500,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(orient,[status(thm)],[t432]) ).
cnf(t510,plain,
join(X1,join(join(X2,X1),X3)) = join(join(X1,X2),X3),
inference(cp,[status(thm)],[t21,t500]) ).
cnf(t112539,plain,
join(X1,join(X2,join(X1,X3))) = join(join(X1,X2),X3),
inference(step,[status(thm)],[t510,t21]) ).
cnf(t112540,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(step,[status(thm)],[t112539,t21]) ).
cnf(t18812,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t112540]) ).
fof(f6,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
fof(f6_nnf,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t11,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t27,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
cnf(t57,plain,
composition(join(converse(X1),X2),converse(X3)) = join(converse(composition(X3,X1)),composition(X2,converse(X3))),
inference(cp,[status(thm)],[t27,t53]) ).
cnf(t32985,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(orient,[status(thm)],[t57]) ).
cnf(t32989,plain,
composition(join(converse(one),X1),converse(X2)) = join(converse(X2),composition(X1,converse(X2))),
inference(cp,[status(thm)],[t32985,t17]) ).
cnf(t113089,plain,
composition(join(one,X1),converse(X2)) = join(converse(X2),composition(X1,converse(X2))),
inference(step,[status(thm)],[t32989,t170]) ).
cnf(t76667,plain,
join(converse(X1),composition(X2,converse(X1))) = composition(join(one,X2),converse(X1)),
inference(orient,[status(thm)],[t113089]) ).
cnf(t6938,plain,
converse(composition(X1,meet(one,X2))) = composition(meet(one,converse(X2)),converse(X1)),
inference(cp,[status(thm)],[t53,t6921]) ).
cnf(t70296,plain,
composition(meet(one,converse(X1)),converse(X2)) = converse(composition(X2,meet(one,X1))),
inference(orient,[status(thm)],[t6938]) ).
cnf(t76719,plain,
composition(join(one,meet(one,converse(X1))),converse(X2)) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(cp,[status(thm)],[t76667,t70296]) ).
cnf(t113090,plain,
composition(one,converse(X2)) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t76719,t467]) ).
cnf(t113091,plain,
converse(X2) = join(converse(X2),converse(composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t113090,t181]) ).
cnf(t113092,plain,
converse(X2) = converse(join(X2,composition(X2,meet(one,X1)))),
inference(step,[status(thm)],[t113091,t34]) ).
cnf(t76872,plain,
converse(join(X1,composition(X1,meet(one,X2)))) = converse(X1),
inference(orient,[status(thm)],[t113092]) ).
cnf(t6939,plain,
converse(composition(meet(one,X1),X2)) = composition(converse(X2),meet(one,converse(X1))),
inference(cp,[status(thm)],[t53,t6921]) ).
cnf(t70407,plain,
composition(converse(X1),meet(one,converse(X2))) = converse(composition(meet(one,X2),X1)),
inference(orient,[status(thm)],[t6939]) ).
cnf(t76880,plain,
converse(converse(X1)) = converse(join(converse(X1),converse(composition(meet(one,X2),X1)))),
inference(cp,[status(thm)],[t76872,t70407]) ).
cnf(t113093,plain,
X1 = converse(join(converse(X1),converse(composition(meet(one,X2),X1)))),
inference(step,[status(thm)],[t76880,t18]) ).
cnf(t113094,plain,
X1 = join(X1,converse(converse(composition(meet(one,X2),X1)))),
inference(step,[status(thm)],[t113093,t117]) ).
cnf(t113095,plain,
X1 = join(X1,composition(meet(one,X2),X1)),
inference(step,[status(thm)],[t113094,t18]) ).
cnf(t77040,plain,
join(X1,composition(meet(one,X2),X1)) = X1,
inference(orient,[status(thm)],[t113095]) ).
cnf(t672,plain,
X1 = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t664,t19]) ).
cnf(t688,plain,
meet(X1,join(X2,X1)) = X1,
inference(orient,[status(thm)],[t672]) ).
cnf(t174,plain,
converse(join(X1,one)) = join(converse(X1),one),
inference(cp,[status(thm)],[t34,t170]) ).
cnf(t112126,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(step,[status(thm)],[t174,t19]) ).
cnf(t195,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(orient,[status(thm)],[t112126]) ).
fof(f13,conjecture,
! [X0] :
( join(X0,one) = one
=> meet(complement(composition(X0,top)),one) = meet(complement(X0),one) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13_neg,negated_conjecture,
~ ! [X0] :
( join(X0,one) = one
=> meet(complement(composition(X0,top)),one) = meet(complement(X0),one) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [X0] :
( meet(complement(composition(X0,top)),one) != meet(complement(X0),one)
& join(X0,one) = one ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( meet(complement(composition(sk0,top)),one) != meet(complement(sk0),one)
& join(sk0,one) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f13_nnf]) ).
cnf(c13,plain,
join(sk0,one) = one,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t2,plain,
join(sk0,one) = one,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t39,plain,
join(sk0,one) = one,
inference(orient,[status(thm)],[t2]) ).
cnf(t197,plain,
join(one,converse(sk0)) = converse(one),
inference(cp,[status(thm)],[t195,t39]) ).
cnf(t112127,plain,
join(one,converse(sk0)) = one,
inference(step,[status(thm)],[t197,t170]) ).
cnf(t209,plain,
join(one,converse(sk0)) = one,
inference(orient,[status(thm)],[t112127]) ).
cnf(t700,plain,
converse(sk0) = meet(converse(sk0),one),
inference(cp,[status(thm)],[t688,t209]) ).
cnf(t112196,plain,
converse(sk0) = meet(one,converse(sk0)),
inference(step,[status(thm)],[t700,t71]) ).
cnf(t709,plain,
meet(one,converse(sk0)) = converse(sk0),
inference(orient,[status(thm)],[t112196]) ).
cnf(t77051,plain,
X1 = join(X1,composition(converse(sk0),X1)),
inference(cp,[status(thm)],[t77040,t709]) ).
cnf(t77174,plain,
join(X1,composition(converse(sk0),X1)) = X1,
inference(orient,[status(thm)],[t77051]) ).
cnf(t77239,plain,
join(X1,converse(composition(converse(sk0),converse(X1)))) = converse(converse(X1)),
inference(cp,[status(thm)],[t117,t77174]) ).
cnf(t113096,plain,
join(X1,composition(converse(converse(X1)),sk0)) = converse(converse(X1)),
inference(step,[status(thm)],[t77239,t148]) ).
cnf(t113097,plain,
join(X1,composition(X1,sk0)) = converse(converse(X1)),
inference(step,[status(thm)],[t113096,t18]) ).
cnf(t113098,plain,
join(X1,composition(X1,sk0)) = X1,
inference(step,[status(thm)],[t113097,t18]) ).
cnf(t77290,plain,
join(X1,composition(X1,sk0)) = X1,
inference(orient,[status(thm)],[t113098]) ).
cnf(t77326,plain,
join(X1,join(X2,composition(X1,sk0))) = join(X1,join(X2,X1)),
inference(cp,[status(thm)],[t18812,t77290]) ).
cnf(t113246,plain,
join(X1,join(X2,composition(X1,sk0))) = join(X1,X2),
inference(step,[status(thm)],[t77326,t500]) ).
cnf(t86175,plain,
join(X1,join(X2,composition(X1,sk0))) = join(X1,X2),
inference(orient,[status(thm)],[t113246]) ).
cnf(t182,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(cp,[status(thm)],[t27,t181]) ).
cnf(t105649,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(orient,[status(thm)],[t182]) ).
cnf(t106024,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(cp,[status(thm)],[t105649,t24]) ).
cnf(t106470,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(orient,[status(thm)],[t106024]) ).
cnf(t106498,plain,
join(complement(one),sk0) = join(complement(one),composition(top,sk0)),
inference(cp,[status(thm)],[t86175,t106470]) ).
cnf(t113423,plain,
join(sk0,complement(one)) = join(complement(one),composition(top,sk0)),
inference(step,[status(thm)],[t106498,t19]) ).
cnf(t107194,plain,
join(complement(one),composition(top,sk0)) = join(sk0,complement(one)),
inference(orient,[status(thm)],[t113423]) ).
cnf(t107199,plain,
meet(complement(complement(one)),composition(top,sk0)) = meet(complement(complement(one)),join(sk0,complement(one))),
inference(cp,[status(thm)],[t5986,t107194]) ).
cnf(t113451,plain,
meet(composition(top,sk0),complement(complement(one))) = meet(complement(complement(one)),join(sk0,complement(one))),
inference(step,[status(thm)],[t107199,t71]) ).
cnf(t113452,plain,
meet(composition(top,sk0),one) = meet(complement(complement(one)),join(sk0,complement(one))),
inference(step,[status(thm)],[t113451,t321]) ).
cnf(t113453,plain,
meet(one,composition(top,sk0)) = meet(complement(complement(one)),join(sk0,complement(one))),
inference(step,[status(thm)],[t113452,t71]) ).
cnf(t4885,plain,
meet(complement(X1),join(X2,X1)) = complement(join(X1,complement(X2))),
inference(cp,[status(thm)],[t852,t4787]) ).
cnf(t112323,plain,
meet(complement(X1),join(X2,X1)) = meet(complement(X1),X2),
inference(step,[status(thm)],[t4885,t852]) ).
cnf(t5868,plain,
meet(complement(X1),join(X2,X1)) = meet(complement(X1),X2),
inference(orient,[status(thm)],[t112323]) ).
cnf(t113454,plain,
meet(one,composition(top,sk0)) = meet(complement(complement(one)),sk0),
inference(step,[status(thm)],[t113453,t5868]) ).
cnf(t113455,plain,
meet(one,composition(top,sk0)) = meet(sk0,complement(complement(one))),
inference(step,[status(thm)],[t113454,t71]) ).
cnf(t113456,plain,
meet(one,composition(top,sk0)) = meet(sk0,one),
inference(step,[status(thm)],[t113455,t321]) ).
cnf(t666,plain,
sk0 = meet(sk0,one),
inference(cp,[status(thm)],[t664,t39]) ).
cnf(t677,plain,
meet(sk0,one) = sk0,
inference(orient,[status(thm)],[t666]) ).
cnf(t113457,plain,
meet(one,composition(top,sk0)) = sk0,
inference(step,[status(thm)],[t113456,t677]) ).
cnf(t108834,plain,
meet(one,composition(top,sk0)) = sk0,
inference(orient,[status(thm)],[t113457]) ).
cnf(t108889,plain,
meet(one,converse(complement(composition(top,sk0)))) = meet(one,converse(complement(sk0))),
inference(cp,[status(thm)],[t20913,t108834]) ).
cnf(t463,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(cp,[status(thm)],[t53,t459]) ).
cnf(t491,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(orient,[status(thm)],[t463]) ).
cnf(t6850,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(cp,[status(thm)],[t6840,t117]) ).
cnf(t7360,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(orient,[status(thm)],[t6850]) ).
cnf(t6861,plain,
complement(meet(converse(X1),X2)) = join(converse(complement(X1)),complement(X2)),
inference(cp,[status(thm)],[t757,t6840]) ).
cnf(t7571,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(orient,[status(thm)],[t6861]) ).
cnf(t7613,plain,
complement(join(complement(X1),converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(cp,[status(thm)],[t7360,t7571]) ).
cnf(t112385,plain,
meet(X1,complement(converse(complement(X2)))) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t7613,t988]) ).
cnf(t112386,plain,
meet(X1,converse(X2)) = converse(complement(complement(meet(converse(X1),X2)))),
inference(step,[status(thm)],[t112385,t6795]) ).
cnf(t112387,plain,
meet(X1,converse(X2)) = converse(meet(converse(X1),X2)),
inference(step,[status(thm)],[t112386,t321]) ).
cnf(t7621,plain,
converse(meet(converse(X1),X2)) = meet(X1,converse(X2)),
inference(orient,[status(thm)],[t112387]) ).
cnf(t7643,plain,
meet(composition(top,X1),converse(X2)) = converse(meet(composition(converse(X1),top),X2)),
inference(cp,[status(thm)],[t7621,t491]) ).
cnf(t72015,plain,
converse(meet(composition(converse(X1),top),X2)) = meet(composition(top,X1),converse(X2)),
inference(orient,[status(thm)],[t7643]) ).
cnf(t4478,plain,
X1 = join(meet(X1,X2),meet(complement(X2),X1)),
inference(cp,[status(thm)],[t4444,t71]) ).
cnf(t12109,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(orient,[status(thm)],[t4478]) ).
cnf(t893,plain,
zero = meet(complement(join(X1,X2)),X2),
inference(cp,[status(thm)],[t883,t688]) ).
cnf(t112211,plain,
zero = meet(X2,complement(join(X1,X2))),
inference(step,[status(thm)],[t893,t71]) ).
cnf(t947,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(orient,[status(thm)],[t112211]) ).
cnf(t951,plain,
zero = meet(composition(converse(X1),complement(composition(X1,X2))),complement(complement(X2))),
inference(cp,[status(thm)],[t947,t30]) ).
cnf(t112685,plain,
zero = meet(complement(complement(X2)),composition(converse(X1),complement(composition(X1,X2)))),
inference(step,[status(thm)],[t951,t71]) ).
cnf(t112686,plain,
zero = meet(X2,composition(converse(X1),complement(composition(X1,X2)))),
inference(step,[status(thm)],[t112685,t321]) ).
cnf(t31710,plain,
meet(X1,composition(converse(X2),complement(composition(X2,X1)))) = zero,
inference(orient,[status(thm)],[t112686]) ).
cnf(t31,plain,
complement(X1) = join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))),
inference(cp,[status(thm)],[t30,t18]) ).
cnf(t6302,plain,
join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t6308,plain,
complement(top) = join(zero,composition(X1,complement(composition(converse(X1),top)))),
inference(cp,[status(thm)],[t6302,t62]) ).
cnf(t112327,plain,
zero = join(zero,composition(X1,complement(composition(converse(X1),top)))),
inference(step,[status(thm)],[t6308,t62]) ).
cnf(t112328,plain,
zero = composition(X1,complement(composition(converse(X1),top))),
inference(step,[status(thm)],[t112327,t285]) ).
cnf(t6354,plain,
composition(X1,complement(composition(converse(X1),top))) = zero,
inference(orient,[status(thm)],[t112328]) ).
cnf(t6382,plain,
composition(converse(complement(composition(converse(converse(X1)),top))),X1) = converse(zero),
inference(cp,[status(thm)],[t148,t6354]) ).
cnf(t112342,plain,
composition(converse(complement(composition(X1,top))),X1) = converse(zero),
inference(step,[status(thm)],[t6382,t18]) ).
cnf(t37,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(cp,[status(thm)],[t34,t18]) ).
cnf(t126,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t291,plain,
join(converse(zero),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t126,t285]) ).
cnf(t112159,plain,
join(converse(zero),X1) = X1,
inference(step,[status(thm)],[t291,t18]) ).
cnf(t340,plain,
join(converse(zero),X1) = X1,
inference(orient,[status(thm)],[t112159]) ).
cnf(t342,plain,
zero = converse(zero),
inference(cp,[status(thm)],[t340,t308]) ).
cnf(t345,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t342]) ).
cnf(t112343,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(step,[status(thm)],[t112342,t345]) ).
cnf(t6465,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(orient,[status(thm)],[t112343]) ).
cnf(t31758,plain,
zero = meet(X1,composition(converse(converse(complement(composition(X1,top)))),complement(zero))),
inference(cp,[status(thm)],[t31710,t6465]) ).
cnf(t112687,plain,
zero = meet(X1,composition(complement(composition(X1,top)),complement(zero))),
inference(step,[status(thm)],[t31758,t18]) ).
cnf(t286,plain,
complement(zero) = top,
inference(cp,[status(thm)],[t285,t24]) ).
cnf(t296,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t286]) ).
cnf(t112688,plain,
zero = meet(X1,composition(complement(composition(X1,top)),top)),
inference(step,[status(thm)],[t112687,t296]) ).
cnf(t31860,plain,
meet(X1,composition(complement(composition(X1,top)),top)) = zero,
inference(orient,[status(thm)],[t112688]) ).
cnf(t31878,plain,
X1 = join(zero,meet(complement(composition(complement(composition(X1,top)),top)),X1)),
inference(cp,[status(thm)],[t12109,t31860]) ).
cnf(t112843,plain,
X1 = meet(complement(composition(complement(composition(X1,top)),top)),X1),
inference(step,[status(thm)],[t31878,t285]) ).
cnf(t112844,plain,
X1 = meet(X1,complement(composition(complement(composition(X1,top)),top))),
inference(step,[status(thm)],[t112843,t71]) ).
cnf(t40937,plain,
meet(X1,complement(composition(complement(composition(X1,top)),top))) = X1,
inference(orient,[status(thm)],[t112844]) ).
cnf(t72064,plain,
meet(composition(top,X1),converse(complement(composition(complement(composition(composition(converse(X1),top),top)),top)))) = converse(composition(converse(X1),top)),
inference(cp,[status(thm)],[t72015,t40937]) ).
fof(f4,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
fof(f4_nnf,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t9,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t48,plain,
composition(composition(X1,X2),X3) = composition(X1,composition(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t113071,plain,
meet(composition(top,X1),converse(complement(composition(complement(composition(converse(X1),composition(top,top))),top)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t72064,t48]) ).
cnf(t6363,plain,
zero = composition(top,complement(composition(top,top))),
inference(cp,[status(thm)],[t6354,t459]) ).
cnf(t6383,plain,
composition(top,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t6363]) ).
cnf(t6386,plain,
composition(join(top,X1),complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(cp,[status(thm)],[t27,t6383]) ).
cnf(t112329,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t6386,t441]) ).
cnf(t112330,plain,
zero = join(zero,composition(X1,complement(composition(top,top)))),
inference(step,[status(thm)],[t112329,t6383]) ).
cnf(t112331,plain,
zero = composition(X1,complement(composition(top,top))),
inference(step,[status(thm)],[t112330,t285]) ).
cnf(t6393,plain,
composition(X1,complement(composition(top,top))) = zero,
inference(orient,[status(thm)],[t112331]) ).
cnf(t6394,plain,
zero = complement(composition(top,top)),
inference(cp,[status(thm)],[t6393,t181]) ).
cnf(t6412,plain,
complement(composition(top,top)) = zero,
inference(orient,[status(thm)],[t6394]) ).
cnf(t6419,plain,
composition(top,top) = complement(zero),
inference(cp,[status(thm)],[t321,t6412]) ).
cnf(t112341,plain,
composition(top,top) = top,
inference(step,[status(thm)],[t6419,t296]) ).
cnf(t6437,plain,
composition(top,top) = top,
inference(orient,[status(thm)],[t112341]) ).
cnf(t113072,plain,
meet(composition(top,X1),converse(complement(composition(complement(composition(converse(X1),top)),top)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t113071,t6437]) ).
cnf(t6845,plain,
converse(complement(composition(top,X1))) = complement(composition(converse(X1),top)),
inference(cp,[status(thm)],[t6840,t491]) ).
cnf(t6979,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))),
inference(orient,[status(thm)],[t6845]) ).
cnf(t113073,plain,
meet(composition(top,X1),converse(complement(composition(converse(complement(composition(top,X1))),top)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t113072,t6979]) ).
cnf(t113074,plain,
meet(composition(top,X1),converse(converse(complement(composition(top,complement(composition(top,X1))))))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t113073,t6979]) ).
cnf(t113075,plain,
meet(composition(top,X1),complement(composition(top,complement(composition(top,X1))))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t113074,t18]) ).
cnf(t462,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t53,t459]) ).
cnf(t480,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t462]) ).
cnf(t488,plain,
join(converse(X1),composition(X2,top)) = converse(join(X1,composition(top,converse(X2)))),
inference(cp,[status(thm)],[t126,t480]) ).
cnf(t43349,plain,
converse(join(X1,composition(top,converse(X2)))) = join(converse(X1),composition(X2,top)),
inference(orient,[status(thm)],[t488]) ).
cnf(t43350,plain,
join(converse(converse(composition(X1,X2))),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(cp,[status(thm)],[t43349,t32985]) ).
cnf(t112871,plain,
join(composition(X1,X2),composition(X1,top)) = converse(composition(join(converse(X2),top),converse(X1))),
inference(step,[status(thm)],[t43350,t18]) ).
cnf(t122,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(cp,[status(thm)],[t53,t117]) ).
cnf(t42056,plain,
converse(composition(join(converse(X1),X2),X3)) = composition(converse(X3),join(X1,converse(X2))),
inference(orient,[status(thm)],[t122]) ).
cnf(t112872,plain,
join(composition(X1,X2),composition(X1,top)) = composition(converse(converse(X1)),join(X2,converse(top))),
inference(step,[status(thm)],[t112871,t42056]) ).
cnf(t112873,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,join(X2,converse(top))),
inference(step,[status(thm)],[t112872,t18]) ).
cnf(t112874,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,converse(top)),
inference(step,[status(thm)],[t112873,t454]) ).
cnf(t112875,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(step,[status(thm)],[t112874,t459]) ).
cnf(t43479,plain,
join(composition(X1,X2),composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t112875]) ).
cnf(t43482,plain,
composition(X1,top) = join(X1,composition(X1,top)),
inference(cp,[status(thm)],[t43479,t17]) ).
cnf(t43524,plain,
join(X1,composition(X1,top)) = composition(X1,top),
inference(orient,[status(thm)],[t43482]) ).
cnf(t43558,plain,
join(X1,converse(composition(converse(X1),top))) = converse(composition(converse(X1),top)),
inference(cp,[status(thm)],[t117,t43524]) ).
cnf(t112879,plain,
join(X1,composition(converse(top),X1)) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t43558,t148]) ).
cnf(t112880,plain,
join(X1,composition(top,X1)) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t112879,t459]) ).
cnf(t112881,plain,
join(X1,composition(top,X1)) = composition(converse(top),X1),
inference(step,[status(thm)],[t112880,t148]) ).
cnf(t112882,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(step,[status(thm)],[t112881,t459]) ).
cnf(t43823,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(orient,[status(thm)],[t112882]) ).
cnf(t43846,plain,
meet(X1,complement(composition(top,complement(X1)))) = complement(composition(top,complement(X1))),
inference(cp,[status(thm)],[t988,t43823]) ).
cnf(t54261,plain,
meet(X1,complement(composition(top,complement(X1)))) = complement(composition(top,complement(X1))),
inference(orient,[status(thm)],[t43846]) ).
cnf(t113076,plain,
complement(composition(top,complement(composition(top,X1)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t113075,t54261]) ).
cnf(t113077,plain,
complement(composition(top,complement(composition(top,X1)))) = composition(converse(top),X1),
inference(step,[status(thm)],[t113076,t148]) ).
cnf(t113078,plain,
complement(composition(top,complement(composition(top,X1)))) = composition(top,X1),
inference(step,[status(thm)],[t113077,t459]) ).
cnf(t72277,plain,
complement(composition(top,complement(composition(top,X1)))) = composition(top,X1),
inference(orient,[status(thm)],[t113078]) ).
cnf(t72287,plain,
composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
inference(cp,[status(thm)],[t321,t72277]) ).
cnf(t72419,plain,
composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
inference(orient,[status(thm)],[t72287]) ).
cnf(t6846,plain,
converse(complement(composition(X1,top))) = complement(composition(top,converse(X1))),
inference(cp,[status(thm)],[t6840,t480]) ).
cnf(t7031,plain,
complement(composition(top,converse(X1))) = converse(complement(composition(X1,top))),
inference(orient,[status(thm)],[t6846]) ).
cnf(t72420,plain,
complement(composition(top,converse(X1))) = composition(top,converse(complement(composition(X1,top)))),
inference(cp,[status(thm)],[t72419,t7031]) ).
cnf(t113079,plain,
converse(complement(composition(X1,top))) = composition(top,converse(complement(composition(X1,top)))),
inference(step,[status(thm)],[t72420,t7031]) ).
cnf(t72455,plain,
composition(top,converse(complement(composition(X1,top)))) = converse(complement(composition(X1,top))),
inference(orient,[status(thm)],[t113079]) ).
cnf(t72463,plain,
composition(converse(converse(complement(composition(X1,top)))),top) = converse(converse(complement(composition(X1,top)))),
inference(cp,[status(thm)],[t491,t72455]) ).
cnf(t113080,plain,
composition(complement(composition(X1,top)),top) = converse(converse(complement(composition(X1,top)))),
inference(step,[status(thm)],[t72463,t18]) ).
cnf(t113081,plain,
composition(complement(composition(X1,top)),top) = complement(composition(X1,top)),
inference(step,[status(thm)],[t113080,t18]) ).
cnf(t72501,plain,
composition(complement(composition(X1,top)),top) = complement(composition(X1,top)),
inference(orient,[status(thm)],[t113081]) ).
cnf(t59,plain,
complement(converse(X1)) = join(complement(converse(X1)),composition(converse(converse(X2)),complement(converse(composition(X1,X2))))),
inference(cp,[status(thm)],[t30,t53]) ).
cnf(t112772,plain,
converse(complement(X1)) = join(complement(converse(X1)),composition(converse(converse(X2)),complement(converse(composition(X1,X2))))),
inference(step,[status(thm)],[t59,t6840]) ).
cnf(t112773,plain,
converse(complement(X1)) = join(converse(complement(X1)),composition(converse(converse(X2)),complement(converse(composition(X1,X2))))),
inference(step,[status(thm)],[t112772,t6840]) ).
cnf(t112774,plain,
converse(complement(X1)) = join(converse(complement(X1)),composition(X2,complement(converse(composition(X1,X2))))),
inference(step,[status(thm)],[t112773,t18]) ).
cnf(t112775,plain,
converse(complement(X1)) = join(converse(complement(X1)),composition(X2,converse(complement(composition(X1,X2))))),
inference(step,[status(thm)],[t112774,t6840]) ).
cnf(t37079,plain,
join(converse(complement(X1)),composition(X2,converse(complement(composition(X1,X2))))) = converse(complement(X1)),
inference(orient,[status(thm)],[t112775]) ).
cnf(t77303,plain,
composition(X1,sk0) = meet(composition(X1,sk0),X1),
inference(cp,[status(thm)],[t688,t77290]) ).
cnf(t113099,plain,
composition(X1,sk0) = meet(X1,composition(X1,sk0)),
inference(step,[status(thm)],[t77303,t71]) ).
cnf(t77394,plain,
meet(X1,composition(X1,sk0)) = composition(X1,sk0),
inference(orient,[status(thm)],[t113099]) ).
cnf(t4589,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,join(meet(X3,X1),X2)),
inference(cp,[status(thm)],[t1950,t4551]) ).
cnf(t112626,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(step,[status(thm)],[t4589,t1950]) ).
cnf(t23367,plain,
join(X1,meet(X2,complement(meet(X3,X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t112626]) ).
cnf(t23382,plain,
join(X1,X2) = join(X1,meet(X2,join(X3,complement(X1)))),
inference(cp,[status(thm)],[t23367,t820]) ).
cnf(t25464,plain,
join(X1,meet(X2,join(X3,complement(X1)))) = join(X1,X2),
inference(orient,[status(thm)],[t23382]) ).
cnf(t25534,plain,
meet(X1,meet(X2,join(X3,complement(complement(X1))))) = meet(X1,join(complement(X1),X2)),
inference(cp,[status(thm)],[t5192,t25464]) ).
cnf(t112657,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,join(complement(X1),X2)),
inference(step,[status(thm)],[t25534,t321]) ).
cnf(t112658,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(step,[status(thm)],[t112657,t5192]) ).
cnf(t25634,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(orient,[status(thm)],[t112658]) ).
cnf(t25678,plain,
meet(X1,X2) = meet(X1,meet(join(X3,X1),X2)),
inference(cp,[status(thm)],[t25634,t71]) ).
cnf(t26062,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(orient,[status(thm)],[t25678]) ).
cnf(t43535,plain,
X1 = meet(X1,composition(X1,top)),
inference(cp,[status(thm)],[t664,t43524]) ).
cnf(t43611,plain,
meet(X1,composition(X1,top)) = X1,
inference(orient,[status(thm)],[t43535]) ).
cnf(t43671,plain,
meet(X1,converse(composition(converse(X1),top))) = converse(converse(X1)),
inference(cp,[status(thm)],[t7621,t43611]) ).
cnf(t112876,plain,
meet(X1,composition(converse(top),X1)) = converse(converse(X1)),
inference(step,[status(thm)],[t43671,t148]) ).
cnf(t112877,plain,
meet(X1,composition(top,X1)) = converse(converse(X1)),
inference(step,[status(thm)],[t112876,t459]) ).
cnf(t112878,plain,
meet(X1,composition(top,X1)) = X1,
inference(step,[status(thm)],[t112877,t18]) ).
cnf(t43718,plain,
meet(X1,composition(top,X1)) = X1,
inference(orient,[status(thm)],[t112878]) ).
cnf(t43756,plain,
meet(X1,composition(top,join(X2,X1))) = meet(X1,join(X2,X1)),
inference(cp,[status(thm)],[t26062,t43718]) ).
cnf(t112900,plain,
meet(X1,composition(top,join(X2,X1))) = X1,
inference(step,[status(thm)],[t43756,t688]) ).
cnf(t45289,plain,
meet(X1,composition(top,join(X2,X1))) = X1,
inference(orient,[status(thm)],[t112900]) ).
cnf(t52,plain,
complement(X1) = join(complement(X1),composition(converse(composition(X2,X3)),complement(composition(X2,composition(X3,X1))))),
inference(cp,[status(thm)],[t30,t48]) ).
cnf(t21909,plain,
join(complement(X1),composition(converse(composition(X2,X3)),complement(composition(X2,composition(X3,X1))))) = complement(X1),
inference(orient,[status(thm)],[t52]) ).
cnf(t6370,plain,
zero = composition(converse(X1),complement(composition(X1,top))),
inference(cp,[status(thm)],[t6354,t18]) ).
cnf(t6445,plain,
composition(converse(X1),complement(composition(X1,top))) = zero,
inference(orient,[status(thm)],[t6370]) ).
cnf(t21978,plain,
complement(complement(composition(X1,top))) = join(complement(complement(composition(X1,top))),composition(converse(composition(X2,converse(X1))),complement(composition(X2,zero)))),
inference(cp,[status(thm)],[t21909,t6445]) ).
cnf(t112648,plain,
composition(X1,top) = join(complement(complement(composition(X1,top))),composition(converse(composition(X2,converse(X1))),complement(composition(X2,zero)))),
inference(step,[status(thm)],[t21978,t321]) ).
cnf(t112649,plain,
composition(X1,top) = join(composition(X1,top),composition(converse(composition(X2,converse(X1))),complement(composition(X2,zero)))),
inference(step,[status(thm)],[t112648,t321]) ).
cnf(t54,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(cp,[status(thm)],[t53,t18]) ).
cnf(t136,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(orient,[status(thm)],[t54]) ).
cnf(t112650,plain,
composition(X1,top) = join(composition(X1,top),composition(composition(X1,converse(X2)),complement(composition(X2,zero)))),
inference(step,[status(thm)],[t112649,t136]) ).
cnf(t112651,plain,
composition(X1,top) = join(composition(X1,top),composition(X1,composition(converse(X2),complement(composition(X2,zero))))),
inference(step,[status(thm)],[t112650,t48]) ).
cnf(t6395,plain,
zero = composition(X1,composition(X2,complement(composition(top,top)))),
inference(cp,[status(thm)],[t6393,t48]) ).
cnf(t112332,plain,
zero = composition(X1,zero),
inference(step,[status(thm)],[t6395,t6393]) ).
cnf(t6401,plain,
composition(X1,zero) = zero,
inference(orient,[status(thm)],[t112332]) ).
cnf(t112652,plain,
composition(X1,top) = join(composition(X1,top),composition(X1,composition(converse(X2),complement(zero)))),
inference(step,[status(thm)],[t112651,t6401]) ).
cnf(t112653,plain,
composition(X1,top) = join(composition(X1,top),composition(X1,composition(converse(X2),top))),
inference(step,[status(thm)],[t112652,t296]) ).
cnf(t51,plain,
composition(join(X1,composition(X2,X3)),Y3) = join(composition(X1,Y3),composition(X2,composition(X3,Y3))),
inference(cp,[status(thm)],[t27,t48]) ).
cnf(t18411,plain,
join(composition(X1,X2),composition(X3,composition(Y3,X2))) = composition(join(X1,composition(X3,Y3)),X2),
inference(orient,[status(thm)],[t51]) ).
cnf(t112654,plain,
composition(X1,top) = composition(join(X1,composition(X1,converse(X2))),top),
inference(step,[status(thm)],[t112653,t18411]) ).
cnf(t25276,plain,
composition(join(X1,composition(X1,converse(X2))),top) = composition(X1,top),
inference(orient,[status(thm)],[t112654]) ).
cnf(t25310,plain,
composition(X1,top) = composition(join(X1,composition(X1,X2)),top),
inference(cp,[status(thm)],[t25276,t18]) ).
cnf(t25334,plain,
composition(join(X1,composition(X1,X2)),top) = composition(X1,top),
inference(orient,[status(thm)],[t25310]) ).
cnf(t42058,plain,
composition(converse(top),join(X1,converse(composition(converse(X1),X2)))) = converse(composition(converse(X1),top)),
inference(cp,[status(thm)],[t42056,t25334]) ).
cnf(t112866,plain,
composition(top,join(X1,converse(composition(converse(X1),X2)))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t42058,t459]) ).
cnf(t112867,plain,
composition(top,join(X1,composition(converse(X2),X1))) = converse(composition(converse(X1),top)),
inference(step,[status(thm)],[t112866,t148]) ).
cnf(t112868,plain,
composition(top,join(X1,composition(converse(X2),X1))) = composition(converse(top),X1),
inference(step,[status(thm)],[t112867,t148]) ).
cnf(t112869,plain,
composition(top,join(X1,composition(converse(X2),X1))) = composition(top,X1),
inference(step,[status(thm)],[t112868,t459]) ).
cnf(t42212,plain,
composition(top,join(X1,composition(converse(X2),X1))) = composition(top,X1),
inference(orient,[status(thm)],[t112869]) ).
cnf(t42249,plain,
composition(top,X1) = composition(top,join(X1,composition(X2,X1))),
inference(cp,[status(thm)],[t42212,t18]) ).
cnf(t42312,plain,
composition(top,join(X1,composition(X2,X1))) = composition(top,X1),
inference(orient,[status(thm)],[t42249]) ).
cnf(t45291,plain,
composition(X1,X2) = meet(composition(X1,X2),composition(top,X2)),
inference(cp,[status(thm)],[t45289,t42312]) ).
cnf(t47614,plain,
meet(composition(X1,X2),composition(top,X2)) = composition(X1,X2),
inference(orient,[status(thm)],[t45291]) ).
cnf(t47638,plain,
zero = meet(complement(composition(top,X1)),composition(X2,X1)),
inference(cp,[status(thm)],[t883,t47614]) ).
cnf(t52836,plain,
meet(complement(composition(top,X1)),composition(X2,X1)) = zero,
inference(orient,[status(thm)],[t47638]) ).
cnf(t77395,plain,
composition(complement(composition(top,sk0)),sk0) = zero,
inference(cp,[status(thm)],[t77394,t52836]) ).
cnf(t78339,plain,
composition(complement(composition(top,sk0)),sk0) = zero,
inference(orient,[status(thm)],[t77395]) ).
cnf(t78354,plain,
converse(complement(complement(composition(top,sk0)))) = join(converse(complement(complement(composition(top,sk0)))),composition(sk0,converse(complement(zero)))),
inference(cp,[status(thm)],[t37079,t78339]) ).
cnf(t113213,plain,
converse(composition(top,sk0)) = join(converse(complement(complement(composition(top,sk0)))),composition(sk0,converse(complement(zero)))),
inference(step,[status(thm)],[t78354,t321]) ).
cnf(t113214,plain,
composition(converse(sk0),top) = join(converse(complement(complement(composition(top,sk0)))),composition(sk0,converse(complement(zero)))),
inference(step,[status(thm)],[t113213,t491]) ).
cnf(t113215,plain,
composition(converse(sk0),top) = join(composition(sk0,converse(complement(zero))),converse(complement(complement(composition(top,sk0))))),
inference(step,[status(thm)],[t113214,t19]) ).
cnf(t113216,plain,
composition(converse(sk0),top) = join(composition(sk0,converse(top)),converse(complement(complement(composition(top,sk0))))),
inference(step,[status(thm)],[t113215,t296]) ).
cnf(t113217,plain,
composition(converse(sk0),top) = join(composition(sk0,top),converse(complement(complement(composition(top,sk0))))),
inference(step,[status(thm)],[t113216,t459]) ).
cnf(t113218,plain,
composition(converse(sk0),top) = join(composition(sk0,top),converse(composition(top,sk0))),
inference(step,[status(thm)],[t113217,t321]) ).
cnf(t113219,plain,
composition(converse(sk0),top) = join(composition(sk0,top),composition(converse(sk0),top)),
inference(step,[status(thm)],[t113218,t491]) ).
cnf(t113220,plain,
composition(converse(sk0),top) = composition(join(sk0,converse(sk0)),top),
inference(step,[status(thm)],[t113219,t27]) ).
cnf(t77423,plain,
X1 = join(X1,composition(composition(one,sk0),X1)),
inference(cp,[status(thm)],[t77040,t77394]) ).
cnf(t113100,plain,
X1 = join(X1,composition(one,composition(sk0,X1))),
inference(step,[status(thm)],[t77423,t48]) ).
cnf(t113101,plain,
X1 = join(X1,composition(sk0,X1)),
inference(step,[status(thm)],[t113100,t181]) ).
cnf(t77648,plain,
join(X1,composition(sk0,X1)) = X1,
inference(orient,[status(thm)],[t113101]) ).
cnf(t77660,plain,
composition(sk0,X1) = meet(composition(sk0,X1),X1),
inference(cp,[status(thm)],[t688,t77648]) ).
cnf(t113104,plain,
composition(sk0,X1) = meet(X1,composition(sk0,X1)),
inference(step,[status(thm)],[t77660,t71]) ).
cnf(t77820,plain,
meet(X1,composition(sk0,X1)) = composition(sk0,X1),
inference(orient,[status(thm)],[t113104]) ).
cnf(t43498,plain,
composition(X1,X2) = meet(composition(X1,X2),composition(X1,top)),
inference(cp,[status(thm)],[t664,t43479]) ).
cnf(t45880,plain,
meet(composition(X1,X2),composition(X1,top)) = composition(X1,X2),
inference(orient,[status(thm)],[t43498]) ).
cnf(t45899,plain,
zero = meet(complement(composition(X1,top)),composition(X1,X2)),
inference(cp,[status(thm)],[t883,t45880]) ).
cnf(t52636,plain,
meet(complement(composition(X1,top)),composition(X1,X2)) = zero,
inference(orient,[status(thm)],[t45899]) ).
cnf(t77821,plain,
composition(sk0,complement(composition(sk0,top))) = zero,
inference(cp,[status(thm)],[t77820,t52636]) ).
cnf(t79029,plain,
composition(sk0,complement(composition(sk0,top))) = zero,
inference(orient,[status(thm)],[t77821]) ).
cnf(t79041,plain,
complement(complement(composition(sk0,top))) = join(complement(complement(composition(sk0,top))),composition(converse(sk0),complement(zero))),
inference(cp,[status(thm)],[t30,t79029]) ).
cnf(t113121,plain,
composition(sk0,top) = join(complement(complement(composition(sk0,top))),composition(converse(sk0),complement(zero))),
inference(step,[status(thm)],[t79041,t321]) ).
cnf(t113122,plain,
composition(sk0,top) = join(composition(converse(sk0),complement(zero)),complement(complement(composition(sk0,top)))),
inference(step,[status(thm)],[t113121,t19]) ).
cnf(t113123,plain,
composition(sk0,top) = join(composition(converse(sk0),top),complement(complement(composition(sk0,top)))),
inference(step,[status(thm)],[t113122,t296]) ).
cnf(t113124,plain,
composition(sk0,top) = join(composition(converse(sk0),top),composition(sk0,top)),
inference(step,[status(thm)],[t113123,t321]) ).
cnf(t113125,plain,
composition(sk0,top) = composition(join(converse(sk0),sk0),top),
inference(step,[status(thm)],[t113124,t27]) ).
cnf(t113126,plain,
composition(sk0,top) = composition(join(sk0,converse(sk0)),top),
inference(step,[status(thm)],[t113125,t19]) ).
cnf(t79047,plain,
composition(join(sk0,converse(sk0)),top) = composition(sk0,top),
inference(orient,[status(thm)],[t113126]) ).
cnf(t113221,plain,
composition(converse(sk0),top) = composition(sk0,top),
inference(step,[status(thm)],[t113220,t79047]) ).
cnf(t84461,plain,
composition(converse(sk0),top) = composition(sk0,top),
inference(orient,[status(thm)],[t113221]) ).
cnf(t84480,plain,
complement(composition(converse(sk0),top)) = composition(complement(composition(sk0,top)),top),
inference(cp,[status(thm)],[t72501,t84461]) ).
cnf(t113224,plain,
converse(complement(composition(top,sk0))) = composition(complement(composition(sk0,top)),top),
inference(step,[status(thm)],[t84480,t6979]) ).
cnf(t113225,plain,
converse(complement(composition(top,sk0))) = complement(composition(sk0,top)),
inference(step,[status(thm)],[t113224,t72501]) ).
cnf(t84623,plain,
converse(complement(composition(top,sk0))) = complement(composition(sk0,top)),
inference(orient,[status(thm)],[t113225]) ).
cnf(t113485,plain,
meet(one,complement(composition(sk0,top))) = meet(one,converse(complement(sk0))),
inference(step,[status(thm)],[t108889,t84623]) ).
cnf(t7631,plain,
meet(X1,converse(X2)) = converse(meet(X2,converse(X1))),
inference(cp,[status(thm)],[t7621,t71]) ).
cnf(t7681,plain,
converse(meet(X1,converse(X2))) = meet(X2,converse(X1)),
inference(orient,[status(thm)],[t7631]) ).
cnf(t40,plain,
join(sk0,join(one,X1)) = join(one,X1),
inference(cp,[status(thm)],[t21,t39]) ).
cnf(t74,plain,
join(sk0,join(one,X1)) = join(one,X1),
inference(orient,[status(thm)],[t40]) ).
cnf(t507,plain,
join(join(one,X1),sk0) = join(join(one,X1),join(one,X1)),
inference(cp,[status(thm)],[t500,t74]) ).
cnf(t112177,plain,
join(one,join(X1,sk0)) = join(join(one,X1),join(one,X1)),
inference(step,[status(thm)],[t507,t21]) ).
cnf(t112178,plain,
join(one,join(X1,sk0)) = join(one,join(X1,join(one,X1))),
inference(step,[status(thm)],[t112177,t21]) ).
cnf(t112179,plain,
join(one,join(X1,sk0)) = join(one,join(X1,one)),
inference(step,[status(thm)],[t112178,t500]) ).
cnf(t112180,plain,
join(one,join(X1,sk0)) = join(one,X1),
inference(step,[status(thm)],[t112179,t500]) ).
cnf(t512,plain,
join(one,join(X1,sk0)) = join(one,X1),
inference(orient,[status(thm)],[t112180]) ).
cnf(t516,plain,
join(one,X1) = join(one,join(sk0,X1)),
inference(cp,[status(thm)],[t512,t19]) ).
cnf(t519,plain,
join(one,join(sk0,X1)) = join(one,X1),
inference(orient,[status(thm)],[t516]) ).
cnf(t523,plain,
join(one,complement(sk0)) = join(one,top),
inference(cp,[status(thm)],[t519,t24]) ).
cnf(t112181,plain,
join(one,complement(sk0)) = top,
inference(step,[status(thm)],[t523,t435]) ).
cnf(t526,plain,
join(one,complement(sk0)) = top,
inference(orient,[status(thm)],[t112181]) ).
cnf(t529,plain,
join(one,join(complement(sk0),X1)) = join(top,X1),
inference(cp,[status(thm)],[t21,t526]) ).
cnf(t112187,plain,
join(one,join(complement(sk0),X1)) = top,
inference(step,[status(thm)],[t529,t441]) ).
cnf(t549,plain,
join(one,join(complement(sk0),X1)) = top,
inference(orient,[status(thm)],[t112187]) ).
cnf(t4836,plain,
join(join(complement(sk0),X1),complement(one)) = join(join(complement(sk0),X1),complement(top)),
inference(cp,[status(thm)],[t4787,t549]) ).
cnf(t112473,plain,
join(complement(sk0),join(X1,complement(one))) = join(join(complement(sk0),X1),complement(top)),
inference(step,[status(thm)],[t4836,t21]) ).
cnf(t112474,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(sk0),join(X1,complement(top))),
inference(step,[status(thm)],[t112473,t21]) ).
cnf(t112475,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(top),join(complement(sk0),X1)),
inference(step,[status(thm)],[t112474,t563]) ).
cnf(t112476,plain,
join(complement(sk0),join(X1,complement(one))) = join(zero,join(complement(sk0),X1)),
inference(step,[status(thm)],[t112475,t62]) ).
cnf(t112477,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(sk0),X1),
inference(step,[status(thm)],[t112476,t285]) ).
cnf(t15073,plain,
join(complement(sk0),join(X1,complement(one))) = join(complement(sk0),X1),
inference(orient,[status(thm)],[t112477]) ).
cnf(t15082,plain,
meet(complement(complement(sk0)),join(X1,complement(one))) = meet(complement(complement(sk0)),join(complement(sk0),X1)),
inference(cp,[status(thm)],[t5986,t15073]) ).
cnf(t112478,plain,
meet(sk0,join(X1,complement(one))) = meet(complement(complement(sk0)),join(complement(sk0),X1)),
inference(step,[status(thm)],[t15082,t321]) ).
cnf(t112479,plain,
meet(sk0,join(X1,complement(one))) = meet(complement(complement(sk0)),X1),
inference(step,[status(thm)],[t112478,t5986]) ).
cnf(t112480,plain,
meet(sk0,join(X1,complement(one))) = meet(sk0,X1),
inference(step,[status(thm)],[t112479,t321]) ).
cnf(t15114,plain,
meet(sk0,join(X1,complement(one))) = meet(sk0,X1),
inference(orient,[status(thm)],[t112480]) ).
cnf(t15118,plain,
meet(sk0,X1) = meet(sk0,join(complement(one),X1)),
inference(cp,[status(thm)],[t15114,t19]) ).
cnf(t15153,plain,
meet(sk0,join(complement(one),X1)) = meet(sk0,X1),
inference(orient,[status(thm)],[t15118]) ).
cnf(t6862,plain,
complement(meet(X1,converse(X2))) = join(complement(X1),converse(complement(X2))),
inference(cp,[status(thm)],[t757,t6840]) ).
cnf(t8060,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(orient,[status(thm)],[t6862]) ).
cnf(t15155,plain,
meet(sk0,converse(complement(X1))) = meet(sk0,complement(meet(one,converse(X1)))),
inference(cp,[status(thm)],[t15153,t8060]) ).
cnf(t6937,plain,
converse(complement(meet(one,X1))) = complement(meet(one,converse(X1))),
inference(cp,[status(thm)],[t6840,t6921]) ).
cnf(t7127,plain,
complement(meet(one,converse(X1))) = converse(complement(meet(one,X1))),
inference(orient,[status(thm)],[t6937]) ).
cnf(t112566,plain,
meet(sk0,converse(complement(X1))) = meet(sk0,converse(complement(meet(one,X1)))),
inference(step,[status(thm)],[t15155,t7127]) ).
cnf(t20977,plain,
meet(sk0,converse(complement(meet(one,X1)))) = meet(sk0,converse(complement(X1))),
inference(orient,[status(thm)],[t112566]) ).
cnf(t21024,plain,
meet(complement(meet(one,X1)),converse(sk0)) = converse(meet(sk0,converse(complement(X1)))),
inference(cp,[status(thm)],[t7681,t20977]) ).
cnf(t112586,plain,
meet(converse(sk0),complement(meet(one,X1))) = converse(meet(sk0,converse(complement(X1)))),
inference(step,[status(thm)],[t21024,t71]) ).
cnf(t112587,plain,
meet(converse(sk0),complement(meet(one,X1))) = meet(complement(X1),converse(sk0)),
inference(step,[status(thm)],[t112586,t7681]) ).
cnf(t112588,plain,
meet(converse(sk0),complement(meet(one,X1))) = meet(converse(sk0),complement(X1)),
inference(step,[status(thm)],[t112587,t71]) ).
cnf(t21656,plain,
meet(converse(sk0),complement(meet(one,X1))) = meet(converse(sk0),complement(X1)),
inference(orient,[status(thm)],[t112588]) ).
cnf(t21657,plain,
meet(converse(sk0),complement(complement(X1))) = meet(converse(sk0),join(complement(one),X1)),
inference(cp,[status(thm)],[t21656,t836]) ).
cnf(t112603,plain,
meet(converse(sk0),X1) = meet(converse(sk0),join(complement(one),X1)),
inference(step,[status(thm)],[t21657,t321]) ).
cnf(t22147,plain,
meet(converse(sk0),join(complement(one),X1)) = meet(converse(sk0),X1),
inference(orient,[status(thm)],[t112603]) ).
cnf(t107220,plain,
meet(converse(sk0),composition(top,sk0)) = meet(converse(sk0),join(sk0,complement(one))),
inference(cp,[status(thm)],[t22147,t107194]) ).
cnf(t521,plain,
join(one,meet(sk0,X1)) = join(one,sk0),
inference(cp,[status(thm)],[t519,t467]) ).
cnf(t112183,plain,
join(one,meet(sk0,X1)) = join(sk0,one),
inference(step,[status(thm)],[t521,t19]) ).
cnf(t112184,plain,
join(one,meet(sk0,X1)) = one,
inference(step,[status(thm)],[t112183,t39]) ).
cnf(t533,plain,
join(one,meet(sk0,X1)) = one,
inference(orient,[status(thm)],[t112184]) ).
cnf(t537,plain,
join(one,converse(meet(sk0,X1))) = converse(one),
inference(cp,[status(thm)],[t185,t533]) ).
cnf(t112188,plain,
join(one,converse(meet(sk0,X1))) = one,
inference(step,[status(thm)],[t537,t170]) ).
cnf(t553,plain,
join(one,converse(meet(sk0,X1))) = one,
inference(orient,[status(thm)],[t112188]) ).
cnf(t694,plain,
converse(meet(sk0,X1)) = meet(converse(meet(sk0,X1)),one),
inference(cp,[status(thm)],[t688,t553]) ).
cnf(t112251,plain,
converse(meet(sk0,X1)) = meet(one,converse(meet(sk0,X1))),
inference(step,[status(thm)],[t694,t71]) ).
cnf(t1582,plain,
meet(one,converse(meet(sk0,X1))) = converse(meet(sk0,X1)),
inference(orient,[status(thm)],[t112251]) ).
cnf(t78353,plain,
zero = meet(sk0,composition(converse(complement(composition(top,sk0))),complement(zero))),
inference(cp,[status(thm)],[t31710,t78339]) ).
cnf(t113157,plain,
zero = meet(sk0,composition(converse(complement(composition(top,sk0))),top)),
inference(step,[status(thm)],[t78353,t296]) ).
cnf(t72427,plain,
composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
inference(cp,[status(thm)],[t491,t72419]) ).
cnf(t72539,plain,
composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
inference(orient,[status(thm)],[t72427]) ).
cnf(t113158,plain,
zero = meet(sk0,converse(complement(composition(top,sk0)))),
inference(step,[status(thm)],[t113157,t72539]) ).
cnf(t82031,plain,
meet(sk0,converse(complement(composition(top,sk0)))) = zero,
inference(orient,[status(thm)],[t113158]) ).
cnf(t82038,plain,
sk0 = join(zero,meet(complement(converse(complement(composition(top,sk0)))),sk0)),
inference(cp,[status(thm)],[t12109,t82031]) ).
cnf(t113159,plain,
sk0 = meet(complement(converse(complement(composition(top,sk0)))),sk0),
inference(step,[status(thm)],[t82038,t285]) ).
cnf(t113160,plain,
sk0 = meet(sk0,complement(converse(complement(composition(top,sk0))))),
inference(step,[status(thm)],[t113159,t71]) ).
cnf(t113161,plain,
sk0 = meet(sk0,converse(composition(top,sk0))),
inference(step,[status(thm)],[t113160,t6795]) ).
cnf(t113162,plain,
sk0 = meet(sk0,composition(converse(sk0),top)),
inference(step,[status(thm)],[t113161,t491]) ).
cnf(t82052,plain,
meet(sk0,composition(converse(sk0),top)) = sk0,
inference(orient,[status(thm)],[t113162]) ).
cnf(t82115,plain,
converse(meet(sk0,composition(converse(sk0),top))) = meet(one,converse(sk0)),
inference(cp,[status(thm)],[t1582,t82052]) ).
cnf(t7712,plain,
meet(composition(top,X1),converse(X2)) = converse(meet(X2,composition(converse(X1),top))),
inference(cp,[status(thm)],[t7681,t491]) ).
cnf(t73046,plain,
converse(meet(X1,composition(converse(X2),top))) = meet(composition(top,X2),converse(X1)),
inference(orient,[status(thm)],[t7712]) ).
cnf(t113163,plain,
meet(composition(top,sk0),converse(sk0)) = meet(one,converse(sk0)),
inference(step,[status(thm)],[t82115,t73046]) ).
cnf(t113164,plain,
meet(converse(sk0),composition(top,sk0)) = meet(one,converse(sk0)),
inference(step,[status(thm)],[t113163,t71]) ).
cnf(t113165,plain,
meet(converse(sk0),composition(top,sk0)) = converse(sk0),
inference(step,[status(thm)],[t113164,t709]) ).
cnf(t82134,plain,
meet(converse(sk0),composition(top,sk0)) = converse(sk0),
inference(orient,[status(thm)],[t113165]) ).
cnf(t113424,plain,
converse(sk0) = meet(converse(sk0),join(sk0,complement(one))),
inference(step,[status(thm)],[t107220,t82134]) ).
cnf(t21672,plain,
meet(converse(sk0),complement(complement(meet(one,X1)))) = meet(converse(sk0),complement(meet(one,complement(X1)))),
inference(cp,[status(thm)],[t21656,t5808]) ).
cnf(t112592,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),complement(meet(one,complement(X1)))),
inference(step,[status(thm)],[t21672,t321]) ).
cnf(t112593,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),complement(complement(X1))),
inference(step,[status(thm)],[t112592,t21656]) ).
cnf(t112594,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),X1),
inference(step,[status(thm)],[t112593,t321]) ).
cnf(t21781,plain,
meet(converse(sk0),meet(one,X1)) = meet(converse(sk0),X1),
inference(orient,[status(thm)],[t112594]) ).
cnf(t21796,plain,
meet(converse(sk0),join(X1,complement(one))) = meet(converse(sk0),meet(one,X1)),
inference(cp,[status(thm)],[t21781,t5152]) ).
cnf(t112604,plain,
meet(converse(sk0),join(X1,complement(one))) = meet(converse(sk0),X1),
inference(step,[status(thm)],[t21796,t21781]) ).
cnf(t22202,plain,
meet(converse(sk0),join(X1,complement(one))) = meet(converse(sk0),X1),
inference(orient,[status(thm)],[t112604]) ).
cnf(t113425,plain,
converse(sk0) = meet(converse(sk0),sk0),
inference(step,[status(thm)],[t113424,t22202]) ).
cnf(t113426,plain,
converse(sk0) = meet(sk0,converse(sk0)),
inference(step,[status(thm)],[t113425,t71]) ).
cnf(t107257,plain,
meet(sk0,converse(sk0)) = converse(sk0),
inference(orient,[status(thm)],[t113426]) ).
cnf(t107308,plain,
meet(sk0,converse(sk0)) = converse(converse(sk0)),
inference(cp,[status(thm)],[t7681,t107257]) ).
cnf(t113427,plain,
converse(sk0) = converse(converse(sk0)),
inference(step,[status(thm)],[t107308,t107257]) ).
cnf(t113428,plain,
converse(sk0) = sk0,
inference(step,[status(thm)],[t113427,t18]) ).
cnf(t107341,plain,
converse(sk0) = sk0,
inference(orient,[status(thm)],[t113428]) ).
cnf(t107344,plain,
converse(complement(sk0)) = complement(sk0),
inference(cp,[status(thm)],[t6840,t107341]) ).
cnf(t107479,plain,
converse(complement(sk0)) = complement(sk0),
inference(orient,[status(thm)],[t107344]) ).
cnf(t113486,plain,
meet(one,complement(composition(sk0,top))) = meet(one,complement(sk0)),
inference(step,[status(thm)],[t113485,t107479]) ).
cnf(t112051,plain,
meet(one,complement(composition(sk0,top))) = meet(one,complement(sk0)),
inference(orient,[status(thm)],[t113486]) ).
cnf(c14,plain,
meet(complement(composition(sk0,top)),one) != meet(complement(sk0),one),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
meet(complement(composition(sk0,top)),one) != meet(complement(sk0),one),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
meet(one,complement(composition(sk0,top))) != meet(complement(sk0),one),
inference(rw,[status(thm)],[goal_0,t71]) ).
cnf(g0_1,plain,
meet(one,complement(sk0)) != meet(complement(sk0),one),
inference(rw,[status(thm)],[g0_0,t112051]) ).
cnf(g0_2,plain,
meet(one,complement(sk0)) != meet(one,complement(sk0)),
inference(rw,[status(thm)],[g0_1,t71]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL027+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 07:24:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 45.01/6.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.01/6.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------