%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL025-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:24:53 AM UTC 2026
% Result : Unsatisfiable 9.08s 1.70s
% Output : CNFRefutation 9.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 15
% Syntax : Number of formulae : 357 ( 357 unt; 0 def)
% Number of atoms : 357 ( 356 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 417 ( 17 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(maddux3_a_kind_of_de_Morgan_3,axiom,
! [VAR_0,VAR_1] : VAR_0 = join(complement(join(complement(VAR_0),complement(VAR_1))),complement(join(complement(VAR_0),VAR_1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c_4,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c_4438,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_4438]) ).
fof(maddux4_definiton_of_meet_4,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c_6,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet_4]) ).
fof(composition_associativity_5,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(VAR_0,composition(VAR_1,VAR_2)) = composition(composition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',composition_associativity_5) ).
cnf(c_7,plain,
composition(A,composition(B,C)) = composition(composition(A,B),C),
inference(clausify,[status(thm)],[composition_associativity_5]) ).
cnf(c_8,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(copy,[status(thm)],[c_7]) ).
fof(composition_identity_6,axiom,
! [VAR_0] : composition(VAR_0,one) = VAR_0,
file('theBenchmark.p',composition_identity_6) ).
cnf(c_9,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity_6]) ).
fof(composition_distributivity_7,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(join(VAR_0,VAR_1),VAR_2) = join(composition(VAR_0,VAR_2),composition(VAR_1,VAR_2)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c_10,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity_7]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_11,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_12,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
fof(converse_multiplicativity_10,axiom,
! [VAR_0,VAR_1] : converse(composition(VAR_0,VAR_1)) = composition(converse(VAR_1),converse(VAR_0)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c_13,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity_10]) ).
fof(converse_cancellativity_11,axiom,
! [VAR_0,VAR_1] : join(composition(converse(VAR_0),complement(composition(VAR_0,VAR_1))),complement(VAR_1)) = complement(VAR_1),
file('theBenchmark.p',converse_cancellativity_11) ).
cnf(c_14,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(clausify,[status(thm)],[converse_cancellativity_11]) ).
cnf(c_15,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_14]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_16,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_17,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_16]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_18,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_4439,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_4440,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_4439]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_4440]) ).
fof(goals_14,axiom,
join(sk1,one) = one,
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
join(sk1,one) = one,
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_21,plain,
join(one,sk1) = one,
inference(paramod,[status(thm)],[c_1,c_20]) ).
fof(goals_15,axiom,
converse(sk1) != sk1,
file('theBenchmark.p',goals_15) ).
cnf(c_22,plain,
converse(sk1) != sk1,
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_4441,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_24,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_4441]) ).
cnf(c_25,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_26,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_4442,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_27,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_4442]) ).
cnf(c_4443,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_5,c_5]) ).
cnf(c_4444,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_1,c_4443]) ).
cnf(c_4445,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_3,c_4444]) ).
cnf(c_29,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_1,c_4445]) ).
cnf(c_4446,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_33,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_4446]) ).
cnf(c_4447,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_35,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_4447]) ).
cnf(c_41,plain,
join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A),
inference(paramod,[status(thm)],[c_11,c_15]) ).
cnf(c_4448,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_4449,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_4448]) ).
cnf(c_4450,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_4449]) ).
cnf(c_42,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_4450]) ).
cnf(c_4451,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_43,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_4451]) ).
cnf(c_4452,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_45,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_4452]) ).
cnf(c_4453,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_47,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_4453]) ).
cnf(c_4454,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_48,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_4454]) ).
cnf(c_4455,plain,
join(one,A) = join(one,join(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_53,plain,
join(one,join(sk1,A)) = join(one,A),
inference(copy,[status(thm)],[c_4455]) ).
cnf(c_4456,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_55,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_4456]) ).
cnf(c_4457,plain,
converse(one) = join(converse(one),converse(sk1)),
inference(paramod,[status(thm)],[c_21,c_12]) ).
cnf(c_56,plain,
join(converse(one),converse(sk1)) = converse(one),
inference(copy,[status(thm)],[c_4457]) ).
cnf(c_4458,plain,
join(A,B) = join(complement(join(complement(B),C)),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_5,c_24]) ).
cnf(c_58,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_4458]) ).
cnf(c_4459,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_25,c_1]) ).
cnf(c_62,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_4459]) ).
cnf(c_4460,plain,
join(A,B) = join(complement(join(C,complement(A))),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_25,c_3]) ).
cnf(c_64,plain,
join(complement(join(A,complement(B))),join(complement(join(complement(B),complement(A))),C)) = join(B,C),
inference(copy,[status(thm)],[c_4460]) ).
cnf(c_4461,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_26]) ).
cnf(c_4462,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_4461]) ).
cnf(c_4463,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_4462]) ).
cnf(c_81,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_4463]) ).
cnf(c_4464,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_26,c_26]) ).
cnf(c_4465,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_1,c_4464]) ).
cnf(c_4466,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_3,c_4465]) ).
cnf(c_86,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_1,c_4466]) ).
cnf(c_87,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_81,c_45]) ).
cnf(c_88,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_81]) ).
cnf(c_4467,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_33]) ).
cnf(c_96,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_4467]) ).
cnf(c_4468,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_96,c_9]) ).
cnf(c_98,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_4468]) ).
cnf(c_102,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_15]) ).
cnf(c_103,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_98,c_96]) ).
cnf(c_4469,plain,
join(one,converse(sk1)) = converse(one),
inference(paramod,[status(thm)],[c_98,c_56]) ).
cnf(c_104,plain,
join(one,converse(sk1)) = one,
inference(paramod,[status(thm)],[c_98,c_4469]) ).
cnf(c_4470,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_103,c_55]) ).
cnf(c_105,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_103,c_4470]) ).
cnf(c_106,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_103,c_102]) ).
cnf(c_4471,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_104,c_10]) ).
cnf(c_4472,plain,
A = join(composition(one,A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_103,c_4471]) ).
cnf(c_4473,plain,
A = join(A,composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_103,c_4472]) ).
cnf(c_108,plain,
join(A,composition(converse(sk1),A)) = A,
inference(copy,[status(thm)],[c_4473]) ).
cnf(c_4474,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_25,c_27]) ).
cnf(c_4475,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_1,c_4474]) ).
cnf(c_126,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_87,c_4475]) ).
cnf(c_4476,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_29,c_24]) ).
cnf(c_139,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_4476]) ).
cnf(c_4477,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_29,c_25]) ).
cnf(c_4478,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_87,c_4477]) ).
cnf(c_141,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_1,c_4478]) ).
cnf(c_4479,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_27,c_29]) ).
cnf(c_4480,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_1,c_4479]) ).
cnf(c_147,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_27,c_4480]) ).
cnf(c_4481,plain,
converse(A) = join(converse(A),converse(composition(sk1,A))),
inference(paramod,[status(thm)],[c_105,c_12]) ).
cnf(c_4482,plain,
converse(A) = join(converse(A),composition(converse(A),converse(sk1))),
inference(paramod,[status(thm)],[c_13,c_4481]) ).
cnf(c_165,plain,
join(converse(A),composition(converse(A),converse(sk1))) = converse(A),
inference(copy,[status(thm)],[c_4482]) ).
cnf(c_4483,plain,
join(A,B) = join(B,join(A,composition(sk1,B))),
inference(paramod,[status(thm)],[c_105,c_24]) ).
cnf(c_166,plain,
join(A,join(B,composition(sk1,A))) = join(B,A),
inference(copy,[status(thm)],[c_4483]) ).
cnf(c_4484,plain,
join(complement(complement(A)),complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_106,c_5]) ).
cnf(c_4485,plain,
join(A,complement(join(complement(A),complement(complement(A))))) = A,
inference(paramod,[status(thm)],[c_87,c_4484]) ).
cnf(c_4486,plain,
join(A,complement(join(complement(A),A))) = A,
inference(paramod,[status(thm)],[c_87,c_4485]) ).
cnf(c_4487,plain,
join(A,complement(join(A,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_4486]) ).
cnf(c_4488,plain,
join(A,complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_4487]) ).
cnf(c_176,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_19,c_4488]) ).
cnf(c_4489,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_106,c_5]) ).
cnf(c_4490,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_1,c_4489]) ).
cnf(c_4491,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_17,c_4490]) ).
cnf(c_4492,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_19,c_4491]) ).
cnf(c_177,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_87,c_4492]) ).
cnf(c_4493,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_106,c_27]) ).
cnf(c_4494,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_5,c_4493]) ).
cnf(c_180,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_4494]) ).
cnf(c_189,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_177,c_88]) ).
cnf(c_192,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_180,c_86]) ).
cnf(c_4495,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_192,c_147]) ).
cnf(c_194,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_1,c_4495]) ).
cnf(c_4496,plain,
converse(A) = join(converse(A),converse(zero)),
inference(paramod,[status(thm)],[c_176,c_12]) ).
cnf(c_202,plain,
join(converse(A),converse(zero)) = converse(A),
inference(copy,[status(thm)],[c_4496]) ).
cnf(c_207,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_177,c_17]) ).
cnf(c_4497,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = join(complement(A),composition(sk1,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_105,c_35]) ).
cnf(c_4498,plain,
complement(A) = join(complement(A),composition(sk1,composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_4497]) ).
cnf(c_244,plain,
join(complement(A),composition(sk1,composition(converse(B),complement(composition(B,A))))) = complement(A),
inference(copy,[status(thm)],[c_4498]) ).
cnf(c_4499,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_189,c_5]) ).
cnf(c_4500,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_189,c_4499]) ).
cnf(c_4501,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_4500]) ).
cnf(c_255,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_4501]) ).
cnf(c_4502,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_255,c_27]) ).
cnf(c_4503,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_4502]) ).
cnf(c_4504,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_180,c_4503]) ).
cnf(c_259,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_4504]) ).
cnf(c_4505,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_259,c_141]) ).
cnf(c_4506,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_1,c_4505]) ).
cnf(c_4507,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_192,c_4506]) ).
cnf(c_261,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_4507]) ).
cnf(c_264,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_261,c_139]) ).
cnf(c_4508,plain,
join(A,converse(zero)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_202]) ).
cnf(c_267,plain,
join(A,converse(zero)) = A,
inference(paramod,[status(thm)],[c_11,c_4508]) ).
cnf(c_4509,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_267,c_177]) ).
cnf(c_273,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_4509]) ).
cnf(c_4510,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_5]) ).
cnf(c_328,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_4510]) ).
cnf(c_4511,plain,
join(zero,composition(A,complement(composition(converse(A),top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_41]) ).
cnf(c_4512,plain,
composition(A,complement(composition(converse(A),top))) = complement(top),
inference(paramod,[status(thm)],[c_177,c_4511]) ).
cnf(c_366,plain,
composition(A,complement(composition(converse(A),top))) = zero,
inference(paramod,[status(thm)],[c_19,c_4512]) ).
cnf(c_4513,plain,
join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_19,c_42]) ).
cnf(c_4514,plain,
join(zero,composition(converse(complement(composition(A,top))),A)) = converse(complement(top)),
inference(paramod,[status(thm)],[c_273,c_4513]) ).
cnf(c_4515,plain,
composition(converse(complement(composition(A,top))),A) = converse(complement(top)),
inference(paramod,[status(thm)],[c_177,c_4514]) ).
cnf(c_4516,plain,
composition(converse(complement(composition(A,top))),A) = converse(zero),
inference(paramod,[status(thm)],[c_19,c_4515]) ).
cnf(c_373,plain,
composition(converse(complement(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_273,c_4516]) ).
cnf(c_4517,plain,
converse(A) = join(converse(A),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_108,c_12]) ).
cnf(c_4518,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_4517]) ).
cnf(c_4519,plain,
converse(A) = join(converse(A),composition(converse(A),sk1)),
inference(paramod,[status(thm)],[c_11,c_4518]) ).
cnf(c_387,plain,
join(converse(A),composition(converse(A),sk1)) = converse(A),
inference(copy,[status(thm)],[c_4519]) ).
cnf(c_4520,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_255,c_43]) ).
cnf(c_4521,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_17,c_4520]) ).
cnf(c_410,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_4521]) ).
cnf(c_4522,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_255,c_43]) ).
cnf(c_4523,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_1,c_4522]) ).
cnf(c_411,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_410,c_4523]) ).
cnf(c_436,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_103,c_47]) ).
cnf(c_4524,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_411,c_1]) ).
cnf(c_441,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_4524]) ).
cnf(c_4525,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_411,c_12]) ).
cnf(c_443,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_4525]) ).
cnf(c_458,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_443]) ).
cnf(c_461,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_458,c_441]) ).
cnf(c_470,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_461,c_48]) ).
cnf(c_4526,plain,
join(one,top) = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_17,c_53]) ).
cnf(c_4527,plain,
top = join(one,complement(sk1)),
inference(paramod,[status(thm)],[c_411,c_4526]) ).
cnf(c_477,plain,
join(one,complement(sk1)) = top,
inference(copy,[status(thm)],[c_4527]) ).
cnf(c_4528,plain,
join(complement(join(zero,A)),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_19,c_58]) ).
cnf(c_4529,plain,
join(complement(A),join(B,complement(join(complement(top),complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_177,c_4528]) ).
cnf(c_4530,plain,
join(complement(A),join(B,complement(join(zero,complement(A))))) = join(B,top),
inference(paramod,[status(thm)],[c_19,c_4529]) ).
cnf(c_4531,plain,
join(complement(A),join(B,complement(complement(A)))) = join(B,top),
inference(paramod,[status(thm)],[c_177,c_4530]) ).
cnf(c_4532,plain,
join(complement(A),join(B,A)) = join(B,top),
inference(paramod,[status(thm)],[c_87,c_4531]) ).
cnf(c_542,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_411,c_4532]) ).
cnf(c_4533,plain,
join(complement(join(complement(sk1),complement(one))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_477,c_62]) ).
cnf(c_4534,plain,
join(complement(join(complement(one),complement(sk1))),complement(top)) = sk1,
inference(paramod,[status(thm)],[c_1,c_4533]) ).
cnf(c_4535,plain,
join(complement(join(complement(one),complement(sk1))),zero) = sk1,
inference(paramod,[status(thm)],[c_19,c_4534]) ).
cnf(c_4536,plain,
join(zero,complement(join(complement(one),complement(sk1)))) = sk1,
inference(paramod,[status(thm)],[c_1,c_4535]) ).
cnf(c_586,plain,
complement(join(complement(one),complement(sk1))) = sk1,
inference(paramod,[status(thm)],[c_177,c_4536]) ).
cnf(c_4537,plain,
join(complement(join(A,complement(B))),join(complement(join(complement(B),complement(A))),B)) = B,
inference(paramod,[status(thm)],[c_255,c_64]) ).
cnf(c_4538,plain,
join(complement(join(A,complement(B))),join(B,complement(join(complement(B),complement(A))))) = B,
inference(paramod,[status(thm)],[c_1,c_4537]) ).
cnf(c_4539,plain,
join(complement(join(A,complement(B))),B) = B,
inference(paramod,[status(thm)],[c_259,c_4538]) ).
cnf(c_599,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_4539]) ).
cnf(c_621,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_98,c_470]) ).
cnf(c_4540,plain,
complement(sk1) = join(complement(one),complement(sk1)),
inference(paramod,[status(thm)],[c_586,c_87]) ).
cnf(c_683,plain,
join(complement(one),complement(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_4540]) ).
cnf(c_4541,plain,
join(A,composition(converse(converse(A)),sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_387]) ).
cnf(c_4542,plain,
join(A,composition(A,sk1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_4541]) ).
cnf(c_762,plain,
join(A,composition(A,sk1)) = A,
inference(paramod,[status(thm)],[c_11,c_4542]) ).
cnf(c_4543,plain,
join(A,B) = join(A,join(composition(A,sk1),B)),
inference(paramod,[status(thm)],[c_762,c_3]) ).
cnf(c_767,plain,
join(A,join(composition(A,sk1),B)) = join(A,B),
inference(copy,[status(thm)],[c_4543]) ).
cnf(c_4544,plain,
join(complement(composition(A,sk1)),A) = top,
inference(paramod,[status(thm)],[c_762,c_542]) ).
cnf(c_773,plain,
join(A,complement(composition(A,sk1))) = top,
inference(paramod,[status(thm)],[c_1,c_4544]) ).
cnf(c_4545,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_436,c_12]) ).
cnf(c_4546,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_13,c_4545]) ).
cnf(c_4547,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_461,c_4546]) ).
cnf(c_4548,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_13,c_4547]) ).
cnf(c_819,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_4548]) ).
cnf(c_4549,plain,
join(A,composition(converse(converse(A)),converse(sk1))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_165]) ).
cnf(c_4550,plain,
join(A,composition(A,converse(sk1))) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_4549]) ).
cnf(c_904,plain,
join(A,composition(A,converse(sk1))) = A,
inference(paramod,[status(thm)],[c_11,c_4550]) ).
cnf(c_4551,plain,
join(complement(composition(A,converse(sk1))),A) = top,
inference(paramod,[status(thm)],[c_904,c_542]) ).
cnf(c_1066,plain,
join(A,complement(composition(A,converse(sk1)))) = top,
inference(paramod,[status(thm)],[c_1,c_4551]) ).
cnf(c_4552,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_126,c_35]) ).
cnf(c_4553,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_264,c_4552]) ).
cnf(c_4554,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_24,c_4553]) ).
cnf(c_4555,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_35,c_4554]) ).
cnf(c_4556,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_87,c_4555]) ).
cnf(c_1177,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_4556]) ).
cnf(c_1241,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_1,c_1177]) ).
cnf(c_4557,plain,
join(converse(complement(A)),complement(top)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_470,c_1177]) ).
cnf(c_4558,plain,
join(converse(complement(A)),zero) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_19,c_4557]) ).
cnf(c_4559,plain,
join(zero,converse(complement(A))) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_4558]) ).
cnf(c_4560,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_177,c_4559]) ).
cnf(c_1255,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_4560]) ).
cnf(c_4561,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_621,c_1177]) ).
cnf(c_4562,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_19,c_4561]) ).
cnf(c_4563,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_4562]) ).
cnf(c_4564,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_177,c_4563]) ).
cnf(c_1256,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_4564]) ).
cnf(c_4565,plain,
join(complement(composition(A,sk1)),complement(top)) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_773,c_1177]) ).
cnf(c_4566,plain,
join(complement(composition(A,sk1)),zero) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_19,c_4565]) ).
cnf(c_4567,plain,
join(zero,complement(composition(A,sk1))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_1,c_4566]) ).
cnf(c_4568,plain,
complement(composition(A,sk1)) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_177,c_4567]) ).
cnf(c_1260,plain,
join(complement(A),complement(composition(A,sk1))) = complement(composition(A,sk1)),
inference(copy,[status(thm)],[c_4568]) ).
cnf(c_4569,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1256,c_12]) ).
cnf(c_4570,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_11,c_4569]) ).
cnf(c_4571,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_11,c_4570]) ).
cnf(c_4572,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_4571]) ).
cnf(c_4573,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1256,c_4572]) ).
cnf(c_1468,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_4573]) ).
cnf(c_1476,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_1468,c_819]) ).
cnf(c_4574,plain,
join(composition(A,B),complement(composition(top,B))) = join(complement(composition(complement(A),B)),composition(A,B)),
inference(paramod,[status(thm)],[c_47,c_1241]) ).
cnf(c_4575,plain,
join(composition(A,B),complement(composition(top,B))) = join(composition(A,B),complement(composition(complement(A),B))),
inference(paramod,[status(thm)],[c_1,c_4574]) ).
cnf(c_1684,plain,
join(composition(A,B),complement(composition(complement(A),B))) = join(composition(A,B),complement(composition(top,B))),
inference(copy,[status(thm)],[c_4575]) ).
cnf(c_1861,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_11,c_1255]) ).
cnf(c_4576,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_1255,c_12]) ).
cnf(c_4577,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_4576]) ).
cnf(c_4578,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_4577]) ).
cnf(c_4579,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_4578]) ).
cnf(c_4580,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_1861,c_4579]) ).
cnf(c_1862,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_4580]) ).
cnf(c_1873,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_1862,c_11]) ).
cnf(c_4581,plain,
composition(complement(converse(composition(A,top))),A) = zero,
inference(paramod,[status(thm)],[c_1873,c_373]) ).
cnf(c_4582,plain,
composition(complement(composition(converse(top),converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_13,c_4581]) ).
cnf(c_1922,plain,
composition(complement(composition(top,converse(A))),A) = zero,
inference(paramod,[status(thm)],[c_461,c_4582]) ).
cnf(c_4583,plain,
join(complement(join(complement(complement(A)),B)),complement(join(complement(complement(composition(A,sk1))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_1260,c_194]) ).
cnf(c_4584,plain,
join(complement(join(A,B)),complement(join(complement(complement(composition(A,sk1))),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_87,c_4583]) ).
cnf(c_4585,plain,
join(complement(join(A,B)),complement(join(composition(A,sk1),complement(join(complement(join(complement(complement(A)),complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_87,c_4584]) ).
cnf(c_4586,plain,
join(complement(join(A,B)),complement(join(composition(A,sk1),complement(join(complement(join(A,complement(B))),complement(composition(A,sk1))))))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_87,c_4585]) ).
cnf(c_4587,plain,
join(complement(join(A,B)),complement(composition(A,sk1))) = join(complement(A),complement(composition(A,sk1))),
inference(paramod,[status(thm)],[c_599,c_4586]) ).
cnf(c_2255,plain,
join(complement(join(A,B)),complement(composition(A,sk1))) = complement(composition(A,sk1)),
inference(paramod,[status(thm)],[c_1260,c_4587]) ).
cnf(c_4588,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_1476]) ).
cnf(c_4589,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_4588]) ).
cnf(c_2657,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_4589]) ).
cnf(c_2688,plain,
join(complement(one),composition(sk1,top)) = join(sk1,complement(one)),
inference(paramod,[status(thm)],[c_2657,c_166]) ).
cnf(c_4590,plain,
join(complement(one),complement(join(sk1,complement(one)))) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_2688,c_1241]) ).
cnf(c_4591,plain,
join(complement(sk1),complement(one)) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_1177,c_4590]) ).
cnf(c_4592,plain,
join(complement(one),complement(sk1)) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_1,c_4591]) ).
cnf(c_4593,plain,
complement(sk1) = join(complement(composition(sk1,top)),complement(one)),
inference(paramod,[status(thm)],[c_683,c_4592]) ).
cnf(c_4594,plain,
complement(sk1) = join(complement(one),complement(composition(sk1,top))),
inference(paramod,[status(thm)],[c_1,c_4593]) ).
cnf(c_2714,plain,
join(complement(one),complement(composition(sk1,top))) = complement(sk1),
inference(copy,[status(thm)],[c_4594]) ).
cnf(c_4595,plain,
converse(complement(sk1)) = join(converse(complement(one)),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_2714,c_12]) ).
cnf(c_4596,plain,
complement(converse(sk1)) = join(converse(complement(one)),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_1873,c_4595]) ).
cnf(c_4597,plain,
complement(converse(sk1)) = join(complement(converse(one)),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_1873,c_4596]) ).
cnf(c_4598,plain,
complement(converse(sk1)) = join(complement(one),converse(complement(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_98,c_4597]) ).
cnf(c_4599,plain,
complement(converse(sk1)) = join(complement(one),complement(converse(composition(sk1,top)))),
inference(paramod,[status(thm)],[c_1873,c_4598]) ).
cnf(c_4600,plain,
complement(converse(sk1)) = join(complement(one),complement(composition(converse(top),converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_4599]) ).
cnf(c_4601,plain,
complement(converse(sk1)) = join(complement(one),complement(composition(top,converse(sk1)))),
inference(paramod,[status(thm)],[c_461,c_4600]) ).
cnf(c_2721,plain,
join(complement(one),complement(composition(top,converse(sk1)))) = complement(converse(sk1)),
inference(copy,[status(thm)],[c_4601]) ).
cnf(c_4602,plain,
converse(zero) = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_366,c_13]) ).
cnf(c_4603,plain,
zero = composition(converse(complement(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_273,c_4602]) ).
cnf(c_4604,plain,
zero = composition(complement(converse(composition(converse(A),top))),converse(A)),
inference(paramod,[status(thm)],[c_1873,c_4603]) ).
cnf(c_4605,plain,
zero = composition(complement(composition(converse(top),converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_13,c_4604]) ).
cnf(c_4606,plain,
zero = composition(complement(composition(top,converse(converse(A)))),converse(A)),
inference(paramod,[status(thm)],[c_461,c_4605]) ).
cnf(c_4607,plain,
zero = composition(complement(composition(top,A)),converse(A)),
inference(paramod,[status(thm)],[c_11,c_4606]) ).
cnf(c_2868,plain,
composition(complement(composition(top,A)),converse(A)) = zero,
inference(copy,[status(thm)],[c_4607]) ).
cnf(c_4608,plain,
join(zero,composition(complement(complement(composition(top,A))),converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_2868,c_47]) ).
cnf(c_4609,plain,
join(zero,composition(composition(top,A),converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_87,c_4608]) ).
cnf(c_4610,plain,
join(zero,composition(top,composition(A,converse(A)))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_8,c_4609]) ).
cnf(c_2923,plain,
composition(top,composition(A,converse(A))) = composition(top,converse(A)),
inference(paramod,[status(thm)],[c_177,c_4610]) ).
cnf(c_4611,plain,
join(zero,composition(complement(complement(composition(top,converse(A)))),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_1922,c_47]) ).
cnf(c_4612,plain,
join(zero,composition(composition(top,converse(A)),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_87,c_4611]) ).
cnf(c_4613,plain,
join(zero,composition(top,composition(converse(A),A))) = composition(top,A),
inference(paramod,[status(thm)],[c_8,c_4612]) ).
cnf(c_3359,plain,
composition(top,composition(converse(A),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_177,c_4613]) ).
cnf(c_4614,plain,
join(complement(complement(composition(A,sk1))),complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_1260,c_2255]) ).
cnf(c_4615,plain,
join(composition(A,sk1),complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_87,c_4614]) ).
cnf(c_4616,plain,
join(composition(A,sk1),complement(composition(top,sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_1684,c_4615]) ).
cnf(c_3726,plain,
complement(composition(complement(A),sk1)) = join(composition(A,sk1),complement(composition(top,sk1))),
inference(copy,[status(thm)],[c_4616]) ).
cnf(c_4617,plain,
join(complement(complement(A)),complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_244,c_2255]) ).
cnf(c_4618,plain,
join(A,complement(composition(complement(A),sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_87,c_4617]) ).
cnf(c_4619,plain,
join(A,join(composition(A,sk1),complement(composition(top,sk1)))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_3726,c_4618]) ).
cnf(c_4620,plain,
join(A,complement(composition(top,sk1))) = complement(composition(complement(A),sk1)),
inference(paramod,[status(thm)],[c_767,c_4619]) ).
cnf(c_4621,plain,
join(A,complement(composition(top,sk1))) = join(composition(A,sk1),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_3726,c_4620]) ).
cnf(c_3731,plain,
join(composition(A,sk1),complement(composition(top,sk1))) = join(A,complement(composition(top,sk1))),
inference(copy,[status(thm)],[c_4621]) ).
cnf(c_3748,plain,
complement(composition(complement(A),sk1)) = join(A,complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_3731,c_3726]) ).
cnf(c_3764,plain,
complement(composition(A,sk1)) = join(complement(A),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_87,c_3748]) ).
cnf(c_4622,plain,
complement(zero) = join(composition(top,converse(sk1)),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_1922,c_3748]) ).
cnf(c_4623,plain,
top = join(composition(top,converse(sk1)),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_207,c_4622]) ).
cnf(c_4624,plain,
top = join(complement(composition(top,sk1)),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_1,c_4623]) ).
cnf(c_3776,plain,
join(complement(composition(top,sk1)),composition(top,converse(sk1))) = top,
inference(copy,[status(thm)],[c_4624]) ).
cnf(c_4625,plain,
join(composition(top,converse(sk1)),complement(top)) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_3776,c_1177]) ).
cnf(c_4626,plain,
join(composition(top,converse(sk1)),zero) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_19,c_4625]) ).
cnf(c_4627,plain,
join(zero,composition(top,converse(sk1))) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_1,c_4626]) ).
cnf(c_4628,plain,
composition(top,converse(sk1)) = join(complement(complement(composition(top,sk1))),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_177,c_4627]) ).
cnf(c_4629,plain,
composition(top,converse(sk1)) = join(composition(top,sk1),composition(top,converse(sk1))),
inference(paramod,[status(thm)],[c_87,c_4628]) ).
cnf(c_4069,plain,
join(composition(top,sk1),composition(top,converse(sk1))) = composition(top,converse(sk1)),
inference(copy,[status(thm)],[c_4629]) ).
cnf(c_4630,plain,
complement(sk1) = join(complement(one),complement(composition(top,sk1))),
inference(paramod,[status(thm)],[c_103,c_3764]) ).
cnf(c_4084,plain,
join(complement(one),complement(composition(top,sk1))) = complement(sk1),
inference(copy,[status(thm)],[c_4630]) ).
cnf(c_4631,plain,
join(complement(A),complement(complement(composition(A,sk1)))) = join(complement(complement(composition(top,sk1))),complement(A)),
inference(paramod,[status(thm)],[c_3764,c_1241]) ).
cnf(c_4632,plain,
join(complement(A),composition(A,sk1)) = join(complement(complement(composition(top,sk1))),complement(A)),
inference(paramod,[status(thm)],[c_87,c_4631]) ).
cnf(c_4633,plain,
join(complement(A),composition(A,sk1)) = join(composition(top,sk1),complement(A)),
inference(paramod,[status(thm)],[c_87,c_4632]) ).
cnf(c_4106,plain,
join(composition(top,sk1),complement(A)) = join(complement(A),composition(A,sk1)),
inference(copy,[status(thm)],[c_4633]) ).
cnf(c_4634,plain,
join(complement(composition(composition(top,sk1),converse(sk1))),composition(composition(composition(top,sk1),converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_4106,c_1066]) ).
cnf(c_4635,plain,
join(complement(composition(top,composition(sk1,converse(sk1)))),composition(composition(composition(top,sk1),converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_8,c_4634]) ).
cnf(c_4636,plain,
join(complement(composition(top,converse(sk1))),composition(composition(composition(top,sk1),converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_2923,c_4635]) ).
cnf(c_4637,plain,
join(complement(composition(top,converse(sk1))),composition(composition(top,composition(sk1,converse(sk1))),sk1)) = top,
inference(paramod,[status(thm)],[c_8,c_4636]) ).
cnf(c_4638,plain,
join(complement(composition(top,converse(sk1))),composition(composition(top,converse(sk1)),sk1)) = top,
inference(paramod,[status(thm)],[c_2923,c_4637]) ).
cnf(c_4639,plain,
join(complement(composition(top,converse(sk1))),composition(top,composition(converse(sk1),sk1))) = top,
inference(paramod,[status(thm)],[c_8,c_4638]) ).
cnf(c_4640,plain,
join(complement(composition(top,converse(sk1))),composition(top,sk1)) = top,
inference(paramod,[status(thm)],[c_3359,c_4639]) ).
cnf(c_4180,plain,
join(composition(top,sk1),complement(composition(top,converse(sk1)))) = top,
inference(paramod,[status(thm)],[c_1,c_4640]) ).
cnf(c_4641,plain,
join(complement(composition(top,converse(sk1))),complement(join(composition(top,sk1),complement(composition(top,converse(sk1)))))) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_4069,c_328]) ).
cnf(c_4642,plain,
join(complement(composition(top,converse(sk1))),complement(top)) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_4180,c_4641]) ).
cnf(c_4643,plain,
join(complement(composition(top,converse(sk1))),zero) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_19,c_4642]) ).
cnf(c_4644,plain,
join(zero,complement(composition(top,converse(sk1)))) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_1,c_4643]) ).
cnf(c_4375,plain,
complement(composition(top,converse(sk1))) = complement(composition(top,sk1)),
inference(paramod,[status(thm)],[c_177,c_4644]) ).
cnf(c_4645,plain,
join(complement(one),complement(composition(top,sk1))) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_4375,c_2721]) ).
cnf(c_4646,plain,
complement(sk1) = complement(converse(sk1)),
inference(paramod,[status(thm)],[c_4084,c_4645]) ).
cnf(c_4386,plain,
complement(converse(sk1)) = complement(sk1),
inference(copy,[status(thm)],[c_4646]) ).
cnf(c_4647,plain,
complement(complement(sk1)) = converse(sk1),
inference(paramod,[status(thm)],[c_4386,c_87]) ).
cnf(c_4648,plain,
sk1 = converse(sk1),
inference(paramod,[status(thm)],[c_87,c_4647]) ).
cnf(c_4436,plain,
converse(sk1) = sk1,
inference(copy,[status(thm)],[c_4648]) ).
cnf(c_4437,plain,
$false,
inference(resolve,[status(thm)],[c_4436,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL025-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 05:27:17 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 4128667 was started by sandbox on n017,
% 0.17/0.45 % Sat Sep 26 05:27:17 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 9.08/1.70
% 9.08/1.70 % SZS status Unsatisfiable for theBenchmark
% 9.08/1.70
% 9.08/1.70 % Proof 1 at 0.97 (+ 0.23) seconds.
% 9.08/1.70 % Length of proof is 131.
% 9.08/1.70 % Level of proof is 25.
% 9.08/1.70 % Maximum clause weight is 93.000.
% 9.08/1.70 % Given clauses 301.
% 9.08/1.70
% 9.08/1.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------