%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL030+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 54.03s 7.27s
% Output : CNFRefutation 54.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 16
% Syntax : Number of formulae : 365 ( 361 unt; 0 def)
% Number of atoms : 369 ( 368 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 : 12 ( 3 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 : 484 ( 20 sgn 37 !; 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_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(dedekind_law,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('theBenchmark.p',dedekind_law) ).
fof(modular_law_1,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2),
file('theBenchmark.p',modular_law_1) ).
fof(modular_law_2,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2),
file('theBenchmark.p',modular_law_2) ).
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_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_20,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_21,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_22,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_24,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_27,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_28,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_29,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_9494,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_30,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_9494]) ).
cnf(c_31,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_32,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_9495,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_9495]) ).
cnf(c_34,plain,
composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(clausify,[status(thm)],[dedekind_law]) ).
cnf(c_9496,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_34]) ).
cnf(c_9497,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_9496]) ).
cnf(c_9498,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_9497]) ).
cnf(c_9499,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_9498]) ).
cnf(c_9500,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B)))))),
inference(paramod,[status(thm)],[c_22,c_9499]) ).
cnf(c_35,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C))))),
inference(copy,[status(thm)],[c_9500]) ).
cnf(c_36,plain,
meet(composition(A,meet(B,composition(converse(A),C))),C) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)),
inference(clausify,[status(thm)],[modular_law_1]) ).
cnf(c_9501,plain,
meet(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))),C) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)),
inference(paramod,[status(thm)],[c_22,c_36]) ).
cnf(c_9502,plain,
complement(join(complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))),complement(C))) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)),
inference(paramod,[status(thm)],[c_22,c_9501]) ).
cnf(c_9503,plain,
complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))))) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)),
inference(paramod,[status(thm)],[c_18,c_9502]) ).
cnf(c_9504,plain,
complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))))) = join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(A,meet(B,composition(converse(A),C))),C)),
inference(paramod,[status(thm)],[c_22,c_9503]) ).
cnf(c_9505,plain,
complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))))) = join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))),C)),
inference(paramod,[status(thm)],[c_22,c_9504]) ).
cnf(c_9506,plain,
complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))))) = join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))),complement(C)))),
inference(paramod,[status(thm)],[c_22,c_9505]) ).
cnf(c_9507,plain,
complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))))) = join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))))))),
inference(paramod,[status(thm)],[c_18,c_9506]) ).
cnf(c_37,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C))))))))) = complement(join(complement(C),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),C)))))))),
inference(copy,[status(thm)],[c_9507]) ).
cnf(c_38,plain,
meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(clausify,[status(thm)],[modular_law_2]) ).
cnf(c_9508,plain,
meet(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_22,c_38]) ).
cnf(c_9509,plain,
complement(join(complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)),complement(B))) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_22,c_9508]) ).
cnf(c_9510,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_18,c_9509]) ).
cnf(c_9511,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_22,c_9510]) ).
cnf(c_9512,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),meet(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C),B)),
inference(paramod,[status(thm)],[c_22,c_9511]) ).
cnf(c_9513,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),complement(join(complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)),complement(B)))),
inference(paramod,[status(thm)],[c_22,c_9512]) ).
cnf(c_9514,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C))))),
inference(paramod,[status(thm)],[c_18,c_9513]) ).
cnf(c_39,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)))),
inference(copy,[status(thm)],[c_9514]) ).
fof(nnf_17,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_17]) ).
cnf(c_40,negated_conjecture,
join(sK0,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,negated_conjecture,
join(one,sK0) = one,
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_42,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_9515,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != meet(composition(sK0,sK1),complement(sK2)),
inference(paramod,[status(thm)],[c_22,c_42]) ).
cnf(c_9516,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_22,c_9515]) ).
cnf(c_43,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_18,c_9516]) ).
cnf(c_9517,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_45,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_19,c_9517]) ).
cnf(c_46,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_47,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_9518,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_48,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_9518]) ).
cnf(c_9519,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_21,c_21]) ).
cnf(c_9520,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_18,c_9519]) ).
cnf(c_9521,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_19,c_9520]) ).
cnf(c_50,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_18,c_9521]) ).
cnf(c_9522,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_54,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_9522]) ).
cnf(c_9523,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_30,c_19]) ).
cnf(c_56,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_9523]) ).
cnf(c_9524,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_31,c_19]) ).
cnf(c_64,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_9524]) ).
cnf(c_9525,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_66,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_9525]) ).
cnf(c_9526,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_31,c_25]) ).
cnf(c_68,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_9526]) ).
cnf(c_9527,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_69,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_9527]) ).
cnf(c_77,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_24,c_35]) ).
cnf(c_9528,plain,
join(complement(join(complement(composition(A,B)),complement(one))),complement(join(complement(one),complement(composition(A,complement(join(complement(B),complement(converse(A))))))))) = complement(join(complement(one),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),one)))))))),
inference(paramod,[status(thm)],[c_24,c_37]) ).
cnf(c_9529,plain,
join(complement(join(complement(one),complement(composition(A,B)))),complement(join(complement(one),complement(composition(A,complement(join(complement(B),complement(converse(A))))))))) = complement(join(complement(one),complement(composition(A,complement(join(complement(B),complement(composition(converse(A),one)))))))),
inference(paramod,[status(thm)],[c_18,c_9528]) ).
cnf(c_89,plain,
join(complement(join(complement(one),complement(composition(A,B)))),complement(join(complement(one),complement(composition(A,complement(join(complement(B),complement(converse(A))))))))) = complement(join(complement(one),complement(composition(A,complement(join(complement(B),complement(converse(A)))))))),
inference(paramod,[status(thm)],[c_24,c_9529]) ).
cnf(c_9530,plain,
join(one,A) = join(one,join(sK0,A)),
inference(paramod,[status(thm)],[c_41,c_19]) ).
cnf(c_99,plain,
join(one,join(sK0,A)) = join(one,A),
inference(copy,[status(thm)],[c_9530]) ).
cnf(c_9531,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_41,c_25]) ).
cnf(c_101,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_9531]) ).
cnf(c_9532,plain,
converse(one) = join(converse(one),converse(sK0)),
inference(paramod,[status(thm)],[c_41,c_27]) ).
cnf(c_102,plain,
join(converse(one),converse(sK0)) = converse(one),
inference(copy,[status(thm)],[c_9532]) ).
cnf(c_9533,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_46,c_18]) ).
cnf(c_108,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_9533]) ).
cnf(c_9534,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_9535,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_9534]) ).
cnf(c_9536,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_9535]) ).
cnf(c_127,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_9536]) ).
cnf(c_9537,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_47,c_47]) ).
cnf(c_9538,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_18,c_9537]) ).
cnf(c_9539,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_19,c_9538]) ).
cnf(c_132,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_18,c_9539]) ).
cnf(c_133,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_127,c_66]) ).
cnf(c_134,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_127]) ).
cnf(c_9540,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_133,c_43]) ).
cnf(c_137,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_133,c_9540]) ).
cnf(c_9541,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_54]) ).
cnf(c_144,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_9541]) ).
cnf(c_9542,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(converse(one)),complement(composition(B,converse(converse(A)))))),complement(join(complement(converse(A)),complement(composition(converse(converse(one)),B)))))) = composition(complement(join(complement(converse(one)),complement(composition(B,converse(converse(A)))))),complement(join(complement(converse(A)),complement(composition(converse(converse(one)),B))))),
inference(paramod,[status(thm)],[c_54,c_35]) ).
cnf(c_9543,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(converse(one)),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(converse(converse(one)),B)))))) = composition(complement(join(complement(converse(one)),complement(composition(B,converse(converse(A)))))),complement(join(complement(converse(A)),complement(composition(converse(converse(one)),B))))),
inference(paramod,[status(thm)],[c_26,c_9542]) ).
cnf(c_9544,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(converse(one)),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B)))))) = composition(complement(join(complement(converse(one)),complement(composition(B,converse(converse(A)))))),complement(join(complement(converse(A)),complement(composition(converse(converse(one)),B))))),
inference(paramod,[status(thm)],[c_26,c_9543]) ).
cnf(c_9545,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(converse(one)),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B)))))) = composition(complement(join(complement(converse(one)),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(converse(converse(one)),B))))),
inference(paramod,[status(thm)],[c_26,c_9544]) ).
cnf(c_146,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(converse(one)),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B)))))) = composition(complement(join(complement(converse(one)),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B))))),
inference(paramod,[status(thm)],[c_26,c_9545]) ).
cnf(c_9546,plain,
join(complement(join(complement(converse(A)),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,converse(converse(A)))))),converse(A)))))) = complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,converse(converse(A)))))),converse(A))))),
inference(paramod,[status(thm)],[c_54,c_39]) ).
cnf(c_9547,plain,
join(complement(join(complement(converse(A)),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,A)))),converse(A)))))) = complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,converse(converse(A)))))),converse(A))))),
inference(paramod,[status(thm)],[c_26,c_9546]) ).
cnf(c_151,plain,
join(complement(join(complement(converse(A)),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,A)))),converse(A)))))) = complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,A)))),converse(A))))),
inference(paramod,[status(thm)],[c_26,c_9547]) ).
cnf(c_9548,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_144,c_24]) ).
cnf(c_153,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_9548]) ).
cnf(c_157,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_144,c_30]) ).
cnf(c_9549,plain,
join(complement(join(complement(converse(A)),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(one),complement(composition(B,A)))),converse(A)))))) = complement(join(complement(B),complement(composition(complement(join(complement(converse(one)),complement(composition(B,A)))),converse(A))))),
inference(paramod,[status(thm)],[c_153,c_151]) ).
cnf(c_169,plain,
join(complement(join(complement(converse(A)),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(one),complement(composition(B,A)))),converse(A)))))) = complement(join(complement(B),complement(composition(complement(join(complement(one),complement(composition(B,A)))),converse(A))))),
inference(paramod,[status(thm)],[c_153,c_9549]) ).
cnf(c_9550,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(one),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B)))))) = composition(complement(join(complement(converse(one)),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B))))),
inference(paramod,[status(thm)],[c_153,c_146]) ).
cnf(c_171,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(one),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B)))))) = composition(complement(join(complement(one),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B))))),
inference(paramod,[status(thm)],[c_153,c_9550]) ).
cnf(c_172,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_153,c_144]) ).
cnf(c_9551,plain,
join(one,converse(sK0)) = converse(one),
inference(paramod,[status(thm)],[c_153,c_102]) ).
cnf(c_174,plain,
join(one,converse(sK0)) = one,
inference(paramod,[status(thm)],[c_153,c_9551]) ).
cnf(c_9552,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(composition(B,one)))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_153,c_77]) ).
cnf(c_9553,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,converse(one))))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_24,c_9552]) ).
cnf(c_9554,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(composition(B,one)))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_153,c_9553]) ).
cnf(c_175,plain,
join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B)))))) = composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(A),B))))),
inference(paramod,[status(thm)],[c_24,c_9554]) ).
cnf(c_9555,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_172,c_101]) ).
cnf(c_176,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_172,c_9555]) ).
cnf(c_9556,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(one),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(B))))) = composition(complement(join(complement(one),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(composition(one,B))))),
inference(paramod,[status(thm)],[c_172,c_171]) ).
cnf(c_178,plain,
join(complement(join(complement(converse(A)),complement(B))),composition(complement(join(complement(one),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(B))))) = composition(complement(join(complement(one),complement(composition(B,A)))),complement(join(complement(converse(A)),complement(B)))),
inference(paramod,[status(thm)],[c_172,c_9556]) ).
cnf(c_179,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_172,c_157]) ).
cnf(c_9557,plain,
composition(one,A) = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_174,c_25]) ).
cnf(c_9558,plain,
A = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_172,c_9557]) ).
cnf(c_9559,plain,
A = join(A,composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_172,c_9558]) ).
cnf(c_181,plain,
join(A,composition(converse(sK0),A)) = A,
inference(copy,[status(thm)],[c_9559]) ).
cnf(c_9560,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_46,c_48]) ).
cnf(c_9561,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_18,c_9560]) ).
cnf(c_202,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_133,c_9561]) ).
cnf(c_9562,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_50,c_45]) ).
cnf(c_215,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_9562]) ).
cnf(c_9563,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_50,c_46]) ).
cnf(c_9564,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_133,c_9563]) ).
cnf(c_217,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_18,c_9564]) ).
cnf(c_9565,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_48,c_50]) ).
cnf(c_9566,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_18,c_9565]) ).
cnf(c_223,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_48,c_9566]) ).
cnf(c_9567,plain,
converse(A) = join(converse(A),converse(composition(sK0,A))),
inference(paramod,[status(thm)],[c_176,c_27]) ).
cnf(c_9568,plain,
converse(A) = join(converse(A),composition(converse(A),converse(sK0))),
inference(paramod,[status(thm)],[c_28,c_9567]) ).
cnf(c_241,plain,
join(converse(A),composition(converse(A),converse(sK0))) = converse(A),
inference(copy,[status(thm)],[c_9568]) ).
cnf(c_9569,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_179,c_21]) ).
cnf(c_9570,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_18,c_9569]) ).
cnf(c_9571,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_31,c_9570]) ).
cnf(c_9572,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_33,c_9571]) ).
cnf(c_253,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_133,c_9572]) ).
cnf(c_9573,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_179,c_48]) ).
cnf(c_9574,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_21,c_9573]) ).
cnf(c_256,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_9574]) ).
cnf(c_265,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_253,c_134]) ).
cnf(c_275,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_256,c_132]) ).
cnf(c_9575,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_275,c_223]) ).
cnf(c_277,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_18,c_9575]) ).
cnf(c_9576,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_176,c_56]) ).
cnf(c_9577,plain,
complement(A) = join(complement(A),composition(sK0,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_30,c_9576]) ).
cnf(c_334,plain,
join(complement(A),composition(sK0,composition(converse(B),complement(composition(B,A))))) = complement(A),
inference(copy,[status(thm)],[c_9577]) ).
cnf(c_9578,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_265,c_21]) ).
cnf(c_9579,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_265,c_9578]) ).
cnf(c_9580,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_21,c_9579]) ).
cnf(c_348,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_9580]) ).
cnf(c_9581,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_348,c_19]) ).
cnf(c_353,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_18,c_9581]) ).
cnf(c_9582,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_348,c_48]) ).
cnf(c_9583,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_18,c_9582]) ).
cnf(c_9584,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_256,c_9583]) ).
cnf(c_354,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_18,c_9584]) ).
cnf(c_9585,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_354,c_217]) ).
cnf(c_9586,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_18,c_9585]) ).
cnf(c_9587,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_275,c_9586]) ).
cnf(c_356,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_9587]) ).
cnf(c_359,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_356,c_215]) ).
cnf(c_9588,plain,
converse(A) = join(converse(A),converse(composition(converse(sK0),A))),
inference(paramod,[status(thm)],[c_181,c_27]) ).
cnf(c_9589,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sK0)))),
inference(paramod,[status(thm)],[c_28,c_9588]) ).
cnf(c_9590,plain,
converse(A) = join(converse(A),composition(converse(A),sK0)),
inference(paramod,[status(thm)],[c_26,c_9589]) ).
cnf(c_503,plain,
join(converse(A),composition(converse(A),sK0)) = converse(A),
inference(copy,[status(thm)],[c_9590]) ).
cnf(c_9591,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_348,c_64]) ).
cnf(c_9592,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_31,c_9591]) ).
cnf(c_537,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_9592]) ).
cnf(c_9593,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_348,c_64]) ).
cnf(c_9594,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_18,c_9593]) ).
cnf(c_538,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_537,c_9594]) ).
cnf(c_9595,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_538,c_18]) ).
cnf(c_572,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_9595]) ).
cnf(c_9596,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_538,c_27]) ).
cnf(c_574,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_9596]) ).
cnf(c_594,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_574]) ).
cnf(c_597,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_594,c_572]) ).
cnf(c_608,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_597,c_69]) ).
cnf(c_731,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_26,c_608]) ).
cnf(c_9597,plain,
join(one,top) = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_31,c_99]) ).
cnf(c_9598,plain,
top = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_538,c_9597]) ).
cnf(c_739,plain,
join(one,complement(sK0)) = top,
inference(copy,[status(thm)],[c_9598]) ).
cnf(c_9599,plain,
join(A,composition(converse(converse(A)),sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_503]) ).
cnf(c_9600,plain,
join(A,composition(A,sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_9599]) ).
cnf(c_900,plain,
join(A,composition(A,sK0)) = A,
inference(paramod,[status(thm)],[c_26,c_9600]) ).
cnf(c_9601,plain,
join(A,B) = join(A,join(composition(A,sK0),B)),
inference(paramod,[status(thm)],[c_900,c_19]) ).
cnf(c_904,plain,
join(A,join(composition(A,sK0),B)) = join(A,B),
inference(copy,[status(thm)],[c_9601]) ).
cnf(c_9602,plain,
join(complement(join(A,complement(B))),complement(join(B,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_108]) ).
cnf(c_943,plain,
join(complement(join(A,complement(B))),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_9602]) ).
cnf(c_9603,plain,
join(complement(join(complement(sK0),complement(one))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_739,c_108]) ).
cnf(c_9604,plain,
join(complement(join(complement(one),complement(sK0))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_18,c_9603]) ).
cnf(c_9605,plain,
join(complement(join(complement(one),complement(sK0))),zero) = sK0,
inference(paramod,[status(thm)],[c_33,c_9604]) ).
cnf(c_9606,plain,
join(zero,complement(join(complement(one),complement(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_18,c_9605]) ).
cnf(c_944,plain,
complement(join(complement(one),complement(sK0))) = sK0,
inference(paramod,[status(thm)],[c_253,c_9606]) ).
cnf(c_9607,plain,
join(complement(join(A,complement(B))),B) = join(complement(join(complement(B),complement(A))),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_108,c_353]) ).
cnf(c_9608,plain,
join(B,complement(join(A,complement(B)))) = join(complement(join(complement(B),complement(A))),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_9607]) ).
cnf(c_9609,plain,
join(B,complement(join(A,complement(B)))) = complement(complement(B)),
inference(paramod,[status(thm)],[c_943,c_9608]) ).
cnf(c_945,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_133,c_9609]) ).
cnf(c_9610,plain,
complement(sK0) = join(complement(one),complement(sK0)),
inference(paramod,[status(thm)],[c_944,c_133]) ).
cnf(c_978,plain,
join(complement(one),complement(sK0)) = complement(sK0),
inference(copy,[status(thm)],[c_9610]) ).
cnf(c_9611,plain,
join(complement(sK0),A) = join(complement(one),join(complement(sK0),A)),
inference(paramod,[status(thm)],[c_978,c_19]) ).
cnf(c_984,plain,
join(complement(one),join(complement(sK0),A)) = join(complement(sK0),A),
inference(copy,[status(thm)],[c_9611]) ).
cnf(c_9612,plain,
join(A,composition(converse(converse(A)),converse(sK0))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_241]) ).
cnf(c_9613,plain,
join(A,composition(A,converse(sK0))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_9612]) ).
cnf(c_1162,plain,
join(A,composition(A,converse(sK0))) = A,
inference(paramod,[status(thm)],[c_26,c_9613]) ).
cnf(c_9614,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(complement(A)),C)))) = complement(A),
inference(paramod,[status(thm)],[c_354,c_56]) ).
cnf(c_9615,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(A,C)))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_9614]) ).
cnf(c_1401,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_56,c_9615]) ).
cnf(c_1414,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_1401]) ).
cnf(c_9616,plain,
join(complement(composition(A,sK0)),complement(A)) = complement(composition(A,sK0)),
inference(paramod,[status(thm)],[c_900,c_1414]) ).
cnf(c_1451,plain,
join(complement(A),complement(composition(A,sK0))) = complement(composition(A,sK0)),
inference(paramod,[status(thm)],[c_18,c_9616]) ).
cnf(c_9617,plain,
join(complement(composition(A,converse(sK0))),complement(A)) = complement(composition(A,converse(sK0))),
inference(paramod,[status(thm)],[c_1162,c_1414]) ).
cnf(c_1453,plain,
join(complement(A),complement(composition(A,converse(sK0)))) = complement(composition(A,converse(sK0))),
inference(paramod,[status(thm)],[c_18,c_9617]) ).
cnf(c_9618,plain,
join(complement(complement(sK0)),composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0)))))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_978,c_175]) ).
cnf(c_9619,plain,
join(sK0,composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0)))))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_133,c_9618]) ).
cnf(c_9620,plain,
join(sK0,composition(complement(complement(sK0)),complement(join(complement(one),complement(composition(converse(one),sK0)))))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_978,c_9619]) ).
cnf(c_9621,plain,
join(sK0,composition(sK0,complement(join(complement(one),complement(composition(converse(one),sK0)))))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_133,c_9620]) ).
cnf(c_9622,plain,
join(sK0,composition(sK0,complement(join(complement(one),complement(composition(one,sK0)))))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_153,c_9621]) ).
cnf(c_9623,plain,
join(sK0,composition(sK0,complement(join(complement(one),complement(sK0))))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_172,c_9622]) ).
cnf(c_9624,plain,
join(sK0,composition(sK0,complement(complement(sK0)))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_978,c_9623]) ).
cnf(c_9625,plain,
join(sK0,composition(sK0,sK0)) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_133,c_9624]) ).
cnf(c_9626,plain,
sK0 = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_900,c_9625]) ).
cnf(c_9627,plain,
sK0 = composition(complement(complement(sK0)),complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_978,c_9626]) ).
cnf(c_9628,plain,
sK0 = composition(sK0,complement(join(complement(one),complement(composition(converse(one),sK0))))),
inference(paramod,[status(thm)],[c_133,c_9627]) ).
cnf(c_9629,plain,
sK0 = composition(sK0,complement(join(complement(one),complement(composition(one,sK0))))),
inference(paramod,[status(thm)],[c_153,c_9628]) ).
cnf(c_9630,plain,
sK0 = composition(sK0,complement(join(complement(one),complement(sK0)))),
inference(paramod,[status(thm)],[c_172,c_9629]) ).
cnf(c_9631,plain,
sK0 = composition(sK0,complement(complement(sK0))),
inference(paramod,[status(thm)],[c_978,c_9630]) ).
cnf(c_9632,plain,
sK0 = composition(sK0,sK0),
inference(paramod,[status(thm)],[c_133,c_9631]) ).
cnf(c_1478,plain,
composition(sK0,sK0) = sK0,
inference(copy,[status(thm)],[c_9632]) ).
cnf(c_9633,plain,
join(complement(join(complement(one),complement(sK0))),complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0))))))))) = complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))))),
inference(paramod,[status(thm)],[c_1478,c_89]) ).
cnf(c_9634,plain,
join(complement(complement(sK0)),complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0))))))))) = complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))))),
inference(paramod,[status(thm)],[c_978,c_9633]) ).
cnf(c_1528,plain,
join(sK0,complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0))))))))) = complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))))),
inference(paramod,[status(thm)],[c_133,c_9634]) ).
cnf(c_9635,plain,
join(complement(join(complement(converse(sK0)),complement(sK0))),complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(sK0))),converse(sK0)))))) = complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(composition(sK0,sK0)))),converse(sK0))))),
inference(paramod,[status(thm)],[c_1478,c_169]) ).
cnf(c_9636,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(sK0))),converse(sK0)))))) = complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(composition(sK0,sK0)))),converse(sK0))))),
inference(paramod,[status(thm)],[c_18,c_9635]) ).
cnf(c_9637,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),complement(join(complement(sK0),complement(composition(complement(complement(sK0)),converse(sK0)))))) = complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(composition(sK0,sK0)))),converse(sK0))))),
inference(paramod,[status(thm)],[c_978,c_9636]) ).
cnf(c_9638,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),complement(join(complement(sK0),complement(composition(sK0,converse(sK0)))))) = complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(composition(sK0,sK0)))),converse(sK0))))),
inference(paramod,[status(thm)],[c_133,c_9637]) ).
cnf(c_9639,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),complement(complement(composition(sK0,converse(sK0))))) = complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(composition(sK0,sK0)))),converse(sK0))))),
inference(paramod,[status(thm)],[c_1453,c_9638]) ).
cnf(c_9640,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,converse(sK0))) = complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(composition(sK0,sK0)))),converse(sK0))))),
inference(paramod,[status(thm)],[c_133,c_9639]) ).
cnf(c_9641,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,converse(sK0))) = complement(join(complement(sK0),complement(composition(complement(join(complement(one),complement(sK0))),converse(sK0))))),
inference(paramod,[status(thm)],[c_1478,c_9640]) ).
cnf(c_9642,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,converse(sK0))) = complement(join(complement(sK0),complement(composition(complement(complement(sK0)),converse(sK0))))),
inference(paramod,[status(thm)],[c_978,c_9641]) ).
cnf(c_9643,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,converse(sK0))) = complement(join(complement(sK0),complement(composition(sK0,converse(sK0))))),
inference(paramod,[status(thm)],[c_133,c_9642]) ).
cnf(c_9644,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,converse(sK0))) = complement(complement(composition(sK0,converse(sK0)))),
inference(paramod,[status(thm)],[c_1453,c_9643]) ).
cnf(c_1532,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,converse(sK0))) = composition(sK0,converse(sK0)),
inference(paramod,[status(thm)],[c_133,c_9644]) ).
cnf(c_9645,plain,
join(complement(join(complement(converse(sK0)),complement(sK0))),composition(complement(join(complement(one),complement(sK0))),complement(join(complement(converse(sK0)),complement(sK0))))) = composition(complement(join(complement(one),complement(composition(sK0,sK0)))),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_1478,c_178]) ).
cnf(c_9646,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(complement(join(complement(one),complement(sK0))),complement(join(complement(converse(sK0)),complement(sK0))))) = composition(complement(join(complement(one),complement(composition(sK0,sK0)))),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_18,c_9645]) ).
cnf(c_9647,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(complement(complement(sK0)),complement(join(complement(converse(sK0)),complement(sK0))))) = composition(complement(join(complement(one),complement(composition(sK0,sK0)))),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_978,c_9646]) ).
cnf(c_9648,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,complement(join(complement(converse(sK0)),complement(sK0))))) = composition(complement(join(complement(one),complement(composition(sK0,sK0)))),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_133,c_9647]) ).
cnf(c_9649,plain,
join(complement(join(complement(sK0),complement(converse(sK0)))),composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))) = composition(complement(join(complement(one),complement(composition(sK0,sK0)))),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_18,c_9648]) ).
cnf(c_9650,plain,
complement(join(complement(sK0),complement(converse(sK0)))) = composition(complement(join(complement(one),complement(composition(sK0,sK0)))),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_176,c_9649]) ).
cnf(c_9651,plain,
complement(join(complement(sK0),complement(converse(sK0)))) = composition(complement(join(complement(one),complement(sK0))),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_1478,c_9650]) ).
cnf(c_9652,plain,
complement(join(complement(sK0),complement(converse(sK0)))) = composition(complement(complement(sK0)),complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_978,c_9651]) ).
cnf(c_9653,plain,
complement(join(complement(sK0),complement(converse(sK0)))) = composition(sK0,complement(join(complement(converse(sK0)),complement(sK0)))),
inference(paramod,[status(thm)],[c_133,c_9652]) ).
cnf(c_9654,plain,
complement(join(complement(sK0),complement(converse(sK0)))) = composition(sK0,complement(join(complement(sK0),complement(converse(sK0))))),
inference(paramod,[status(thm)],[c_18,c_9653]) ).
cnf(c_1534,plain,
composition(sK0,complement(join(complement(sK0),complement(converse(sK0))))) = complement(join(complement(sK0),complement(converse(sK0)))),
inference(copy,[status(thm)],[c_9654]) ).
cnf(c_9655,plain,
join(sK0,complement(join(complement(one),complement(complement(join(complement(sK0),complement(converse(sK0)))))))) = complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))))),
inference(paramod,[status(thm)],[c_1534,c_1528]) ).
cnf(c_9656,plain,
join(sK0,complement(join(complement(one),join(complement(sK0),complement(converse(sK0)))))) = complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))))),
inference(paramod,[status(thm)],[c_133,c_9655]) ).
cnf(c_9657,plain,
join(sK0,complement(join(complement(sK0),complement(converse(sK0))))) = complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))))),
inference(paramod,[status(thm)],[c_984,c_9656]) ).
cnf(c_9658,plain,
sK0 = complement(join(complement(one),complement(composition(sK0,complement(join(complement(sK0),complement(converse(sK0)))))))),
inference(paramod,[status(thm)],[c_354,c_9657]) ).
cnf(c_9659,plain,
sK0 = complement(join(complement(one),complement(complement(join(complement(sK0),complement(converse(sK0))))))),
inference(paramod,[status(thm)],[c_1534,c_9658]) ).
cnf(c_9660,plain,
sK0 = complement(join(complement(one),join(complement(sK0),complement(converse(sK0))))),
inference(paramod,[status(thm)],[c_133,c_9659]) ).
cnf(c_9661,plain,
sK0 = complement(join(complement(sK0),complement(converse(sK0)))),
inference(paramod,[status(thm)],[c_984,c_9660]) ).
cnf(c_1535,plain,
complement(join(complement(sK0),complement(converse(sK0)))) = sK0,
inference(copy,[status(thm)],[c_9661]) ).
cnf(c_9662,plain,
join(sK0,composition(sK0,converse(sK0))) = composition(sK0,converse(sK0)),
inference(paramod,[status(thm)],[c_1535,c_1532]) ).
cnf(c_9663,plain,
sK0 = composition(sK0,converse(sK0)),
inference(paramod,[status(thm)],[c_1162,c_9662]) ).
cnf(c_1536,plain,
composition(sK0,converse(sK0)) = sK0,
inference(copy,[status(thm)],[c_9663]) ).
cnf(c_9664,plain,
converse(sK0) = composition(converse(converse(sK0)),converse(sK0)),
inference(paramod,[status(thm)],[c_1536,c_28]) ).
cnf(c_9665,plain,
converse(sK0) = composition(sK0,converse(sK0)),
inference(paramod,[status(thm)],[c_26,c_9664]) ).
cnf(c_1538,plain,
converse(sK0) = sK0,
inference(paramod,[status(thm)],[c_1536,c_9665]) ).
cnf(c_9666,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_202,c_56]) ).
cnf(c_9667,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_359,c_9666]) ).
cnf(c_9668,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_45,c_9667]) ).
cnf(c_9669,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_56,c_9668]) ).
cnf(c_9670,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_133,c_9669]) ).
cnf(c_1999,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_9670]) ).
cnf(c_2118,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_18,c_1999]) ).
cnf(c_9671,plain,
join(converse(complement(A)),complement(top)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_608,c_1999]) ).
cnf(c_9672,plain,
join(converse(complement(A)),zero) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_33,c_9671]) ).
cnf(c_9673,plain,
join(zero,converse(complement(A))) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_18,c_9672]) ).
cnf(c_9674,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_253,c_9673]) ).
cnf(c_2129,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_9674]) ).
cnf(c_9675,plain,
join(converse(complement(converse(A))),complement(top)) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_731,c_1999]) ).
cnf(c_9676,plain,
join(converse(complement(converse(A))),zero) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_33,c_9675]) ).
cnf(c_9677,plain,
join(zero,converse(complement(converse(A)))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_9676]) ).
cnf(c_9678,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_253,c_9677]) ).
cnf(c_2145,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_9678]) ).
cnf(c_9679,plain,
join(composition(A,B),complement(composition(top,B))) = join(complement(composition(complement(A),B)),composition(A,B)),
inference(paramod,[status(thm)],[c_68,c_2118]) ).
cnf(c_9680,plain,
join(composition(A,B),complement(composition(top,B))) = join(composition(A,B),complement(composition(complement(A),B))),
inference(paramod,[status(thm)],[c_18,c_9679]) ).
cnf(c_2457,plain,
join(composition(A,B),complement(composition(complement(A),B))) = join(composition(A,B),complement(composition(top,B))),
inference(copy,[status(thm)],[c_9680]) ).
cnf(c_9681,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_2129,c_27]) ).
cnf(c_9682,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_26,c_9681]) ).
cnf(c_9683,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_26,c_9682]) ).
cnf(c_9684,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_9683]) ).
cnf(c_9685,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_2145,c_9684]) ).
cnf(c_2488,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_9685]) ).
cnf(c_2496,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_2488,c_26]) ).
cnf(c_9686,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_1451,c_277]) ).
cnf(c_9687,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_133,c_9686]) ).
cnf(c_9688,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_133,c_9687]) ).
cnf(c_9689,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_133,c_9688]) ).
cnf(c_9690,plain,
join(complement(join(A,B)),complement(composition(A,sK0))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_945,c_9689]) ).
cnf(c_3157,plain,
join(complement(join(A,B)),complement(composition(A,sK0))) = complement(composition(A,sK0)),
inference(paramod,[status(thm)],[c_1451,c_9690]) ).
cnf(c_9691,plain,
join(complement(complement(composition(A,sK0))),complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_1451,c_3157]) ).
cnf(c_9692,plain,
join(composition(A,sK0),complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_133,c_9691]) ).
cnf(c_9693,plain,
join(composition(A,sK0),complement(composition(top,sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_2457,c_9692]) ).
cnf(c_4305,plain,
complement(composition(complement(A),sK0)) = join(composition(A,sK0),complement(composition(top,sK0))),
inference(copy,[status(thm)],[c_9693]) ).
cnf(c_9694,plain,
join(complement(complement(A)),complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_334,c_3157]) ).
cnf(c_9695,plain,
join(A,complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_133,c_9694]) ).
cnf(c_9696,plain,
join(A,join(composition(A,sK0),complement(composition(top,sK0)))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_4305,c_9695]) ).
cnf(c_9697,plain,
join(A,complement(composition(top,sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_904,c_9696]) ).
cnf(c_9698,plain,
join(A,complement(composition(top,sK0))) = join(composition(A,sK0),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_4305,c_9697]) ).
cnf(c_4329,plain,
join(composition(A,sK0),complement(composition(top,sK0))) = join(A,complement(composition(top,sK0))),
inference(copy,[status(thm)],[c_9698]) ).
cnf(c_4350,plain,
complement(composition(complement(A),sK0)) = join(A,complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_4329,c_4305]) ).
cnf(c_4424,plain,
complement(composition(A,sK0)) = join(complement(A),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_133,c_4350]) ).
cnf(c_9699,plain,
converse(complement(composition(A,sK0))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_4424,c_27]) ).
cnf(c_9700,plain,
complement(converse(composition(A,sK0))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_2496,c_9699]) ).
cnf(c_9701,plain,
complement(composition(converse(sK0),converse(A))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_28,c_9700]) ).
cnf(c_9702,plain,
complement(composition(sK0,converse(A))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_1538,c_9701]) ).
cnf(c_9703,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_2496,c_9702]) ).
cnf(c_9704,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),complement(converse(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_2496,c_9703]) ).
cnf(c_9705,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),complement(composition(converse(sK0),converse(top)))),
inference(paramod,[status(thm)],[c_28,c_9704]) ).
cnf(c_9706,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),complement(composition(sK0,converse(top)))),
inference(paramod,[status(thm)],[c_1538,c_9705]) ).
cnf(c_9707,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_597,c_9706]) ).
cnf(c_4476,plain,
complement(composition(sK0,converse(A))) = join(complement(composition(sK0,top)),complement(converse(A))),
inference(paramod,[status(thm)],[c_18,c_9707]) ).
cnf(c_9708,plain,
complement(composition(sK0,A)) = join(complement(composition(sK0,top)),complement(converse(converse(A)))),
inference(paramod,[status(thm)],[c_26,c_4476]) ).
cnf(c_5348,plain,
complement(composition(sK0,A)) = join(complement(composition(sK0,top)),complement(A)),
inference(paramod,[status(thm)],[c_26,c_9708]) ).
cnf(c_9709,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_5348,c_137]) ).
cnf(c_9710,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_18,c_9709]) ).
cnf(c_5405,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_19,c_9710]) ).
cnf(c_9711,plain,
join(complement(composition(sK0,top)),complement(complement(composition(sK0,A)))) = join(complement(complement(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_5348,c_2118]) ).
cnf(c_9712,plain,
join(complement(composition(sK0,top)),composition(sK0,A)) = join(complement(complement(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_133,c_9711]) ).
cnf(c_5472,plain,
join(complement(composition(sK0,top)),composition(sK0,A)) = join(A,complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_133,c_9712]) ).
cnf(c_9713,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_5348,c_5405]) ).
cnf(c_5647,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_18,c_9713]) ).
cnf(c_9714,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_5472,c_5647]) ).
cnf(c_9715,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_45,c_9714]) ).
cnf(c_9493,plain,
$false,
inference(copy,[status(thm)],[c_9715]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL030+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.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 : Sat Sep 26 05:34:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 474728 was started by sandbox2 on n006,
% 0.10/0.38 % Sat Sep 26 05:34:42 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 54.03/7.27
% 54.03/7.27 % SZS status Theorem for theBenchmark
% 54.03/7.27
% 54.03/7.27 % Proof 1 at 5.76 (+ 1.06) seconds.
% 54.03/7.27 % Length of proof is 140.
% 54.03/7.27 % Level of proof is 24.
% 54.03/7.27 % Maximum clause weight is 97.000.
% 54.03/7.27 % Given clauses 460.
% 54.03/7.27
% 54.03/7.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------