%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL040-3 : 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 : n026.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 08:25:04 AM UTC 2026
% Result : Unsatisfiable 41.28s 6.44s
% Output : CNFRefutation 41.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 16
% Syntax : Number of formulae : 215 ( 215 unt; 0 def)
% Number of atoms : 215 ( 214 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 344 ( 23 sgn 28 !; 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_3532,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_3532]) ).
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_3533,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_3534,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_3533]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_3534]) ).
fof(dedekind_law_14,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(composition(VAR_0,VAR_1),VAR_2),composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),meet(VAR_1,composition(converse(VAR_0),VAR_2)))) = composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),meet(VAR_1,composition(converse(VAR_0),VAR_2))),
file('theBenchmark.p',dedekind_law_14) ).
cnf(c_20,plain,
join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(clausify,[status(thm)],[dedekind_law_14]) ).
cnf(c_3535,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_20]) ).
cnf(c_3536,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_3535]) ).
cnf(c_3537,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_3536]) ).
cnf(c_3538,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),meet(B,composition(converse(A),C))),
inference(paramod,[status(thm)],[c_6,c_3537]) ).
cnf(c_21,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C))))),
inference(paramod,[status(thm)],[c_6,c_3538]) ).
fof(goals_17,axiom,
join(composition(converse(sk1),sk1),one) = one,
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(composition(converse(sk1),sk1),one) = one,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(paramod,[status(thm)],[c_1,c_26]) ).
fof(goals_18,axiom,
composition(sk1,meet(sk2,sk3)) != meet(composition(sk1,sk2),composition(sk1,sk3)),
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
composition(sk1,meet(sk2,sk3)) != meet(composition(sk1,sk2),composition(sk1,sk3)),
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_3539,plain,
composition(sk1,complement(join(complement(sk2),complement(sk3)))) != meet(composition(sk1,sk2),composition(sk1,sk3)),
inference(paramod,[status(thm)],[c_6,c_28]) ).
cnf(c_29,plain,
composition(sk1,complement(join(complement(sk2),complement(sk3)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_6,c_3539]) ).
cnf(c_3540,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_31,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_3540]) ).
cnf(c_32,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_33,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_3541,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_36,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_3541]) ).
cnf(c_3542,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_3543,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_12,c_3542]) ).
cnf(c_3544,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_13,c_3543]) ).
cnf(c_3545,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_13,c_3544]) ).
cnf(c_3546,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),join(converse(A),converse(C))),
inference(paramod,[status(thm)],[c_12,c_3545]) ).
cnf(c_37,plain,
composition(converse(A),join(converse(B),converse(C))) = join(composition(converse(A),converse(B)),composition(converse(A),converse(C))),
inference(copy,[status(thm)],[c_3546]) ).
cnf(c_3547,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_43,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_3547]) ).
cnf(c_3548,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_3549,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_3548]) ).
cnf(c_44,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_3549]) ).
cnf(c_3550,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_49,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_3550]) ).
cnf(c_3551,plain,
composition(one,A) = join(composition(one,A),composition(composition(converse(sk1),sk1),A)),
inference(paramod,[status(thm)],[c_27,c_10]) ).
cnf(c_3552,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk1),composition(sk1,A))),
inference(paramod,[status(thm)],[c_8,c_3551]) ).
cnf(c_52,plain,
join(composition(one,A),composition(converse(sk1),composition(sk1,A))) = composition(one,A),
inference(copy,[status(thm)],[c_3552]) ).
cnf(c_3553,plain,
join(A,top) = join(B,join(A,complement(B))),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_54,plain,
join(A,join(B,complement(A))) = join(B,top),
inference(copy,[status(thm)],[c_3553]) ).
cnf(c_3554,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_36]) ).
cnf(c_66,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_3554]) ).
cnf(c_3555,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_66,c_9]) ).
cnf(c_68,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_3555]) ).
cnf(c_72,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_66,c_15]) ).
cnf(c_73,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_68,c_66]) ).
cnf(c_74,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_73,c_72]) ).
cnf(c_3556,plain,
join(A,composition(converse(sk1),composition(sk1,A))) = composition(one,A),
inference(paramod,[status(thm)],[c_73,c_52]) ).
cnf(c_75,plain,
join(A,composition(converse(sk1),composition(sk1,A))) = A,
inference(paramod,[status(thm)],[c_73,c_3556]) ).
cnf(c_76,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_74,c_44]) ).
cnf(c_3557,plain,
A = join(complement(join(complement(B),complement(A))),complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_33,c_1]) ).
cnf(c_77,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(B),A))) = B,
inference(copy,[status(thm)],[c_3557]) ).
cnf(c_3558,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_33]) ).
cnf(c_3559,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_3558]) ).
cnf(c_3560,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_3559]) ).
cnf(c_79,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_3560]) ).
cnf(c_80,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_79,c_43]) ).
cnf(c_81,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_80,c_79]) ).
cnf(c_82,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_80,c_76]) ).
cnf(c_83,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_82,c_81]) ).
cnf(c_85,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_82,c_49]) ).
cnf(c_3561,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_80,c_5]) ).
cnf(c_98,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_80,c_3561]) ).
cnf(c_3562,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_80,c_32]) ).
cnf(c_100,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_80,c_3562]) ).
cnf(c_3563,plain,
join(complement(join(A,B)),complement(join(complement(B),complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_80,c_33]) ).
cnf(c_101,plain,
join(complement(join(A,B)),complement(join(complement(B),A))) = complement(A),
inference(paramod,[status(thm)],[c_80,c_3563]) ).
cnf(c_3564,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_83,c_17]) ).
cnf(c_3565,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_3564]) ).
cnf(c_105,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_3565]) ).
cnf(c_3566,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_83,c_80]) ).
cnf(c_3567,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_80,c_3566]) ).
cnf(c_106,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_3567]) ).
cnf(c_107,plain,
join(A,join(B,complement(A))) = top,
inference(paramod,[status(thm)],[c_105,c_54]) ).
cnf(c_3568,plain,
composition(A,join(converse(B),converse(C))) = join(composition(converse(converse(A)),converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_11,c_37]) ).
cnf(c_3569,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_11,c_3568]) ).
cnf(c_108,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_3569]) ).
cnf(c_3570,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_105,c_1]) ).
cnf(c_120,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_3570]) ).
cnf(c_3571,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_105,c_12]) ).
cnf(c_122,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_3571]) ).
cnf(c_3572,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_106,c_3]) ).
cnf(c_124,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_3572]) ).
cnf(c_3573,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_106,c_3]) ).
cnf(c_126,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_1,c_3573]) ).
cnf(c_146,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_122]) ).
cnf(c_149,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_146,c_120]) ).
cnf(c_182,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_149,c_85]) ).
cnf(c_3574,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_182,c_10]) ).
cnf(c_3575,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_120,c_3574]) ).
cnf(c_3576,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_182,c_3575]) ).
cnf(c_3577,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_82,c_3576]) ).
cnf(c_189,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_3577]) ).
cnf(c_3578,plain,
zero = composition(A,composition(B,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_189,c_8]) ).
cnf(c_3579,plain,
zero = composition(A,zero),
inference(paramod,[status(thm)],[c_189,c_3578]) ).
cnf(c_191,plain,
composition(A,zero) = zero,
inference(copy,[status(thm)],[c_3579]) ).
cnf(c_237,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_80,c_107]) ).
cnf(c_3580,plain,
join(complement(join(complement(A),B)),complement(join(complement(complement(B)),A))) = complement(B),
inference(paramod,[status(thm)],[c_80,c_77]) ).
cnf(c_239,plain,
join(complement(join(complement(A),B)),complement(join(B,A))) = complement(B),
inference(paramod,[status(thm)],[c_80,c_3580]) ).
cnf(c_3581,plain,
join(complement(join(complement(A),B)),A) = join(complement(join(complement(B),complement(A))),complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_77,c_126]) ).
cnf(c_3582,plain,
join(A,complement(join(complement(A),B))) = join(complement(join(complement(B),complement(A))),complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_1,c_3581]) ).
cnf(c_3583,plain,
join(A,complement(join(complement(A),B))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_239,c_3582]) ).
cnf(c_243,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_80,c_3583]) ).
cnf(c_3584,plain,
join(complement(composition(converse(sk1),composition(sk1,A))),A) = top,
inference(paramod,[status(thm)],[c_75,c_237]) ).
cnf(c_261,plain,
join(A,complement(composition(converse(sk1),composition(sk1,A)))) = top,
inference(paramod,[status(thm)],[c_1,c_3584]) ).
cnf(c_3585,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_98,c_124]) ).
cnf(c_3586,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_3585]) ).
cnf(c_284,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_98,c_3586]) ).
cnf(c_3587,plain,
join(complement(complement(A)),complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_100,c_98]) ).
cnf(c_3588,plain,
join(A,complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_80,c_3587]) ).
cnf(c_3589,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_80,c_3588]) ).
cnf(c_3590,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_1,c_3589]) ).
cnf(c_3591,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_3,c_3590]) ).
cnf(c_3592,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_284,c_3591]) ).
cnf(c_331,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_80,c_3592]) ).
cnf(c_3593,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_100,c_100]) ).
cnf(c_3594,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_80,c_3593]) ).
cnf(c_3595,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_80,c_3594]) ).
cnf(c_3596,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_3595]) ).
cnf(c_3597,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_3596]) ).
cnf(c_3598,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_331,c_3597]) ).
cnf(c_3599,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_124,c_3598]) ).
cnf(c_334,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_80,c_3599]) ).
cnf(c_3600,plain,
join(complement(complement(A)),complement(join(complement(join(complement(B),A)),complement(complement(join(A,B)))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_101,c_100]) ).
cnf(c_3601,plain,
join(A,complement(join(complement(join(complement(B),A)),complement(complement(join(A,B)))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_80,c_3600]) ).
cnf(c_3602,plain,
join(A,complement(join(complement(join(complement(B),A)),join(A,B)))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_80,c_3601]) ).
cnf(c_3603,plain,
join(A,complement(join(join(A,B),complement(join(complement(B),A))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_1,c_3602]) ).
cnf(c_3604,plain,
join(A,complement(join(A,join(B,complement(join(complement(B),A)))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_3,c_3603]) ).
cnf(c_3605,plain,
join(A,complement(join(A,B))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_243,c_3604]) ).
cnf(c_337,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_80,c_3605]) ).
cnf(c_3606,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_108]) ).
cnf(c_369,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_3606]) ).
cnf(c_3607,plain,
composition(A,join(top,converse(B))) = join(composition(A,converse(top)),composition(A,converse(B))),
inference(paramod,[status(thm)],[c_149,c_108]) ).
cnf(c_3608,plain,
composition(A,top) = join(composition(A,converse(top)),composition(A,converse(B))),
inference(paramod,[status(thm)],[c_120,c_3607]) ).
cnf(c_3609,plain,
composition(A,top) = join(composition(A,top),composition(A,converse(B))),
inference(paramod,[status(thm)],[c_149,c_3608]) ).
cnf(c_371,plain,
join(composition(A,top),composition(A,converse(B))) = composition(A,top),
inference(copy,[status(thm)],[c_3609]) ).
cnf(c_388,plain,
join(A,complement(join(B,join(C,A)))) = join(A,complement(join(B,C))),
inference(paramod,[status(thm)],[c_3,c_334]) ).
cnf(c_3610,plain,
join(join(A,B),complement(join(A,join(C,B)))) = join(join(A,B),complement(C)),
inference(paramod,[status(thm)],[c_31,c_334]) ).
cnf(c_3611,plain,
join(A,join(B,complement(join(A,join(C,B))))) = join(join(A,B),complement(C)),
inference(paramod,[status(thm)],[c_3,c_3610]) ).
cnf(c_3612,plain,
join(A,join(B,complement(join(A,C)))) = join(join(A,B),complement(C)),
inference(paramod,[status(thm)],[c_388,c_3611]) ).
cnf(c_392,plain,
join(A,join(B,complement(join(A,C)))) = join(A,join(B,complement(C))),
inference(paramod,[status(thm)],[c_3,c_3612]) ).
cnf(c_3613,plain,
join(join(complement(A),B),C) = join(B,join(complement(join(B,A)),C)),
inference(paramod,[status(thm)],[c_337,c_3]) ).
cnf(c_3614,plain,
join(complement(A),join(B,C)) = join(B,join(complement(join(B,A)),C)),
inference(paramod,[status(thm)],[c_3,c_3613]) ).
cnf(c_430,plain,
join(A,join(complement(join(A,B)),C)) = join(complement(B),join(A,C)),
inference(copy,[status(thm)],[c_3614]) ).
cnf(c_557,plain,
join(composition(A,top),composition(A,B)) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_371]) ).
cnf(c_3615,plain,
join(complement(composition(A,top)),complement(join(composition(A,B),complement(composition(A,top))))) = complement(composition(A,B)),
inference(paramod,[status(thm)],[c_557,c_100]) ).
cnf(c_566,plain,
join(complement(composition(A,top)),complement(composition(A,B))) = complement(composition(A,B)),
inference(paramod,[status(thm)],[c_334,c_3615]) ).
cnf(c_3616,plain,
join(complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))),composition(complement(join(complement(sk1),complement(composition(composition(sk1,complement(A)),converse(A))))),complement(top))) = composition(complement(join(complement(sk1),complement(composition(composition(sk1,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sk1),composition(sk1,complement(A))))))),
inference(paramod,[status(thm)],[c_261,c_21]) ).
cnf(c_3617,plain,
join(complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))),composition(complement(join(complement(sk1),complement(composition(sk1,composition(complement(A),converse(A)))))),complement(top))) = composition(complement(join(complement(sk1),complement(composition(composition(sk1,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sk1),composition(sk1,complement(A))))))),
inference(paramod,[status(thm)],[c_8,c_3616]) ).
cnf(c_3618,plain,
join(complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))),composition(complement(join(complement(sk1),complement(composition(sk1,composition(complement(A),converse(A)))))),zero)) = composition(complement(join(complement(sk1),complement(composition(composition(sk1,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sk1),composition(sk1,complement(A))))))),
inference(paramod,[status(thm)],[c_19,c_3617]) ).
cnf(c_3619,plain,
join(complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))),zero) = composition(complement(join(complement(sk1),complement(composition(composition(sk1,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sk1),composition(sk1,complement(A))))))),
inference(paramod,[status(thm)],[c_191,c_3618]) ).
cnf(c_3620,plain,
join(zero,complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A)))))) = composition(complement(join(complement(sk1),complement(composition(composition(sk1,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sk1),composition(sk1,complement(A))))))),
inference(paramod,[status(thm)],[c_1,c_3619]) ).
cnf(c_3621,plain,
complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = composition(complement(join(complement(sk1),complement(composition(composition(sk1,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sk1),composition(sk1,complement(A))))))),
inference(paramod,[status(thm)],[c_82,c_3620]) ).
cnf(c_3622,plain,
complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = composition(complement(join(complement(sk1),complement(composition(sk1,composition(complement(A),converse(A)))))),complement(join(complement(A),complement(composition(converse(sk1),composition(sk1,complement(A))))))),
inference(paramod,[status(thm)],[c_8,c_3621]) ).
cnf(c_3623,plain,
complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = composition(complement(join(complement(sk1),complement(composition(sk1,composition(complement(A),converse(A)))))),complement(top)),
inference(paramod,[status(thm)],[c_261,c_3622]) ).
cnf(c_3624,plain,
complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = composition(complement(join(complement(sk1),complement(composition(sk1,composition(complement(A),converse(A)))))),zero),
inference(paramod,[status(thm)],[c_19,c_3623]) ).
cnf(c_1141,plain,
complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = zero,
inference(paramod,[status(thm)],[c_191,c_3624]) ).
cnf(c_3625,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_11,c_369]) ).
cnf(c_1824,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_11,c_3625]) ).
cnf(c_3626,plain,
composition(A,top) = join(composition(A,B),composition(A,complement(B))),
inference(paramod,[status(thm)],[c_17,c_1824]) ).
cnf(c_1871,plain,
join(composition(A,B),composition(A,complement(B))) = composition(A,top),
inference(copy,[status(thm)],[c_3626]) ).
cnf(c_3627,plain,
join(composition(A,B),complement(composition(A,top))) = join(complement(composition(A,complement(B))),composition(A,B)),
inference(paramod,[status(thm)],[c_1871,c_337]) ).
cnf(c_3628,plain,
join(composition(A,B),complement(composition(A,top))) = join(composition(A,B),complement(composition(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_3627]) ).
cnf(c_1940,plain,
join(composition(A,B),complement(composition(A,complement(B)))) = join(composition(A,B),complement(composition(A,top))),
inference(copy,[status(thm)],[c_3628]) ).
cnf(c_3629,plain,
join(zero,complement(join(complement(composition(sk1,complement(A))),complement(complement(composition(sk1,A)))))) = complement(complement(composition(sk1,complement(A)))),
inference(paramod,[status(thm)],[c_1141,c_100]) ).
cnf(c_3630,plain,
join(zero,complement(join(complement(composition(sk1,complement(A))),composition(sk1,A)))) = complement(complement(composition(sk1,complement(A)))),
inference(paramod,[status(thm)],[c_80,c_3629]) ).
cnf(c_3631,plain,
join(zero,complement(join(composition(sk1,A),complement(composition(sk1,complement(A)))))) = complement(complement(composition(sk1,complement(A)))),
inference(paramod,[status(thm)],[c_1,c_3630]) ).
cnf(c_3632,plain,
join(zero,complement(join(composition(sk1,A),complement(composition(sk1,top))))) = complement(complement(composition(sk1,complement(A)))),
inference(paramod,[status(thm)],[c_1940,c_3631]) ).
cnf(c_3633,plain,
complement(join(composition(sk1,A),complement(composition(sk1,top)))) = complement(complement(composition(sk1,complement(A)))),
inference(paramod,[status(thm)],[c_82,c_3632]) ).
cnf(c_3634,plain,
complement(join(composition(sk1,A),complement(composition(sk1,top)))) = composition(sk1,complement(A)),
inference(paramod,[status(thm)],[c_80,c_3633]) ).
cnf(c_3528,plain,
composition(sk1,complement(A)) = complement(join(composition(sk1,A),complement(composition(sk1,top)))),
inference(copy,[status(thm)],[c_3634]) ).
cnf(c_3635,plain,
complement(join(composition(sk1,join(complement(sk2),complement(sk3))),complement(composition(sk1,top)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_3528,c_29]) ).
cnf(c_3636,plain,
complement(join(join(composition(sk1,complement(sk2)),composition(sk1,complement(sk3))),complement(composition(sk1,top)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_1824,c_3635]) ).
cnf(c_3637,plain,
complement(join(join(complement(join(composition(sk1,sk2),complement(composition(sk1,top)))),composition(sk1,complement(sk3))),complement(composition(sk1,top)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_3528,c_3636]) ).
cnf(c_3638,plain,
complement(join(join(complement(join(complement(composition(sk1,top)),composition(sk1,sk2))),composition(sk1,complement(sk3))),complement(composition(sk1,top)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_1,c_3637]) ).
cnf(c_3639,plain,
complement(join(join(complement(join(complement(composition(sk1,top)),composition(sk1,sk2))),complement(join(composition(sk1,sk3),complement(composition(sk1,top))))),complement(composition(sk1,top)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_3528,c_3638]) ).
cnf(c_3640,plain,
complement(join(join(complement(join(complement(composition(sk1,top)),composition(sk1,sk2))),complement(join(complement(composition(sk1,top)),composition(sk1,sk3)))),complement(composition(sk1,top)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_1,c_3639]) ).
cnf(c_3641,plain,
complement(join(complement(composition(sk1,top)),join(complement(join(complement(composition(sk1,top)),composition(sk1,sk2))),complement(join(complement(composition(sk1,top)),composition(sk1,sk3)))))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_1,c_3640]) ).
cnf(c_3642,plain,
complement(join(complement(composition(sk1,top)),join(complement(join(complement(composition(sk1,top)),composition(sk1,sk2))),complement(composition(sk1,sk3))))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_392,c_3641]) ).
cnf(c_3643,plain,
complement(join(complement(composition(sk1,sk2)),join(complement(composition(sk1,top)),complement(composition(sk1,sk3))))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_430,c_3642]) ).
cnf(c_3644,plain,
complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))) != complement(join(complement(composition(sk1,sk2)),complement(composition(sk1,sk3)))),
inference(paramod,[status(thm)],[c_566,c_3643]) ).
cnf(c_3531,plain,
$false,
inference(copy,[status(thm)],[c_3644]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL040-3 : 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 : n026.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 05:41:56 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 208761 was started by sandbox on n026,
% 0.10/0.38 % Sat Sep 26 05:41:56 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).
% 41.28/6.44
% 41.28/6.44 % given #500 (T,wt=24): 1263 join(composition(complement(one),A),join(B,A)) = join(composition(top,A),B). [back_rewrite(1243),rewrite([1247(9)])].
% 41.28/6.44
% 41.28/6.44 % SZS status Unsatisfiable for theBenchmark
% 41.28/6.44
% 41.28/6.44 % Proof 1 at 4.55 (+ 1.35) seconds.
% 41.28/6.44 % Length of proof is 86.
% 41.28/6.44 % Level of proof is 18.
% 41.28/6.44 % Maximum clause weight is 64.000.
% 41.28/6.44 % Given clauses 655.
% 41.28/6.44
% 41.28/6.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
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