%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL030+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 : Sun Sep 27 08:24:59 AM UTC 2026
% Result : Theorem 29.88s 9.91s
% Output : CNFRefutation 29.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 89
% Number of leaves : 14
% Syntax : Number of formulae : 382 ( 378 unt; 0 def)
% Number of atoms : 386 ( 385 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 16 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 434 ( 17 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('theBenchmark.p',composition_associativity) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( join(X0,one) = one
=> meet(composition(X0,X1),complement(X2)) = meet(composition(X0,X1),complement(composition(X0,X2))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,one) = one
=> meet(composition(X0,X1),complement(X2)) = meet(composition(X0,X1),complement(composition(X0,X2))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_15,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_16,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_17,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_18,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_15,c_17]) ).
cnf(c_19,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_20,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(clausify,[status(thm)],[composition_associativity]) ).
cnf(c_21,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_22,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_23,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_24,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_26,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_10430,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_15,c_26]) ).
cnf(c_27,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_10430]) ).
cnf(c_28,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_29,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_10431,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_30,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_28,c_10431]) ).
fof(nnf_14,plain,
? [X0,X1,X2] :
( meet(composition(X0,X1),complement(composition(X0,X2))) != meet(composition(X0,X1),complement(X2))
& join(X0,one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( meet(composition(sK0,sK1),complement(composition(sK0,sK2))) != meet(composition(sK0,sK1),complement(sK2))
& join(sK0,one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
join(sK0,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
join(one,sK0) = one,
inference(paramod,[status(thm)],[c_15,c_31]) ).
cnf(c_33,negated_conjecture,
meet(composition(sK0,sK1),complement(composition(sK0,sK2))) != meet(composition(sK0,sK1),complement(sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_10432,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != meet(composition(sK0,sK1),complement(sK2)),
inference(paramod,[status(thm)],[c_19,c_33]) ).
cnf(c_10433,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != complement(join(complement(composition(sK0,sK1)),complement(complement(sK2)))),
inference(paramod,[status(thm)],[c_19,c_10432]) ).
cnf(c_34,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_15,c_10433]) ).
cnf(c_10434,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_36,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_10434]) ).
cnf(c_37,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_38,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_10435,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_39,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_10435]) ).
cnf(c_10436,plain,
join(complement(join(complement(join(complement(A),B)),join(complement(A),complement(B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_18,c_18]) ).
cnf(c_10437,plain,
join(complement(join(join(complement(A),complement(B)),complement(join(complement(A),B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_15,c_10436]) ).
cnf(c_10438,plain,
join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_16,c_10437]) ).
cnf(c_41,plain,
join(complement(A),complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))) = join(complement(A),B),
inference(paramod,[status(thm)],[c_15,c_10438]) ).
cnf(c_10439,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_45,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_10439]) ).
cnf(c_10440,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_47,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_10440]) ).
cnf(c_53,plain,
join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A),
inference(paramod,[status(thm)],[c_23,c_27]) ).
cnf(c_10441,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_27,c_24]) ).
cnf(c_10442,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_25,c_10441]) ).
cnf(c_10443,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_23,c_10442]) ).
cnf(c_54,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_10443]) ).
cnf(c_10444,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_16]) ).
cnf(c_55,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_10444]) ).
cnf(c_10445,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_57,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_10445]) ).
cnf(c_10446,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_22]) ).
cnf(c_59,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_10446]) ).
cnf(c_10447,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_60,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_10447]) ).
cnf(c_10448,plain,
join(one,A) = join(one,join(sK0,A)),
inference(paramod,[status(thm)],[c_32,c_16]) ).
cnf(c_65,plain,
join(one,join(sK0,A)) = join(one,A),
inference(copy,[status(thm)],[c_10448]) ).
cnf(c_10449,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_32,c_22]) ).
cnf(c_67,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_10449]) ).
cnf(c_10450,plain,
converse(one) = join(converse(one),converse(sK0)),
inference(paramod,[status(thm)],[c_32,c_24]) ).
cnf(c_68,plain,
join(converse(one),converse(sK0)) = converse(one),
inference(copy,[status(thm)],[c_10450]) ).
cnf(c_10451,plain,
join(A,B) = join(complement(join(complement(B),C)),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_18,c_36]) ).
cnf(c_70,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_10451]) ).
cnf(c_10452,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_37,c_15]) ).
cnf(c_74,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_10452]) ).
cnf(c_10453,plain,
join(A,B) = join(complement(join(C,complement(A))),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_37,c_16]) ).
cnf(c_76,plain,
join(complement(join(A,complement(B))),join(complement(join(complement(B),complement(A))),C)) = join(B,C),
inference(copy,[status(thm)],[c_10453]) ).
cnf(c_10454,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_10455,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_10454]) ).
cnf(c_10456,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_10455]) ).
cnf(c_93,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_10456]) ).
cnf(c_10457,plain,
join(complement(join(complement(join(complement(A),complement(B))),join(complement(B),A))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_38,c_38]) ).
cnf(c_10458,plain,
join(complement(join(join(complement(B),A),complement(join(complement(A),complement(B))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_15,c_10457]) ).
cnf(c_10459,plain,
join(complement(join(complement(B),join(A,complement(join(complement(A),complement(B)))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_16,c_10458]) ).
cnf(c_98,plain,
join(complement(A),complement(join(complement(A),join(B,complement(join(complement(B),complement(A))))))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_15,c_10459]) ).
cnf(c_99,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_93,c_57]) ).
cnf(c_100,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_93]) ).
cnf(c_10460,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_99,c_34]) ).
cnf(c_102,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_99,c_10460]) ).
cnf(c_10461,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_45]) ).
cnf(c_109,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_10461]) ).
cnf(c_10462,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_109,c_21]) ).
cnf(c_111,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_10462]) ).
cnf(c_115,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_109,c_27]) ).
cnf(c_116,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_111,c_109]) ).
cnf(c_10463,plain,
join(one,converse(sK0)) = converse(one),
inference(paramod,[status(thm)],[c_111,c_68]) ).
cnf(c_117,plain,
join(one,converse(sK0)) = one,
inference(paramod,[status(thm)],[c_111,c_10463]) ).
cnf(c_10464,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_116,c_67]) ).
cnf(c_118,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_116,c_10464]) ).
cnf(c_119,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_116,c_115]) ).
cnf(c_10465,plain,
composition(one,A) = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_117,c_22]) ).
cnf(c_10466,plain,
A = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_116,c_10465]) ).
cnf(c_10467,plain,
A = join(A,composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_116,c_10466]) ).
cnf(c_121,plain,
join(A,composition(converse(sK0),A)) = A,
inference(copy,[status(thm)],[c_10467]) ).
cnf(c_10468,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_10469,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_15,c_10468]) ).
cnf(c_139,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_99,c_10469]) ).
cnf(c_10470,plain,
join(A,join(complement(B),C)) = join(complement(B),join(A,complement(join(complement(B),join(complement(C),complement(join(complement(B),C))))))),
inference(paramod,[status(thm)],[c_41,c_36]) ).
cnf(c_152,plain,
join(complement(A),join(B,complement(join(complement(A),join(complement(C),complement(join(complement(A),C))))))) = join(B,join(complement(A),C)),
inference(copy,[status(thm)],[c_10470]) ).
cnf(c_10471,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(complement(A))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_41,c_37]) ).
cnf(c_10472,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),A))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_99,c_10471]) ).
cnf(c_154,plain,
join(complement(join(complement(A),B)),complement(join(A,complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_15,c_10472]) ).
cnf(c_10473,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),B)),join(complement(join(complement(join(complement(A),complement(B))),C)),complement(join(A,C)))))) = join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)),
inference(paramod,[status(thm)],[c_39,c_41]) ).
cnf(c_10474,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),B)),join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C)))))) = join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)),
inference(paramod,[status(thm)],[c_15,c_10473]) ).
cnf(c_160,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),B)),join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C)))))) = join(A,C),
inference(paramod,[status(thm)],[c_39,c_10474]) ).
cnf(c_10475,plain,
converse(A) = join(converse(A),converse(composition(sK0,A))),
inference(paramod,[status(thm)],[c_118,c_24]) ).
cnf(c_10476,plain,
converse(A) = join(converse(A),composition(converse(A),converse(sK0))),
inference(paramod,[status(thm)],[c_25,c_10475]) ).
cnf(c_178,plain,
join(converse(A),composition(converse(A),converse(sK0))) = converse(A),
inference(copy,[status(thm)],[c_10476]) ).
cnf(c_10477,plain,
join(A,B) = join(B,join(A,composition(sK0,B))),
inference(paramod,[status(thm)],[c_118,c_36]) ).
cnf(c_179,plain,
join(A,join(B,composition(sK0,A))) = join(B,A),
inference(copy,[status(thm)],[c_10477]) ).
cnf(c_10478,plain,
join(complement(complement(A)),complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_10479,plain,
join(A,complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_99,c_10478]) ).
cnf(c_10480,plain,
join(A,complement(join(complement(A),A))) = A,
inference(paramod,[status(thm)],[c_99,c_10479]) ).
cnf(c_10481,plain,
join(A,complement(join(A,complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_10480]) ).
cnf(c_10482,plain,
join(A,complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_10481]) ).
cnf(c_189,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_30,c_10482]) ).
cnf(c_10483,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_10484,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_15,c_10483]) ).
cnf(c_10485,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_28,c_10484]) ).
cnf(c_10486,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_30,c_10485]) ).
cnf(c_190,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_99,c_10486]) ).
cnf(c_10487,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_119,c_39]) ).
cnf(c_10488,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_18,c_10487]) ).
cnf(c_193,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_10488]) ).
cnf(c_202,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_190,c_100]) ).
cnf(c_205,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_193,c_98]) ).
cnf(c_10489,plain,
join(complement(join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C)))),complement(join(complement(A),B))) = join(A,C),
inference(paramod,[status(thm)],[c_205,c_160]) ).
cnf(c_207,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,C)),complement(join(complement(join(complement(A),complement(B))),C))))) = join(A,C),
inference(paramod,[status(thm)],[c_15,c_10489]) ).
cnf(c_10490,plain,
converse(A) = join(converse(A),converse(zero)),
inference(paramod,[status(thm)],[c_189,c_24]) ).
cnf(c_215,plain,
join(converse(A),converse(zero)) = converse(A),
inference(copy,[status(thm)],[c_10490]) ).
cnf(c_220,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_190,c_28]) ).
cnf(c_10491,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = join(complement(A),composition(sK0,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_118,c_47]) ).
cnf(c_10492,plain,
complement(A) = join(complement(A),composition(sK0,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_27,c_10491]) ).
cnf(c_257,plain,
join(complement(A),composition(sK0,composition(converse(B),complement(composition(B,A))))) = complement(A),
inference(copy,[status(thm)],[c_10492]) ).
cnf(c_10493,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_202,c_18]) ).
cnf(c_10494,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_202,c_10493]) ).
cnf(c_10495,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_18,c_10494]) ).
cnf(c_268,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_10495]) ).
cnf(c_10496,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_268,c_39]) ).
cnf(c_10497,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_15,c_10496]) ).
cnf(c_10498,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_193,c_10497]) ).
cnf(c_272,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_15,c_10498]) ).
cnf(c_10499,plain,
join(complement(join(complement(A),B)),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_272,c_154]) ).
cnf(c_10500,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_15,c_10499]) ).
cnf(c_10501,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_205,c_10500]) ).
cnf(c_274,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_10501]) ).
cnf(c_277,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_274,c_152]) ).
cnf(c_10502,plain,
join(A,converse(zero)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_215]) ).
cnf(c_280,plain,
join(A,converse(zero)) = A,
inference(paramod,[status(thm)],[c_23,c_10502]) ).
cnf(c_10503,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_280,c_190]) ).
cnf(c_286,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_10503]) ).
cnf(c_10504,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_18]) ).
cnf(c_341,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_10504]) ).
cnf(c_10505,plain,
join(zero,composition(A,complement(composition(converse(A),top)))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_53]) ).
cnf(c_10506,plain,
composition(A,complement(composition(converse(A),top))) = complement(top),
inference(paramod,[status(thm)],[c_190,c_10505]) ).
cnf(c_379,plain,
composition(A,complement(composition(converse(A),top))) = zero,
inference(paramod,[status(thm)],[c_30,c_10506]) ).
cnf(c_10507,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_30,c_54]) ).
cnf(c_10508,plain,
join(zero,composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_286,c_10507]) ).
cnf(c_10509,plain,
composition(converse(complement(composition(A,top))),A) = converse(complement(top)),
inference(paramod,[status(thm)],[c_190,c_10508]) ).
cnf(c_10510,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_30,c_10509]) ).
cnf(c_386,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_286,c_10510]) ).
cnf(c_10511,plain,
converse(A) = join(converse(A),converse(composition(converse(sK0),A))),
inference(paramod,[status(thm)],[c_121,c_24]) ).
cnf(c_10512,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sK0)))),
inference(paramod,[status(thm)],[c_25,c_10511]) ).
cnf(c_10513,plain,
converse(A) = join(converse(A),composition(converse(A),sK0)),
inference(paramod,[status(thm)],[c_23,c_10512]) ).
cnf(c_400,plain,
join(converse(A),composition(converse(A),sK0)) = converse(A),
inference(copy,[status(thm)],[c_10513]) ).
cnf(c_10514,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_268,c_55]) ).
cnf(c_10515,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_28,c_10514]) ).
cnf(c_423,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_10515]) ).
cnf(c_10516,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_268,c_55]) ).
cnf(c_10517,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_15,c_10516]) ).
cnf(c_424,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_423,c_10517]) ).
cnf(c_449,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_116,c_59]) ).
cnf(c_10518,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_424,c_15]) ).
cnf(c_454,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_10518]) ).
cnf(c_10519,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_424,c_24]) ).
cnf(c_456,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_10519]) ).
cnf(c_471,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_456]) ).
cnf(c_474,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_471,c_454]) ).
cnf(c_483,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_474,c_60]) ).
cnf(c_10520,plain,
join(one,top) = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_28,c_65]) ).
cnf(c_10521,plain,
top = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_424,c_10520]) ).
cnf(c_490,plain,
join(one,complement(sK0)) = top,
inference(copy,[status(thm)],[c_10521]) ).
cnf(c_10522,plain,
join(complement(join(zero,A)),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_30,c_70]) ).
cnf(c_10523,plain,
join(complement(A),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_190,c_10522]) ).
cnf(c_10524,plain,
join(complement(A),join(B,complement(join(zero,complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_30,c_10523]) ).
cnf(c_10525,plain,
join(complement(A),join(B,complement(complement(A)))) = join(B,top),
inference(paramod,[status(thm)],[c_190,c_10524]) ).
cnf(c_10526,plain,
join(complement(A),join(B,A)) = join(B,top),
inference(paramod,[status(thm)],[c_99,c_10525]) ).
cnf(c_555,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_424,c_10526]) ).
cnf(c_10527,plain,
join(complement(join(complement(sK0),complement(one))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_490,c_74]) ).
cnf(c_10528,plain,
join(complement(join(complement(one),complement(sK0))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_15,c_10527]) ).
cnf(c_10529,plain,
join(complement(join(complement(one),complement(sK0))),zero) = sK0,
inference(paramod,[status(thm)],[c_30,c_10528]) ).
cnf(c_10530,plain,
join(zero,complement(join(complement(one),complement(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_15,c_10529]) ).
cnf(c_599,plain,
complement(join(complement(one),complement(sK0))) = sK0,
inference(paramod,[status(thm)],[c_190,c_10530]) ).
cnf(c_10531,plain,
join(complement(join(A,complement(B))),join(complement(join(complement(B),complement(A))),B)) = B,
inference(paramod,[status(thm)],[c_268,c_76]) ).
cnf(c_10532,plain,
join(complement(join(A,complement(B))),join(B,complement(join(complement(B),complement(A))))) = B,
inference(paramod,[status(thm)],[c_15,c_10531]) ).
cnf(c_10533,plain,
join(complement(join(A,complement(B))),B) = B,
inference(paramod,[status(thm)],[c_272,c_10532]) ).
cnf(c_612,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_10533]) ).
cnf(c_634,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_111,c_483]) ).
cnf(c_10534,plain,
complement(sK0) = join(complement(one),complement(sK0)),
inference(paramod,[status(thm)],[c_599,c_99]) ).
cnf(c_696,plain,
join(complement(one),complement(sK0)) = complement(sK0),
inference(copy,[status(thm)],[c_10534]) ).
cnf(c_10535,plain,
join(A,composition(converse(converse(A)),sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_400]) ).
cnf(c_10536,plain,
join(A,composition(A,sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_10535]) ).
cnf(c_775,plain,
join(A,composition(A,sK0)) = A,
inference(paramod,[status(thm)],[c_23,c_10536]) ).
cnf(c_10537,plain,
join(A,B) = join(A,join(composition(A,sK0),B)),
inference(paramod,[status(thm)],[c_775,c_16]) ).
cnf(c_780,plain,
join(A,join(composition(A,sK0),B)) = join(A,B),
inference(copy,[status(thm)],[c_10537]) ).
cnf(c_10538,plain,
join(complement(composition(A,sK0)),A) = top,
inference(paramod,[status(thm)],[c_775,c_555]) ).
cnf(c_786,plain,
join(A,complement(composition(A,sK0))) = top,
inference(paramod,[status(thm)],[c_15,c_10538]) ).
cnf(c_10539,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_449,c_24]) ).
cnf(c_10540,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_25,c_10539]) ).
cnf(c_10541,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_474,c_10540]) ).
cnf(c_10542,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_25,c_10541]) ).
cnf(c_832,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_10542]) ).
cnf(c_10543,plain,
join(A,composition(converse(converse(A)),converse(sK0))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_178]) ).
cnf(c_10544,plain,
join(A,composition(A,converse(sK0))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_10543]) ).
cnf(c_917,plain,
join(A,composition(A,converse(sK0))) = A,
inference(paramod,[status(thm)],[c_23,c_10544]) ).
cnf(c_10545,plain,
join(complement(composition(A,converse(sK0))),A) = top,
inference(paramod,[status(thm)],[c_917,c_555]) ).
cnf(c_1079,plain,
join(A,complement(composition(A,converse(sK0)))) = top,
inference(paramod,[status(thm)],[c_15,c_10545]) ).
cnf(c_10546,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(C),complement(A))))) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_139,c_47]) ).
cnf(c_10547,plain,
join(composition(converse(B),complement(composition(B,A))),join(complement(A),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_277,c_10546]) ).
cnf(c_10548,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_36,c_10547]) ).
cnf(c_10549,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_47,c_10548]) ).
cnf(c_10550,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_99,c_10549]) ).
cnf(c_1190,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_10550]) ).
cnf(c_1254,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_15,c_1190]) ).
cnf(c_10551,plain,
join(converse(complement(A)),complement(top)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_483,c_1190]) ).
cnf(c_10552,plain,
join(converse(complement(A)),zero) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_30,c_10551]) ).
cnf(c_10553,plain,
join(zero,converse(complement(A))) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_10552]) ).
cnf(c_10554,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_190,c_10553]) ).
cnf(c_1268,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_10554]) ).
cnf(c_10555,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_634,c_1190]) ).
cnf(c_10556,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_30,c_10555]) ).
cnf(c_10557,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_10556]) ).
cnf(c_10558,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_190,c_10557]) ).
cnf(c_1269,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_10558]) ).
cnf(c_10559,plain,
join(complement(composition(A,sK0)),complement(top)) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_786,c_1190]) ).
cnf(c_10560,plain,
join(complement(composition(A,sK0)),zero) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_30,c_10559]) ).
cnf(c_10561,plain,
join(zero,complement(composition(A,sK0))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_15,c_10560]) ).
cnf(c_10562,plain,
complement(composition(A,sK0)) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_190,c_10561]) ).
cnf(c_1273,plain,
join(complement(A),complement(composition(A,sK0))) = complement(composition(A,sK0)),
inference(copy,[status(thm)],[c_10562]) ).
cnf(c_10563,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1269,c_24]) ).
cnf(c_10564,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_23,c_10563]) ).
cnf(c_10565,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_23,c_10564]) ).
cnf(c_10566,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_10565]) ).
cnf(c_10567,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1269,c_10566]) ).
cnf(c_1481,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_10567]) ).
cnf(c_1489,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_1481,c_832]) ).
cnf(c_10568,plain,
join(composition(A,B),complement(composition(top,B))) = join(complement(composition(complement(A),B)),composition(A,B)),
inference(paramod,[status(thm)],[c_59,c_1254]) ).
cnf(c_10569,plain,
join(composition(A,B),complement(composition(top,B))) = join(composition(A,B),complement(composition(complement(A),B))),
inference(paramod,[status(thm)],[c_15,c_10568]) ).
cnf(c_1697,plain,
join(composition(A,B),complement(composition(complement(A),B))) = join(composition(A,B),complement(composition(top,B))),
inference(copy,[status(thm)],[c_10569]) ).
cnf(c_1874,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_23,c_1268]) ).
cnf(c_10570,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_1268,c_24]) ).
cnf(c_10571,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_23,c_10570]) ).
cnf(c_10572,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_23,c_10571]) ).
cnf(c_10573,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_10572]) ).
cnf(c_10574,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_1874,c_10573]) ).
cnf(c_1875,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_10574]) ).
cnf(c_1886,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_1875,c_23]) ).
cnf(c_10575,plain,
composition(complement(converse(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_1886,c_386]) ).
cnf(c_10576,plain,
composition(complement(composition(converse(top),converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_25,c_10575]) ).
cnf(c_1935,plain,
composition(complement(composition(top,converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_474,c_10576]) ).
cnf(c_10577,plain,
join(complement(join(complement(complement(A)),B)),complement(join(complement(complement(composition(A,sK0))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sK0))))))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_1273,c_207]) ).
cnf(c_10578,plain,
join(complement(join(A,B)),complement(join(complement(complement(composition(A,sK0))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sK0))))))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_99,c_10577]) ).
cnf(c_10579,plain,
join(complement(join(A,B)),complement(join(composition(A,sK0),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sK0))))))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_99,c_10578]) ).
cnf(c_10580,plain,
join(complement(join(A,B)),complement(join(composition(A,sK0),complement(join(complement(join(A,complement(B))),complement(composition(A,sK0))))))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_99,c_10579]) ).
cnf(c_10581,plain,
join(complement(join(A,B)),complement(composition(A,sK0))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_612,c_10580]) ).
cnf(c_2268,plain,
join(complement(join(A,B)),complement(composition(A,sK0))) = complement(composition(A,sK0)),
inference(paramod,[status(thm)],[c_1273,c_10581]) ).
cnf(c_10582,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_1489]) ).
cnf(c_10583,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_10582]) ).
cnf(c_2670,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_23,c_10583]) ).
cnf(c_2701,plain,
join(complement(one),composition(sK0,top)) = join(sK0,complement(one)),
inference(paramod,[status(thm)],[c_2670,c_179]) ).
cnf(c_10584,plain,
join(complement(one),complement(join(sK0,complement(one)))) = join(complement(composition(sK0,top)),complement(one)),
inference(paramod,[status(thm)],[c_2701,c_1254]) ).
cnf(c_10585,plain,
join(complement(sK0),complement(one)) = join(complement(composition(sK0,top)),complement(one)),
inference(paramod,[status(thm)],[c_1190,c_10584]) ).
cnf(c_10586,plain,
join(complement(one),complement(sK0)) = join(complement(composition(sK0,top)),complement(one)),
inference(paramod,[status(thm)],[c_15,c_10585]) ).
cnf(c_10587,plain,
complement(sK0) = join(complement(composition(sK0,top)),complement(one)),
inference(paramod,[status(thm)],[c_696,c_10586]) ).
cnf(c_10588,plain,
complement(sK0) = join(complement(one),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_15,c_10587]) ).
cnf(c_2727,plain,
join(complement(one),complement(composition(sK0,top))) = complement(sK0),
inference(copy,[status(thm)],[c_10588]) ).
cnf(c_10589,plain,
converse(complement(sK0)) = join(converse(complement(one)),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_2727,c_24]) ).
cnf(c_10590,plain,
complement(converse(sK0)) = join(converse(complement(one)),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_1886,c_10589]) ).
cnf(c_10591,plain,
complement(converse(sK0)) = join(complement(converse(one)),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_1886,c_10590]) ).
cnf(c_10592,plain,
complement(converse(sK0)) = join(complement(one),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_111,c_10591]) ).
cnf(c_10593,plain,
complement(converse(sK0)) = join(complement(one),complement(converse(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_1886,c_10592]) ).
cnf(c_10594,plain,
complement(converse(sK0)) = join(complement(one),complement(composition(converse(top),converse(sK0)))),
inference(paramod,[status(thm)],[c_25,c_10593]) ).
cnf(c_10595,plain,
complement(converse(sK0)) = join(complement(one),complement(composition(top,converse(sK0)))),
inference(paramod,[status(thm)],[c_474,c_10594]) ).
cnf(c_2734,plain,
join(complement(one),complement(composition(top,converse(sK0)))) = complement(converse(sK0)),
inference(copy,[status(thm)],[c_10595]) ).
cnf(c_10596,plain,
converse(zero) = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_379,c_25]) ).
cnf(c_10597,plain,
zero = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_286,c_10596]) ).
cnf(c_10598,plain,
zero = composition(complement(converse(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_1886,c_10597]) ).
cnf(c_10599,plain,
zero = composition(complement(composition(converse(top),converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_25,c_10598]) ).
cnf(c_10600,plain,
zero = composition(complement(composition(top,converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_474,c_10599]) ).
cnf(c_10601,plain,
zero = composition(complement(composition(top,A)),converse(A)),
inference(paramod,[status(thm)],[c_23,c_10600]) ).
cnf(c_2881,plain,
composition(complement(composition(top,A)),converse(A)) = zero,
inference(copy,[status(thm)],[c_10601]) ).
cnf(c_10602,plain,
join(zero,composition(complement(complement(composition(top,A))),converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_2881,c_59]) ).
cnf(c_10603,plain,
join(zero,composition(composition(top,A),converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_99,c_10602]) ).
cnf(c_10604,plain,
join(zero,composition(top,composition(A,converse(A)))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_20,c_10603]) ).
cnf(c_2936,plain,
composition(top,composition(A,converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_190,c_10604]) ).
cnf(c_10605,plain,
join(zero,composition(complement(complement(composition(top,converse(A)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_1935,c_59]) ).
cnf(c_10606,plain,
join(zero,composition(composition(top,converse(A)),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_99,c_10605]) ).
cnf(c_10607,plain,
join(zero,composition(top,composition(converse(A),A))) = composition(top,A),
inference(paramod,[status(thm)],[c_20,c_10606]) ).
cnf(c_3372,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_190,c_10607]) ).
cnf(c_10608,plain,
join(complement(complement(composition(A,sK0))),complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_1273,c_2268]) ).
cnf(c_10609,plain,
join(composition(A,sK0),complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_99,c_10608]) ).
cnf(c_10610,plain,
join(composition(A,sK0),complement(composition(top,sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_1697,c_10609]) ).
cnf(c_3738,plain,
complement(composition(complement(A),sK0)) = join(composition(A,sK0),complement(composition(top,sK0))),
inference(copy,[status(thm)],[c_10610]) ).
cnf(c_10611,plain,
join(complement(complement(A)),complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_257,c_2268]) ).
cnf(c_10612,plain,
join(A,complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_99,c_10611]) ).
cnf(c_10613,plain,
join(A,join(composition(A,sK0),complement(composition(top,sK0)))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_3738,c_10612]) ).
cnf(c_10614,plain,
join(A,complement(composition(top,sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_780,c_10613]) ).
cnf(c_10615,plain,
join(A,complement(composition(top,sK0))) = join(composition(A,sK0),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_3738,c_10614]) ).
cnf(c_3743,plain,
join(composition(A,sK0),complement(composition(top,sK0))) = join(A,complement(composition(top,sK0))),
inference(copy,[status(thm)],[c_10615]) ).
cnf(c_3761,plain,
complement(composition(complement(A),sK0)) = join(A,complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_3743,c_3738]) ).
cnf(c_3777,plain,
complement(composition(A,sK0)) = join(complement(A),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_99,c_3761]) ).
cnf(c_10616,plain,
complement(zero) = join(composition(top,converse(sK0)),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_1935,c_3761]) ).
cnf(c_10617,plain,
top = join(composition(top,converse(sK0)),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_220,c_10616]) ).
cnf(c_10618,plain,
top = join(complement(composition(top,sK0)),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_15,c_10617]) ).
cnf(c_3789,plain,
join(complement(composition(top,sK0)),composition(top,converse(sK0))) = top,
inference(copy,[status(thm)],[c_10618]) ).
cnf(c_10619,plain,
join(composition(top,converse(sK0)),complement(top)) = join(complement(complement(composition(top,sK0))),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_3789,c_1190]) ).
cnf(c_10620,plain,
join(composition(top,converse(sK0)),zero) = join(complement(complement(composition(top,sK0))),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_30,c_10619]) ).
cnf(c_10621,plain,
join(zero,composition(top,converse(sK0))) = join(complement(complement(composition(top,sK0))),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_15,c_10620]) ).
cnf(c_10622,plain,
composition(top,converse(sK0)) = join(complement(complement(composition(top,sK0))),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_190,c_10621]) ).
cnf(c_10623,plain,
composition(top,converse(sK0)) = join(composition(top,sK0),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_99,c_10622]) ).
cnf(c_4083,plain,
join(composition(top,sK0),composition(top,converse(sK0))) = composition(top,converse(sK0)),
inference(copy,[status(thm)],[c_10623]) ).
cnf(c_10624,plain,
converse(complement(composition(A,sK0))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_3777,c_24]) ).
cnf(c_10625,plain,
complement(converse(composition(A,sK0))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_1886,c_10624]) ).
cnf(c_10626,plain,
complement(composition(converse(sK0),converse(A))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_25,c_10625]) ).
cnf(c_10627,plain,
complement(composition(converse(sK0),converse(A))) = join(complement(converse(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_1886,c_10626]) ).
cnf(c_10628,plain,
complement(composition(converse(sK0),converse(A))) = join(complement(converse(A)),complement(converse(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_1886,c_10627]) ).
cnf(c_10629,plain,
complement(composition(converse(sK0),converse(A))) = join(complement(converse(A)),complement(composition(converse(sK0),converse(top)))),
inference(paramod,[status(thm)],[c_25,c_10628]) ).
cnf(c_4094,plain,
complement(composition(converse(sK0),converse(A))) = join(complement(converse(A)),complement(composition(converse(sK0),top))),
inference(paramod,[status(thm)],[c_474,c_10629]) ).
cnf(c_10630,plain,
complement(sK0) = join(complement(one),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_116,c_3777]) ).
cnf(c_4098,plain,
join(complement(one),complement(composition(top,sK0))) = complement(sK0),
inference(copy,[status(thm)],[c_10630]) ).
cnf(c_10631,plain,
join(complement(A),complement(complement(composition(A,sK0)))) = join(complement(complement(composition(top,sK0))),complement(A)),
inference(paramod,[status(thm)],[c_3777,c_1254]) ).
cnf(c_10632,plain,
join(complement(A),composition(A,sK0)) = join(complement(complement(composition(top,sK0))),complement(A)),
inference(paramod,[status(thm)],[c_99,c_10631]) ).
cnf(c_10633,plain,
join(complement(A),composition(A,sK0)) = join(composition(top,sK0),complement(A)),
inference(paramod,[status(thm)],[c_99,c_10632]) ).
cnf(c_4120,plain,
join(composition(top,sK0),complement(A)) = join(complement(A),composition(A,sK0)),
inference(copy,[status(thm)],[c_10633]) ).
cnf(c_10634,plain,
join(complement(composition(composition(top,sK0),converse(sK0))),composition(composition(composition(top,sK0),converse(sK0)),sK0)) = top,
inference(paramod,[status(thm)],[c_4120,c_1079]) ).
cnf(c_10635,plain,
join(complement(composition(top,composition(sK0,converse(sK0)))),composition(composition(composition(top,sK0),converse(sK0)),sK0)) = top,
inference(paramod,[status(thm)],[c_20,c_10634]) ).
cnf(c_10636,plain,
join(complement(composition(top,converse(sK0))),composition(composition(composition(top,sK0),converse(sK0)),sK0)) = top,
inference(paramod,[status(thm)],[c_2936,c_10635]) ).
cnf(c_10637,plain,
join(complement(composition(top,converse(sK0))),composition(composition(top,composition(sK0,converse(sK0))),sK0)) = top,
inference(paramod,[status(thm)],[c_20,c_10636]) ).
cnf(c_10638,plain,
join(complement(composition(top,converse(sK0))),composition(composition(top,converse(sK0)),sK0)) = top,
inference(paramod,[status(thm)],[c_2936,c_10637]) ).
cnf(c_10639,plain,
join(complement(composition(top,converse(sK0))),composition(top,composition(converse(sK0),sK0))) = top,
inference(paramod,[status(thm)],[c_20,c_10638]) ).
cnf(c_10640,plain,
join(complement(composition(top,converse(sK0))),composition(top,sK0)) = top,
inference(paramod,[status(thm)],[c_3372,c_10639]) ).
cnf(c_4194,plain,
join(composition(top,sK0),complement(composition(top,converse(sK0)))) = top,
inference(paramod,[status(thm)],[c_15,c_10640]) ).
cnf(c_10641,plain,
join(complement(composition(top,converse(sK0))),complement(join(composition(top,sK0),complement(composition(top,converse(sK0)))))) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_4083,c_341]) ).
cnf(c_10642,plain,
join(complement(composition(top,converse(sK0))),complement(top)) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_4194,c_10641]) ).
cnf(c_10643,plain,
join(complement(composition(top,converse(sK0))),zero) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_30,c_10642]) ).
cnf(c_10644,plain,
join(zero,complement(composition(top,converse(sK0)))) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_15,c_10643]) ).
cnf(c_4389,plain,
complement(composition(top,converse(sK0))) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_190,c_10644]) ).
cnf(c_10645,plain,
join(complement(one),complement(composition(top,sK0))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_4389,c_2734]) ).
cnf(c_10646,plain,
complement(sK0) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_4098,c_10645]) ).
cnf(c_4400,plain,
complement(converse(sK0)) = complement(sK0),
inference(copy,[status(thm)],[c_10646]) ).
cnf(c_10647,plain,
complement(complement(sK0)) = converse(sK0),
inference(paramod,[status(thm)],[c_4400,c_99]) ).
cnf(c_10648,plain,
sK0 = converse(sK0),
inference(paramod,[status(thm)],[c_99,c_10647]) ).
cnf(c_4450,plain,
converse(sK0) = sK0,
inference(copy,[status(thm)],[c_10648]) ).
cnf(c_10649,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),complement(composition(converse(sK0),top))),
inference(paramod,[status(thm)],[c_4450,c_4094]) ).
cnf(c_10650,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_4450,c_10649]) ).
cnf(c_4487,plain,
complement(composition(sK0,converse(A))) = join(complement(composition(sK0,top)),complement(converse(A))),
inference(paramod,[status(thm)],[c_15,c_10650]) ).
cnf(c_10651,plain,
complement(composition(sK0,A)) = join(complement(composition(sK0,top)),complement(converse(converse(A)))),
inference(paramod,[status(thm)],[c_23,c_4487]) ).
cnf(c_6488,plain,
complement(composition(sK0,A)) = join(complement(composition(sK0,top)),complement(A)),
inference(paramod,[status(thm)],[c_23,c_10651]) ).
cnf(c_10652,plain,
complement(join(join(complement(composition(sK0,top)),complement(sK1)),composition(sK0,sK2))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_6488,c_102]) ).
cnf(c_10653,plain,
complement(join(join(complement(sK1),complement(composition(sK0,top))),composition(sK0,sK2))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_15,c_10652]) ).
cnf(c_6532,plain,
complement(join(complement(sK1),join(complement(composition(sK0,top)),composition(sK0,sK2)))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_16,c_10653]) ).
cnf(c_10654,plain,
join(complement(composition(sK0,top)),complement(complement(composition(sK0,A)))) = join(complement(complement(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_6488,c_1254]) ).
cnf(c_10655,plain,
join(complement(composition(sK0,top)),composition(sK0,A)) = join(complement(complement(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_99,c_10654]) ).
cnf(c_6561,plain,
join(complement(composition(sK0,top)),composition(sK0,A)) = join(A,complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_99,c_10655]) ).
cnf(c_10656,plain,
complement(join(complement(sK1),join(complement(composition(sK0,top)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(composition(sK0,top)),complement(sK1)))),
inference(paramod,[status(thm)],[c_6488,c_6532]) ).
cnf(c_6949,plain,
complement(join(complement(sK1),join(complement(composition(sK0,top)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top))))),
inference(paramod,[status(thm)],[c_15,c_10656]) ).
cnf(c_10657,plain,
complement(join(complement(sK1),join(sK2,complement(composition(sK0,top))))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top))))),
inference(paramod,[status(thm)],[c_6561,c_6949]) ).
cnf(c_10658,plain,
complement(join(sK2,join(complement(sK1),complement(composition(sK0,top))))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top))))),
inference(paramod,[status(thm)],[c_36,c_10657]) ).
cnf(c_10429,plain,
$false,
inference(copy,[status(thm)],[c_10658]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL030+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.57 % Computer : n011.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Sat Sep 26 05:34:34 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.57 % Process 3888569 was started by sandbox on n011,
% 0.09/5.57 % Sat Sep 26 05:34:34 2026
% 0.09/5.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.58
% 0.09/5.58 % From the command line: assign(max_seconds, 300).
% 29.88/9.91
% 29.88/9.91 % SZS status Theorem for theBenchmark
% 29.88/9.91
% 29.88/9.91 % Proof 1 at 3.51 (+ 0.77) seconds.
% 29.88/9.91 % Length of proof is 150.
% 29.88/9.91 % Level of proof is 30.
% 29.88/9.91 % Maximum clause weight is 93.000.
% 29.88/9.91 % Given clauses 474.
% 29.88/9.91
% 29.88/9.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------