%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL042-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:25:05 AM UTC 2026
% Result : Unsatisfiable 8.05s 1.62s
% Output : CNFRefutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 16
% Syntax : Number of formulae : 141 ( 141 unt; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 189 ( 19 sgn 29 !; 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_4623,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_4623]) ).
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_4624,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_4625,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_4624]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_4625]) ).
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_4626,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_4627,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_4626]) ).
cnf(c_4628,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_4627]) ).
cnf(c_4629,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_4628]) ).
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_4629]) ).
fof(goals_17,axiom,
! [VAR_0] : meet(composition(sk1,VAR_0),composition(sk1,complement(VAR_0))) = zero,
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
meet(composition(sk1,A),composition(sk1,complement(A))) = zero,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = zero,
inference(paramod,[status(thm)],[c_6,c_26]) ).
fof(goals_18,axiom,
join(composition(converse(sk1),sk1),one) != one,
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
join(composition(converse(sk1),sk1),one) != one,
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_29,plain,
join(one,composition(converse(sk1),sk1)) != one,
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_4630,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_4630]) ).
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_4631,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_34,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_4631]) ).
cnf(c_4632,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_40,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_4632]) ).
cnf(c_4633,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_52,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_4633]) ).
cnf(c_4634,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_4635,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_4634]) ).
cnf(c_53,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_4635]) ).
cnf(c_4636,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_55,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_4636]) ).
cnf(c_4637,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_58,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_4637]) ).
cnf(c_4638,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C)))))) = composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(converse(A)),C))))),
inference(paramod,[status(thm)],[c_11,c_21]) ).
cnf(c_73,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C)))))) = composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C))))),
inference(paramod,[status(thm)],[c_11,c_4638]) ).
cnf(c_117,plain,
complement(join(complement(sk1),complement(composition(sk1,complement(one))))) = zero,
inference(paramod,[status(thm)],[c_9,c_27]) ).
cnf(c_4639,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_31]) ).
cnf(c_123,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_4639]) ).
cnf(c_4640,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_40]) ).
cnf(c_135,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_4640]) ).
cnf(c_4641,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_135,c_9]) ).
cnf(c_144,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_4641]) ).
cnf(c_148,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_135,c_15]) ).
cnf(c_166,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_144,c_135]) ).
cnf(c_171,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_166,c_148]) ).
cnf(c_172,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_171,c_53]) ).
cnf(c_4642,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_33]) ).
cnf(c_4643,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_4642]) ).
cnf(c_4644,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_4643]) ).
cnf(c_214,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_4644]) ).
cnf(c_222,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_214,c_52]) ).
cnf(c_235,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_222,c_172]) ).
cnf(c_249,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_235,c_58]) ).
cnf(c_4645,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_222,c_5]) ).
cnf(c_251,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_222,c_4645]) ).
cnf(c_4646,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_222,c_171]) ).
cnf(c_4647,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_222,c_4646]) ).
cnf(c_262,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_222,c_4647]) ).
cnf(c_4648,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_262,c_3]) ).
cnf(c_274,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_4648]) ).
cnf(c_4649,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_262,c_34]) ).
cnf(c_4650,plain,
complement(complement(A)) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_251,c_4649]) ).
cnf(c_4651,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_222,c_4650]) ).
cnf(c_296,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_4651]) ).
cnf(c_4652,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_262,c_34]) ).
cnf(c_4653,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_4652]) ).
cnf(c_4654,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_296,c_4653]) ).
cnf(c_297,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_4654]) ).
cnf(c_4655,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_274]) ).
cnf(c_377,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_4655]) ).
cnf(c_4656,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_55,c_274]) ).
cnf(c_378,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_55,c_4656]) ).
cnf(c_4657,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_377,c_1]) ).
cnf(c_381,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_4657]) ).
cnf(c_413,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_378]) ).
cnf(c_418,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_413,c_381]) ).
cnf(c_437,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_418,c_249]) ).
cnf(c_4658,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_437,c_10]) ).
cnf(c_4659,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_381,c_4658]) ).
cnf(c_4660,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_437,c_4659]) ).
cnf(c_4661,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_235,c_4660]) ).
cnf(c_483,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_4661]) ).
cnf(c_4662,plain,
zero = composition(A,composition(B,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_483,c_8]) ).
cnf(c_4663,plain,
zero = composition(A,zero),
inference(paramod,[status(thm)],[c_483,c_4662]) ).
cnf(c_492,plain,
composition(A,zero) = zero,
inference(copy,[status(thm)],[c_4663]) ).
cnf(c_533,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_297]) ).
cnf(c_4664,plain,
join(join(complement(sk1),complement(composition(sk1,complement(one)))),zero) = top,
inference(paramod,[status(thm)],[c_117,c_17]) ).
cnf(c_4665,plain,
join(zero,join(complement(sk1),complement(composition(sk1,complement(one))))) = top,
inference(paramod,[status(thm)],[c_1,c_4664]) ).
cnf(c_1585,plain,
join(complement(sk1),complement(composition(sk1,complement(one)))) = top,
inference(paramod,[status(thm)],[c_235,c_4665]) ).
cnf(c_4666,plain,
join(complement(join(complement(composition(converse(sk1),sk1)),complement(complement(one)))),composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),zero)) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),complement(join(complement(sk1),complement(composition(sk1,complement(one)))))),
inference(paramod,[status(thm)],[c_117,c_73]) ).
cnf(c_4667,plain,
join(complement(join(complement(composition(converse(sk1),sk1)),one)),composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),zero)) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),complement(join(complement(sk1),complement(composition(sk1,complement(one)))))),
inference(paramod,[status(thm)],[c_222,c_4666]) ).
cnf(c_4668,plain,
join(complement(join(one,complement(composition(converse(sk1),sk1)))),composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),zero)) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),complement(join(complement(sk1),complement(composition(sk1,complement(one)))))),
inference(paramod,[status(thm)],[c_1,c_4667]) ).
cnf(c_4669,plain,
join(complement(join(one,complement(composition(converse(sk1),sk1)))),zero) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),complement(join(complement(sk1),complement(composition(sk1,complement(one)))))),
inference(paramod,[status(thm)],[c_492,c_4668]) ).
cnf(c_4670,plain,
join(zero,complement(join(one,complement(composition(converse(sk1),sk1))))) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),complement(join(complement(sk1),complement(composition(sk1,complement(one)))))),
inference(paramod,[status(thm)],[c_1,c_4669]) ).
cnf(c_4671,plain,
complement(join(one,complement(composition(converse(sk1),sk1)))) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),complement(join(complement(sk1),complement(composition(sk1,complement(one)))))),
inference(paramod,[status(thm)],[c_235,c_4670]) ).
cnf(c_4672,plain,
complement(join(one,complement(composition(converse(sk1),sk1)))) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),complement(top)),
inference(paramod,[status(thm)],[c_1585,c_4671]) ).
cnf(c_4673,plain,
complement(join(one,complement(composition(converse(sk1),sk1)))) = composition(complement(join(complement(converse(sk1)),complement(composition(complement(one),converse(sk1))))),zero),
inference(paramod,[status(thm)],[c_19,c_4672]) ).
cnf(c_1589,plain,
complement(join(one,complement(composition(converse(sk1),sk1)))) = zero,
inference(paramod,[status(thm)],[c_492,c_4673]) ).
cnf(c_4674,plain,
join(join(one,complement(composition(converse(sk1),sk1))),zero) = top,
inference(paramod,[status(thm)],[c_1589,c_17]) ).
cnf(c_4675,plain,
join(zero,join(one,complement(composition(converse(sk1),sk1)))) = top,
inference(paramod,[status(thm)],[c_1,c_4674]) ).
cnf(c_1596,plain,
join(one,complement(composition(converse(sk1),sk1))) = top,
inference(paramod,[status(thm)],[c_235,c_4675]) ).
cnf(c_4676,plain,
join(complement(join(complement(A),B)),B) = join(B,A),
inference(paramod,[status(thm)],[c_533,c_123]) ).
cnf(c_3870,plain,
join(A,complement(join(complement(B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_1,c_4676]) ).
cnf(c_3952,plain,
join(A,complement(join(A,complement(B)))) = join(A,B),
inference(paramod,[status(thm)],[c_1,c_3870]) ).
cnf(c_4677,plain,
join(one,complement(top)) = join(one,composition(converse(sk1),sk1)),
inference(paramod,[status(thm)],[c_1596,c_3952]) ).
cnf(c_4678,plain,
join(one,zero) = join(one,composition(converse(sk1),sk1)),
inference(paramod,[status(thm)],[c_19,c_4677]) ).
cnf(c_4679,plain,
join(zero,one) = join(one,composition(converse(sk1),sk1)),
inference(paramod,[status(thm)],[c_1,c_4678]) ).
cnf(c_4680,plain,
one = join(one,composition(converse(sk1),sk1)),
inference(paramod,[status(thm)],[c_235,c_4679]) ).
cnf(c_4621,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(copy,[status(thm)],[c_4680]) ).
cnf(c_4622,plain,
$false,
inference(resolve,[status(thm)],[c_4621,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL042-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 05:41:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 768832 was started by sandbox on n020,
% 0.13/0.36 % Sat Sep 26 05:41:20 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 8.05/1.62
% 8.05/1.62 % SZS status Unsatisfiable for theBenchmark
% 8.05/1.62
% 8.05/1.62 % Proof 1 at 1.04 (+ 0.18) seconds.
% 8.05/1.62 % Length of proof is 67.
% 8.05/1.62 % Level of proof is 17.
% 8.05/1.62 % Maximum clause weight is 49.000.
% 8.05/1.62 % Given clauses 278.
% 8.05/1.62
% 8.05/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------