%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL030+2 : 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 36.74s 5.72s
% Output : CNFRefutation 36.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 14
% Syntax : Number of formulae : 408 ( 378 unt; 0 def)
% Number of atoms : 442 ( 441 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 102 ( 68 ~; 28 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 436 ( 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
=> ( join(meet(composition(X0,X1),complement(composition(X0,X2))),meet(composition(X0,X1),complement(X2))) = meet(composition(X0,X1),complement(X2))
& join(meet(composition(X0,X1),complement(X2)),meet(composition(X0,X1),complement(composition(X0,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
=> ( join(meet(composition(X0,X1),complement(composition(X0,X2))),meet(composition(X0,X1),complement(X2))) = meet(composition(X0,X1),complement(X2))
& join(meet(composition(X0,X1),complement(X2)),meet(composition(X0,X1),complement(composition(X0,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_11101,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_11101]) ).
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_11102,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_11102]) ).
fof(nnf_14,plain,
? [X0,X1,X2] :
( ( meet(composition(X0,X1),complement(X2)) != join(meet(composition(X0,X1),complement(composition(X0,X2))),meet(composition(X0,X1),complement(X2)))
| meet(composition(X0,X1),complement(composition(X0,X2))) != join(meet(composition(X0,X1),complement(X2)),meet(composition(X0,X1),complement(composition(X0,X2)))) )
& join(X0,one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( meet(composition(sK0,sK1),complement(sK2)) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| meet(composition(sK0,sK1),complement(composition(sK0,sK2))) != join(meet(composition(sK0,sK1),complement(sK2)),meet(composition(sK0,sK1),complement(composition(sK0,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(sK2)) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| meet(composition(sK0,sK1),complement(composition(sK0,sK2))) != join(meet(composition(sK0,sK1),complement(sK2)),meet(composition(sK0,sK1),complement(composition(sK0,sK2)))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_11103,negated_conjecture,
( meet(composition(sK0,sK1),complement(sK2)) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(meet(composition(sK0,sK1),complement(sK2)),meet(composition(sK0,sK1),complement(composition(sK0,sK2)))) ),
inference(paramod,[status(thm)],[c_19,c_33]) ).
cnf(c_11104,negated_conjecture,
( meet(composition(sK0,sK1),complement(sK2)) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(composition(sK0,sK1)),complement(complement(sK2)))),meet(composition(sK0,sK1),complement(composition(sK0,sK2)))) ),
inference(paramod,[status(thm)],[c_19,c_11103]) ).
cnf(c_11105,negated_conjecture,
( meet(composition(sK0,sK1),complement(sK2)) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),meet(composition(sK0,sK1),complement(composition(sK0,sK2)))) ),
inference(paramod,[status(thm)],[c_15,c_11104]) ).
cnf(c_11106,negated_conjecture,
( meet(composition(sK0,sK1),complement(sK2)) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) ),
inference(paramod,[status(thm)],[c_19,c_11105]) ).
cnf(c_11107,negated_conjecture,
( complement(join(complement(composition(sK0,sK1)),complement(complement(sK2)))) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) ),
inference(paramod,[status(thm)],[c_19,c_11106]) ).
cnf(c_11108,negated_conjecture,
( complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != join(meet(composition(sK0,sK1),complement(composition(sK0,sK2))),meet(composition(sK0,sK1),complement(sK2)))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) ),
inference(paramod,[status(thm)],[c_15,c_11107]) ).
cnf(c_11109,negated_conjecture,
( complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != join(complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))),meet(composition(sK0,sK1),complement(sK2)))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) ),
inference(paramod,[status(thm)],[c_19,c_11108]) ).
cnf(c_11110,negated_conjecture,
( complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != join(complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))),complement(join(complement(composition(sK0,sK1)),complement(complement(sK2)))))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) ),
inference(paramod,[status(thm)],[c_19,c_11109]) ).
cnf(c_11111,negated_conjecture,
( complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != join(complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))),complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) ),
inference(paramod,[status(thm)],[c_15,c_11110]) ).
cnf(c_11112,negated_conjecture,
( complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))))
| complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) ),
inference(paramod,[status(thm)],[c_15,c_11111]) ).
cnf(c_11113,negated_conjecture,
( complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))) != join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))))
| join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) ),
inference(copy,[status(thm)],[c_11112]) ).
cnf(c_34,negated_conjecture,
( join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1))))
| join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) ),
inference(copy,[status(thm)],[c_11113]) ).
cnf(c_11114,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_11114]) ).
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_11115,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_11115]) ).
cnf(c_11116,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_11117,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_11116]) ).
cnf(c_11118,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_11117]) ).
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_11118]) ).
cnf(c_11119,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_11119]) ).
cnf(c_11120,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_11120]) ).
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_11121,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_11122,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_25,c_11121]) ).
cnf(c_11123,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_23,c_11122]) ).
cnf(c_54,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_11123]) ).
cnf(c_11124,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_11124]) ).
cnf(c_11125,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_11125]) ).
cnf(c_11126,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_11126]) ).
cnf(c_11127,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_11127]) ).
cnf(c_11128,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_11128]) ).
cnf(c_11129,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_11129]) ).
cnf(c_11130,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_11130]) ).
cnf(c_11131,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_11131]) ).
cnf(c_11132,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_11132]) ).
cnf(c_11133,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_11133]) ).
cnf(c_11134,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_11135,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_11134]) ).
cnf(c_11136,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_11135]) ).
cnf(c_93,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_11136]) ).
cnf(c_11137,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_11138,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_11137]) ).
cnf(c_11139,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_11138]) ).
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_11139]) ).
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_11140,negated_conjecture,
( join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) ),
inference(paramod,[status(thm)],[c_99,c_34]) ).
cnf(c_11141,negated_conjecture,
( join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2))))) ),
inference(paramod,[status(thm)],[c_99,c_11140]) ).
cnf(c_11142,negated_conjecture,
( join(complement(join(complement(complement(sK2)),complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))) ),
inference(paramod,[status(thm)],[c_99,c_11141]) ).
cnf(c_11143,negated_conjecture,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),complement(complement(composition(sK0,sK2)))))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))) ),
inference(paramod,[status(thm)],[c_99,c_11142]) ).
cnf(c_11144,negated_conjecture,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(complement(sK2)),complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))) ),
inference(paramod,[status(thm)],[c_99,c_11143]) ).
cnf(c_102,negated_conjecture,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2))) ),
inference(paramod,[status(thm)],[c_99,c_11144]) ).
cnf(c_11145,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_11145]) ).
cnf(c_11146,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_109,c_21]) ).
cnf(c_111,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_11146]) ).
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_11147,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_11147]) ).
cnf(c_11148,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_11148]) ).
cnf(c_119,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_116,c_115]) ).
cnf(c_11149,plain,
composition(one,A) = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_117,c_22]) ).
cnf(c_11150,plain,
A = join(composition(one,A),composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_116,c_11149]) ).
cnf(c_11151,plain,
A = join(A,composition(converse(sK0),A)),
inference(paramod,[status(thm)],[c_116,c_11150]) ).
cnf(c_121,plain,
join(A,composition(converse(sK0),A)) = A,
inference(copy,[status(thm)],[c_11151]) ).
cnf(c_11152,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_11153,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_15,c_11152]) ).
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_11153]) ).
cnf(c_11154,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_11154]) ).
cnf(c_11155,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_11156,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_11155]) ).
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_11156]) ).
cnf(c_11157,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_11158,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_11157]) ).
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_11158]) ).
cnf(c_11159,plain,
converse(A) = join(converse(A),converse(composition(sK0,A))),
inference(paramod,[status(thm)],[c_118,c_24]) ).
cnf(c_11160,plain,
converse(A) = join(converse(A),composition(converse(A),converse(sK0))),
inference(paramod,[status(thm)],[c_25,c_11159]) ).
cnf(c_178,plain,
join(converse(A),composition(converse(A),converse(sK0))) = converse(A),
inference(copy,[status(thm)],[c_11160]) ).
cnf(c_11161,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_11161]) ).
cnf(c_11162,plain,
join(complement(complement(A)),complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_11163,plain,
join(A,complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_99,c_11162]) ).
cnf(c_11164,plain,
join(A,complement(join(complement(A),A))) = A,
inference(paramod,[status(thm)],[c_99,c_11163]) ).
cnf(c_11165,plain,
join(A,complement(join(A,complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_11164]) ).
cnf(c_11166,plain,
join(A,complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_11165]) ).
cnf(c_189,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_30,c_11166]) ).
cnf(c_11167,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_11168,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_15,c_11167]) ).
cnf(c_11169,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_28,c_11168]) ).
cnf(c_11170,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_30,c_11169]) ).
cnf(c_190,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_99,c_11170]) ).
cnf(c_11171,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_11172,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_18,c_11171]) ).
cnf(c_193,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_11172]) ).
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_11173,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_11173]) ).
cnf(c_11174,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_11174]) ).
cnf(c_220,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_190,c_28]) ).
cnf(c_11175,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_11176,plain,
complement(A) = join(complement(A),composition(sK0,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_27,c_11175]) ).
cnf(c_257,plain,
join(complement(A),composition(sK0,composition(converse(B),complement(composition(B,A))))) = complement(A),
inference(copy,[status(thm)],[c_11176]) ).
cnf(c_11177,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_11178,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_202,c_11177]) ).
cnf(c_11179,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_18,c_11178]) ).
cnf(c_268,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_11179]) ).
cnf(c_11180,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_11181,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_15,c_11180]) ).
cnf(c_11182,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_193,c_11181]) ).
cnf(c_272,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_15,c_11182]) ).
cnf(c_11183,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_11184,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_11183]) ).
cnf(c_11185,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_205,c_11184]) ).
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_11185]) ).
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_11186,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_11186]) ).
cnf(c_11187,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_280,c_190]) ).
cnf(c_286,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_11187]) ).
cnf(c_11188,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_11188]) ).
cnf(c_11189,plain,
join(zero,composition(A,complement(composition(converse(A),top)))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_53]) ).
cnf(c_11190,plain,
composition(A,complement(composition(converse(A),top))) = complement(top),
inference(paramod,[status(thm)],[c_190,c_11189]) ).
cnf(c_379,plain,
composition(A,complement(composition(converse(A),top))) = zero,
inference(paramod,[status(thm)],[c_30,c_11190]) ).
cnf(c_11191,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_30,c_54]) ).
cnf(c_11192,plain,
join(zero,composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_286,c_11191]) ).
cnf(c_11193,plain,
composition(converse(complement(composition(A,top))),A) = converse(complement(top)),
inference(paramod,[status(thm)],[c_190,c_11192]) ).
cnf(c_11194,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_30,c_11193]) ).
cnf(c_386,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_286,c_11194]) ).
cnf(c_11195,plain,
converse(A) = join(converse(A),converse(composition(converse(sK0),A))),
inference(paramod,[status(thm)],[c_121,c_24]) ).
cnf(c_11196,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sK0)))),
inference(paramod,[status(thm)],[c_25,c_11195]) ).
cnf(c_11197,plain,
converse(A) = join(converse(A),composition(converse(A),sK0)),
inference(paramod,[status(thm)],[c_23,c_11196]) ).
cnf(c_400,plain,
join(converse(A),composition(converse(A),sK0)) = converse(A),
inference(copy,[status(thm)],[c_11197]) ).
cnf(c_11198,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_268,c_55]) ).
cnf(c_11199,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_28,c_11198]) ).
cnf(c_423,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_11199]) ).
cnf(c_11200,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_268,c_55]) ).
cnf(c_11201,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_15,c_11200]) ).
cnf(c_424,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_423,c_11201]) ).
cnf(c_449,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_116,c_59]) ).
cnf(c_11202,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_11202]) ).
cnf(c_11203,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_11203]) ).
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_11204,plain,
join(one,top) = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_28,c_65]) ).
cnf(c_11205,plain,
top = join(one,complement(sK0)),
inference(paramod,[status(thm)],[c_424,c_11204]) ).
cnf(c_490,plain,
join(one,complement(sK0)) = top,
inference(copy,[status(thm)],[c_11205]) ).
cnf(c_11206,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_11207,plain,
join(complement(A),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_190,c_11206]) ).
cnf(c_11208,plain,
join(complement(A),join(B,complement(join(zero,complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_30,c_11207]) ).
cnf(c_11209,plain,
join(complement(A),join(B,complement(complement(A)))) = join(B,top),
inference(paramod,[status(thm)],[c_190,c_11208]) ).
cnf(c_11210,plain,
join(complement(A),join(B,A)) = join(B,top),
inference(paramod,[status(thm)],[c_99,c_11209]) ).
cnf(c_555,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_424,c_11210]) ).
cnf(c_11211,plain,
join(complement(join(complement(sK0),complement(one))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_490,c_74]) ).
cnf(c_11212,plain,
join(complement(join(complement(one),complement(sK0))),complement(top)) = sK0,
inference(paramod,[status(thm)],[c_15,c_11211]) ).
cnf(c_11213,plain,
join(complement(join(complement(one),complement(sK0))),zero) = sK0,
inference(paramod,[status(thm)],[c_30,c_11212]) ).
cnf(c_11214,plain,
join(zero,complement(join(complement(one),complement(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_15,c_11213]) ).
cnf(c_599,plain,
complement(join(complement(one),complement(sK0))) = sK0,
inference(paramod,[status(thm)],[c_190,c_11214]) ).
cnf(c_11215,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_11216,plain,
join(complement(join(A,complement(B))),join(B,complement(join(complement(B),complement(A))))) = B,
inference(paramod,[status(thm)],[c_15,c_11215]) ).
cnf(c_11217,plain,
join(complement(join(A,complement(B))),B) = B,
inference(paramod,[status(thm)],[c_272,c_11216]) ).
cnf(c_612,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_11217]) ).
cnf(c_634,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_111,c_483]) ).
cnf(c_11218,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_11218]) ).
cnf(c_11219,plain,
join(A,composition(converse(converse(A)),sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_400]) ).
cnf(c_11220,plain,
join(A,composition(A,sK0)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_11219]) ).
cnf(c_775,plain,
join(A,composition(A,sK0)) = A,
inference(paramod,[status(thm)],[c_23,c_11220]) ).
cnf(c_11221,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_11221]) ).
cnf(c_11222,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_11222]) ).
cnf(c_11223,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_449,c_24]) ).
cnf(c_11224,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_25,c_11223]) ).
cnf(c_11225,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_474,c_11224]) ).
cnf(c_11226,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_25,c_11225]) ).
cnf(c_832,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_11226]) ).
cnf(c_11227,plain,
join(A,composition(converse(converse(A)),converse(sK0))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_178]) ).
cnf(c_11228,plain,
join(A,composition(A,converse(sK0))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_11227]) ).
cnf(c_917,plain,
join(A,composition(A,converse(sK0))) = A,
inference(paramod,[status(thm)],[c_23,c_11228]) ).
cnf(c_11229,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_11229]) ).
cnf(c_11230,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_11231,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_11230]) ).
cnf(c_11232,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_11231]) ).
cnf(c_11233,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_47,c_11232]) ).
cnf(c_11234,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_99,c_11233]) ).
cnf(c_1190,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_11234]) ).
cnf(c_1254,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_15,c_1190]) ).
cnf(c_11235,plain,
join(converse(complement(A)),complement(top)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_483,c_1190]) ).
cnf(c_11236,plain,
join(converse(complement(A)),zero) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_30,c_11235]) ).
cnf(c_11237,plain,
join(zero,converse(complement(A))) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_11236]) ).
cnf(c_11238,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_190,c_11237]) ).
cnf(c_1268,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_11238]) ).
cnf(c_11239,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_634,c_1190]) ).
cnf(c_11240,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_30,c_11239]) ).
cnf(c_11241,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_11240]) ).
cnf(c_11242,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_190,c_11241]) ).
cnf(c_1269,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_11242]) ).
cnf(c_11243,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_11244,plain,
join(complement(composition(A,sK0)),zero) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_30,c_11243]) ).
cnf(c_11245,plain,
join(zero,complement(composition(A,sK0))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_15,c_11244]) ).
cnf(c_11246,plain,
complement(composition(A,sK0)) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_190,c_11245]) ).
cnf(c_1273,plain,
join(complement(A),complement(composition(A,sK0))) = complement(composition(A,sK0)),
inference(copy,[status(thm)],[c_11246]) ).
cnf(c_11247,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1269,c_24]) ).
cnf(c_11248,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_23,c_11247]) ).
cnf(c_11249,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_23,c_11248]) ).
cnf(c_11250,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_11249]) ).
cnf(c_11251,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1269,c_11250]) ).
cnf(c_1481,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_11251]) ).
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_11252,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_11253,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_11252]) ).
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_11253]) ).
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_11254,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_1268,c_24]) ).
cnf(c_11255,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_23,c_11254]) ).
cnf(c_11256,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_23,c_11255]) ).
cnf(c_11257,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_11256]) ).
cnf(c_11258,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_1874,c_11257]) ).
cnf(c_1875,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_11258]) ).
cnf(c_1886,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_1875,c_23]) ).
cnf(c_11259,plain,
composition(complement(converse(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_1886,c_386]) ).
cnf(c_11260,plain,
composition(complement(composition(converse(top),converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_25,c_11259]) ).
cnf(c_1935,plain,
composition(complement(composition(top,converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_474,c_11260]) ).
cnf(c_11261,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_11262,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_11261]) ).
cnf(c_11263,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_11262]) ).
cnf(c_11264,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_11263]) ).
cnf(c_11265,plain,
join(complement(join(A,B)),complement(composition(A,sK0))) = join(complement(A),complement(composition(A,sK0))),
inference(paramod,[status(thm)],[c_612,c_11264]) ).
cnf(c_2268,plain,
join(complement(join(A,B)),complement(composition(A,sK0))) = complement(composition(A,sK0)),
inference(paramod,[status(thm)],[c_1273,c_11265]) ).
cnf(c_11266,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_1489]) ).
cnf(c_11267,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_11266]) ).
cnf(c_2670,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_23,c_11267]) ).
cnf(c_2701,plain,
join(complement(one),composition(sK0,top)) = join(sK0,complement(one)),
inference(paramod,[status(thm)],[c_2670,c_179]) ).
cnf(c_11268,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_11269,plain,
join(complement(sK0),complement(one)) = join(complement(composition(sK0,top)),complement(one)),
inference(paramod,[status(thm)],[c_1190,c_11268]) ).
cnf(c_11270,plain,
join(complement(one),complement(sK0)) = join(complement(composition(sK0,top)),complement(one)),
inference(paramod,[status(thm)],[c_15,c_11269]) ).
cnf(c_11271,plain,
complement(sK0) = join(complement(composition(sK0,top)),complement(one)),
inference(paramod,[status(thm)],[c_696,c_11270]) ).
cnf(c_11272,plain,
complement(sK0) = join(complement(one),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_15,c_11271]) ).
cnf(c_2727,plain,
join(complement(one),complement(composition(sK0,top))) = complement(sK0),
inference(copy,[status(thm)],[c_11272]) ).
cnf(c_11273,plain,
converse(complement(sK0)) = join(converse(complement(one)),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_2727,c_24]) ).
cnf(c_11274,plain,
complement(converse(sK0)) = join(converse(complement(one)),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_1886,c_11273]) ).
cnf(c_11275,plain,
complement(converse(sK0)) = join(complement(converse(one)),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_1886,c_11274]) ).
cnf(c_11276,plain,
complement(converse(sK0)) = join(complement(one),converse(complement(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_111,c_11275]) ).
cnf(c_11277,plain,
complement(converse(sK0)) = join(complement(one),complement(converse(composition(sK0,top)))),
inference(paramod,[status(thm)],[c_1886,c_11276]) ).
cnf(c_11278,plain,
complement(converse(sK0)) = join(complement(one),complement(composition(converse(top),converse(sK0)))),
inference(paramod,[status(thm)],[c_25,c_11277]) ).
cnf(c_11279,plain,
complement(converse(sK0)) = join(complement(one),complement(composition(top,converse(sK0)))),
inference(paramod,[status(thm)],[c_474,c_11278]) ).
cnf(c_2734,plain,
join(complement(one),complement(composition(top,converse(sK0)))) = complement(converse(sK0)),
inference(copy,[status(thm)],[c_11279]) ).
cnf(c_11280,plain,
converse(zero) = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_379,c_25]) ).
cnf(c_11281,plain,
zero = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_286,c_11280]) ).
cnf(c_11282,plain,
zero = composition(complement(converse(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_1886,c_11281]) ).
cnf(c_11283,plain,
zero = composition(complement(composition(converse(top),converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_25,c_11282]) ).
cnf(c_11284,plain,
zero = composition(complement(composition(top,converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_474,c_11283]) ).
cnf(c_11285,plain,
zero = composition(complement(composition(top,A)),converse(A)),
inference(paramod,[status(thm)],[c_23,c_11284]) ).
cnf(c_2881,plain,
composition(complement(composition(top,A)),converse(A)) = zero,
inference(copy,[status(thm)],[c_11285]) ).
cnf(c_11286,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_11287,plain,
join(zero,composition(composition(top,A),converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_99,c_11286]) ).
cnf(c_11288,plain,
join(zero,composition(top,composition(A,converse(A)))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_20,c_11287]) ).
cnf(c_2936,plain,
composition(top,composition(A,converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_190,c_11288]) ).
cnf(c_11289,plain,
join(zero,composition(complement(complement(composition(top,converse(A)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_1935,c_59]) ).
cnf(c_11290,plain,
join(zero,composition(composition(top,converse(A)),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_99,c_11289]) ).
cnf(c_11291,plain,
join(zero,composition(top,composition(converse(A),A))) = composition(top,A),
inference(paramod,[status(thm)],[c_20,c_11290]) ).
cnf(c_3372,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_190,c_11291]) ).
cnf(c_11292,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_11293,plain,
join(composition(A,sK0),complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_99,c_11292]) ).
cnf(c_11294,plain,
join(composition(A,sK0),complement(composition(top,sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_1697,c_11293]) ).
cnf(c_3738,plain,
complement(composition(complement(A),sK0)) = join(composition(A,sK0),complement(composition(top,sK0))),
inference(copy,[status(thm)],[c_11294]) ).
cnf(c_11295,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_11296,plain,
join(A,complement(composition(complement(A),sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_99,c_11295]) ).
cnf(c_11297,plain,
join(A,join(composition(A,sK0),complement(composition(top,sK0)))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_3738,c_11296]) ).
cnf(c_11298,plain,
join(A,complement(composition(top,sK0))) = complement(composition(complement(A),sK0)),
inference(paramod,[status(thm)],[c_780,c_11297]) ).
cnf(c_11299,plain,
join(A,complement(composition(top,sK0))) = join(composition(A,sK0),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_3738,c_11298]) ).
cnf(c_3743,plain,
join(composition(A,sK0),complement(composition(top,sK0))) = join(A,complement(composition(top,sK0))),
inference(copy,[status(thm)],[c_11299]) ).
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_11300,plain,
complement(zero) = join(composition(top,converse(sK0)),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_1935,c_3761]) ).
cnf(c_11301,plain,
top = join(composition(top,converse(sK0)),complement(composition(top,sK0))),
inference(paramod,[status(thm)],[c_220,c_11300]) ).
cnf(c_11302,plain,
top = join(complement(composition(top,sK0)),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_15,c_11301]) ).
cnf(c_3789,plain,
join(complement(composition(top,sK0)),composition(top,converse(sK0))) = top,
inference(copy,[status(thm)],[c_11302]) ).
cnf(c_11303,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_11304,plain,
join(composition(top,converse(sK0)),zero) = join(complement(complement(composition(top,sK0))),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_30,c_11303]) ).
cnf(c_11305,plain,
join(zero,composition(top,converse(sK0))) = join(complement(complement(composition(top,sK0))),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_15,c_11304]) ).
cnf(c_11306,plain,
composition(top,converse(sK0)) = join(complement(complement(composition(top,sK0))),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_190,c_11305]) ).
cnf(c_11307,plain,
composition(top,converse(sK0)) = join(composition(top,sK0),composition(top,converse(sK0))),
inference(paramod,[status(thm)],[c_99,c_11306]) ).
cnf(c_4083,plain,
join(composition(top,sK0),composition(top,converse(sK0))) = composition(top,converse(sK0)),
inference(copy,[status(thm)],[c_11307]) ).
cnf(c_11308,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_11309,plain,
complement(converse(composition(A,sK0))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_1886,c_11308]) ).
cnf(c_11310,plain,
complement(composition(converse(sK0),converse(A))) = join(converse(complement(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_25,c_11309]) ).
cnf(c_11311,plain,
complement(composition(converse(sK0),converse(A))) = join(complement(converse(A)),converse(complement(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_1886,c_11310]) ).
cnf(c_11312,plain,
complement(composition(converse(sK0),converse(A))) = join(complement(converse(A)),complement(converse(composition(top,sK0)))),
inference(paramod,[status(thm)],[c_1886,c_11311]) ).
cnf(c_11313,plain,
complement(composition(converse(sK0),converse(A))) = join(complement(converse(A)),complement(composition(converse(sK0),converse(top)))),
inference(paramod,[status(thm)],[c_25,c_11312]) ).
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_11313]) ).
cnf(c_11314,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_11314]) ).
cnf(c_11315,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_11316,plain,
join(complement(A),composition(A,sK0)) = join(complement(complement(composition(top,sK0))),complement(A)),
inference(paramod,[status(thm)],[c_99,c_11315]) ).
cnf(c_11317,plain,
join(complement(A),composition(A,sK0)) = join(composition(top,sK0),complement(A)),
inference(paramod,[status(thm)],[c_99,c_11316]) ).
cnf(c_4120,plain,
join(composition(top,sK0),complement(A)) = join(complement(A),composition(A,sK0)),
inference(copy,[status(thm)],[c_11317]) ).
cnf(c_11318,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_11319,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_11318]) ).
cnf(c_11320,plain,
join(complement(composition(top,converse(sK0))),composition(composition(composition(top,sK0),converse(sK0)),sK0)) = top,
inference(paramod,[status(thm)],[c_2936,c_11319]) ).
cnf(c_11321,plain,
join(complement(composition(top,converse(sK0))),composition(composition(top,composition(sK0,converse(sK0))),sK0)) = top,
inference(paramod,[status(thm)],[c_20,c_11320]) ).
cnf(c_11322,plain,
join(complement(composition(top,converse(sK0))),composition(composition(top,converse(sK0)),sK0)) = top,
inference(paramod,[status(thm)],[c_2936,c_11321]) ).
cnf(c_11323,plain,
join(complement(composition(top,converse(sK0))),composition(top,composition(converse(sK0),sK0))) = top,
inference(paramod,[status(thm)],[c_20,c_11322]) ).
cnf(c_11324,plain,
join(complement(composition(top,converse(sK0))),composition(top,sK0)) = top,
inference(paramod,[status(thm)],[c_3372,c_11323]) ).
cnf(c_4194,plain,
join(composition(top,sK0),complement(composition(top,converse(sK0)))) = top,
inference(paramod,[status(thm)],[c_15,c_11324]) ).
cnf(c_11325,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_11326,plain,
join(complement(composition(top,converse(sK0))),complement(top)) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_4194,c_11325]) ).
cnf(c_11327,plain,
join(complement(composition(top,converse(sK0))),zero) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_30,c_11326]) ).
cnf(c_11328,plain,
join(zero,complement(composition(top,converse(sK0)))) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_15,c_11327]) ).
cnf(c_4389,plain,
complement(composition(top,converse(sK0))) = complement(composition(top,sK0)),
inference(paramod,[status(thm)],[c_190,c_11328]) ).
cnf(c_11329,plain,
join(complement(one),complement(composition(top,sK0))) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_4389,c_2734]) ).
cnf(c_11330,plain,
complement(sK0) = complement(converse(sK0)),
inference(paramod,[status(thm)],[c_4098,c_11329]) ).
cnf(c_4400,plain,
complement(converse(sK0)) = complement(sK0),
inference(copy,[status(thm)],[c_11330]) ).
cnf(c_11331,plain,
complement(complement(sK0)) = converse(sK0),
inference(paramod,[status(thm)],[c_4400,c_99]) ).
cnf(c_11332,plain,
sK0 = converse(sK0),
inference(paramod,[status(thm)],[c_99,c_11331]) ).
cnf(c_4450,plain,
converse(sK0) = sK0,
inference(copy,[status(thm)],[c_11332]) ).
cnf(c_11333,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_11334,plain,
complement(composition(sK0,converse(A))) = join(complement(converse(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_4450,c_11333]) ).
cnf(c_4487,plain,
complement(composition(sK0,converse(A))) = join(complement(composition(sK0,top)),complement(converse(A))),
inference(paramod,[status(thm)],[c_15,c_11334]) ).
cnf(c_11335,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_11335]) ).
cnf(c_6521,plain,
complement(composition(sK0,A)) = join(complement(A),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_6488,c_15]) ).
cnf(c_11336,plain,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(join(complement(composition(sK0,top)),complement(sK1)),composition(sK0,sK2))) ),
inference(paramod,[status(thm)],[c_6488,c_102]) ).
cnf(c_11337,plain,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(join(complement(sK1),complement(composition(sK0,top))),composition(sK0,sK2))) ),
inference(paramod,[status(thm)],[c_15,c_11336]) ).
cnf(c_6534,plain,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,complement(composition(sK0,sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(sK1),join(complement(composition(sK0,top)),composition(sK0,sK2)))) ),
inference(paramod,[status(thm)],[c_16,c_11337]) ).
cnf(c_11338,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_11339,plain,
join(complement(composition(sK0,top)),composition(sK0,A)) = join(complement(complement(A)),complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_99,c_11338]) ).
cnf(c_6565,plain,
join(complement(composition(sK0,top)),composition(sK0,A)) = join(A,complement(composition(sK0,top))),
inference(paramod,[status(thm)],[c_99,c_11339]) ).
cnf(c_11340,plain,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(composition(sK0,top)),complement(sK1))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(sK1),join(complement(composition(sK0,top)),composition(sK0,sK2)))) ),
inference(paramod,[status(thm)],[c_6488,c_6534]) ).
cnf(c_6953,plain,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top)))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(sK1),join(complement(composition(sK0,top)),composition(sK0,sK2)))) ),
inference(paramod,[status(thm)],[c_15,c_11340]) ).
cnf(c_10422,plain,
join(complement(composition(sK0,top)),composition(sK0,A)) = join(complement(composition(sK0,top)),A),
inference(paramod,[status(thm)],[c_6565,c_15]) ).
cnf(c_11341,plain,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top)))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(complement(sK1),join(sK2,complement(composition(sK0,top))))) ),
inference(paramod,[status(thm)],[c_6565,c_6953]) ).
cnf(c_11342,plain,
( join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top)))))
| join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top))))) ),
inference(paramod,[status(thm)],[c_36,c_11341]) ).
cnf(c_10436,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,join(complement(sK1),complement(composition(sK0,top))))),
inference(copy,[status(thm)],[c_11342]) ).
cnf(c_11096,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(composition(sK0,sK1)),composition(sK0,sK2)))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_6521,c_10436]) ).
cnf(c_11343,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),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_11096]) ).
cnf(c_11344,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),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_11343]) ).
cnf(c_11345,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),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_11344]) ).
cnf(c_11346,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(sK1),join(complement(composition(sK0,top)),sK2)))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_10422,c_11345]) ).
cnf(c_11347,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(complement(sK1),join(sK2,complement(composition(sK0,top)))))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_15,c_11346]) ).
cnf(c_11348,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(sK2,join(complement(sK1),complement(composition(sK0,top)))))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_36,c_11347]) ).
cnf(c_11098,plain,
join(complement(join(sK2,join(complement(sK1),complement(composition(sK0,top))))),complement(join(sK2,complement(composition(sK0,sK1))))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_15,c_11348]) ).
cnf(c_11349,plain,
join(complement(join(sK2,complement(composition(sK0,sK1)))),complement(join(sK2,complement(composition(sK0,sK1))))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_6521,c_11098]) ).
cnf(c_11350,plain,
complement(join(sK2,complement(composition(sK0,sK1)))) != complement(join(sK2,complement(composition(sK0,sK1)))),
inference(paramod,[status(thm)],[c_268,c_11349]) ).
cnf(c_11100,plain,
$false,
inference(copy,[status(thm)],[c_11350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL030+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.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 05:34:14 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 3888171 was started by sandbox on n011,
% 0.10/0.38 % Sat Sep 26 05:34:14 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 36.74/5.72
% 36.74/5.72 % SZS status Theorem for theBenchmark
% 36.74/5.72
% 36.74/5.72 % Proof 1 at 4.25 (+ 1.04) seconds.
% 36.74/5.72 % Length of proof is 155.
% 36.74/5.72 % Level of proof is 33.
% 36.74/5.72 % Maximum clause weight is 129.000.
% 36.74/5.72 % Given clauses 488.
% 36.74/5.72
% 36.74/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------