%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL044-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:25:06 AM UTC 2026
% Result : Unsatisfiable 19.77s 2.93s
% Output : CNFRefutation 19.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 157 ( 157 unt; 0 def)
% Number of atoms : 157 ( 156 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 194 ( 23 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_4978,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_4978]) ).
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_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_4979,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_4980,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_4979]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_4980]) ).
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_4981,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_4982,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_4981]) ).
cnf(c_4983,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_4982]) ).
cnf(c_4984,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_4983]) ).
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_4984]) ).
fof(goals_17,axiom,
join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
join(complement(sk3),composition(complement(sk1),sk2)) = complement(sk3),
inference(paramod,[status(thm)],[c_1,c_26]) ).
fof(goals_18,axiom,
join(composition(sk3,converse(sk2)),sk1) != sk1,
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
join(composition(sk3,converse(sk2)),sk1) != sk1,
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_29,plain,
join(sk1,composition(sk3,converse(sk2))) != sk1,
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_4985,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_4985]) ).
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_4986,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_4986]) ).
cnf(c_4987,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_4987]) ).
cnf(c_4988,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_4988]) ).
cnf(c_4989,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_4990,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_4989]) ).
cnf(c_53,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_4990]) ).
cnf(c_4991,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_4991]) ).
cnf(c_4992,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_4992]) ).
cnf(c_4993,plain,
join(complement(join(complement(composition(A,converse(B))),complement(C))),composition(complement(join(complement(A),complement(composition(C,B)))),complement(join(complement(converse(B)),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(converse(B)))))),complement(join(complement(converse(B)),complement(composition(converse(A),C))))),
inference(paramod,[status(thm)],[c_11,c_21]) ).
cnf(c_72,plain,
join(complement(join(complement(composition(A,converse(B))),complement(C))),composition(complement(join(complement(A),complement(composition(C,B)))),complement(join(complement(converse(B)),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,B)))),complement(join(complement(converse(B)),complement(composition(converse(A),C))))),
inference(paramod,[status(thm)],[c_11,c_4993]) ).
cnf(c_4994,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_119,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_4994]) ).
cnf(c_4995,plain,
join(A,top) = join(B,join(A,complement(B))),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_121,plain,
join(A,join(B,complement(A))) = join(B,top),
inference(copy,[status(thm)],[c_4995]) ).
cnf(c_4996,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_40]) ).
cnf(c_132,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_4996]) ).
cnf(c_4997,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_132,c_9]) ).
cnf(c_141,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_4997]) ).
cnf(c_145,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_132,c_15]) ).
cnf(c_163,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_141,c_132]) ).
cnf(c_168,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_163,c_145]) ).
cnf(c_169,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_168,c_53]) ).
cnf(c_4998,plain,
converse(A) = join(converse(zero),converse(complement(complement(A)))),
inference(paramod,[status(thm)],[c_169,c_12]) ).
cnf(c_186,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(copy,[status(thm)],[c_4998]) ).
cnf(c_4999,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_33]) ).
cnf(c_5000,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_4999]) ).
cnf(c_5001,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_5000]) ).
cnf(c_211,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_5001]) ).
cnf(c_219,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_211,c_52]) ).
cnf(c_230,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_219,c_186]) ).
cnf(c_232,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_219,c_169]) ).
cnf(c_246,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_232,c_58]) ).
cnf(c_5002,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_219,c_5]) ).
cnf(c_248,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_219,c_5002]) ).
cnf(c_5003,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_219,c_168]) ).
cnf(c_5004,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_219,c_5003]) ).
cnf(c_259,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_219,c_5004]) ).
cnf(c_5005,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_232,c_1]) ).
cnf(c_270,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_5005]) ).
cnf(c_5006,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_259,c_3]) ).
cnf(c_271,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_5006]) ).
cnf(c_5007,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_259,c_34]) ).
cnf(c_5008,plain,
complement(complement(A)) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_248,c_5007]) ).
cnf(c_5009,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_219,c_5008]) ).
cnf(c_295,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_5009]) ).
cnf(c_5010,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_259,c_34]) ).
cnf(c_5011,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_5010]) ).
cnf(c_5012,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_295,c_5011]) ).
cnf(c_296,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_5012]) ).
cnf(c_5013,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_230]) ).
cnf(c_313,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_11,c_5013]) ).
cnf(c_5014,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_313,c_270]) ).
cnf(c_318,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_5014]) ).
cnf(c_5015,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_271]) ).
cnf(c_378,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_5015]) ).
cnf(c_5016,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_55,c_271]) ).
cnf(c_379,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_55,c_5016]) ).
cnf(c_381,plain,
join(A,join(B,complement(A))) = top,
inference(paramod,[status(thm)],[c_378,c_121]) ).
cnf(c_5017,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_378,c_1]) ).
cnf(c_382,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_5017]) ).
cnf(c_414,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_379]) ).
cnf(c_419,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_414,c_382]) ).
cnf(c_438,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_419,c_246]) ).
cnf(c_454,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_219,c_381]) ).
cnf(c_5018,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_438,c_10]) ).
cnf(c_5019,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_382,c_5018]) ).
cnf(c_5020,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_438,c_5019]) ).
cnf(c_5021,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_232,c_5020]) ).
cnf(c_484,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_5021]) ).
cnf(c_5022,plain,
join(complement(composition(complement(sk1),sk2)),complement(sk3)) = top,
inference(paramod,[status(thm)],[c_27,c_454]) ).
cnf(c_489,plain,
join(complement(sk3),complement(composition(complement(sk1),sk2))) = top,
inference(paramod,[status(thm)],[c_1,c_5022]) ).
cnf(c_5023,plain,
converse(zero) = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_484,c_13]) ).
cnf(c_5024,plain,
zero = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_318,c_5023]) ).
cnf(c_495,plain,
composition(converse(complement(composition(top,top))),converse(A)) = zero,
inference(copy,[status(thm)],[c_5024]) ).
cnf(c_5025,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_484,c_163]) ).
cnf(c_497,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_5025]) ).
cnf(c_5026,plain,
composition(converse(zero),converse(A)) = zero,
inference(paramod,[status(thm)],[c_497,c_495]) ).
cnf(c_500,plain,
composition(zero,converse(A)) = zero,
inference(paramod,[status(thm)],[c_318,c_5026]) ).
cnf(c_521,plain,
composition(zero,A) = zero,
inference(paramod,[status(thm)],[c_11,c_500]) ).
cnf(c_535,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_296]) ).
cnf(c_5027,plain,
join(complement(join(complement(composition(sk3,converse(sk2))),complement(complement(sk1)))),composition(complement(top),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1))))))) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_489,c_72]) ).
cnf(c_5028,plain,
join(complement(join(complement(composition(sk3,converse(sk2))),sk1)),composition(complement(top),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1))))))) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_219,c_5027]) ).
cnf(c_5029,plain,
join(complement(join(sk1,complement(composition(sk3,converse(sk2))))),composition(complement(top),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1))))))) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_1,c_5028]) ).
cnf(c_5030,plain,
join(complement(join(sk1,complement(composition(sk3,converse(sk2))))),composition(zero,complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1))))))) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_19,c_5029]) ).
cnf(c_5031,plain,
join(complement(join(sk1,complement(composition(sk3,converse(sk2))))),composition(zero,complement(join(complement(composition(converse(sk3),complement(sk1))),complement(converse(sk2)))))) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_1,c_5030]) ).
cnf(c_5032,plain,
join(complement(join(sk1,complement(composition(sk3,converse(sk2))))),zero) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_521,c_5031]) ).
cnf(c_5033,plain,
join(zero,complement(join(sk1,complement(composition(sk3,converse(sk2)))))) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_1,c_5032]) ).
cnf(c_5034,plain,
complement(join(sk1,complement(composition(sk3,converse(sk2))))) = composition(complement(join(complement(sk3),complement(composition(complement(sk1),sk2)))),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_232,c_5033]) ).
cnf(c_5035,plain,
complement(join(sk1,complement(composition(sk3,converse(sk2))))) = composition(complement(top),complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_489,c_5034]) ).
cnf(c_5036,plain,
complement(join(sk1,complement(composition(sk3,converse(sk2))))) = composition(zero,complement(join(complement(converse(sk2)),complement(composition(converse(sk3),complement(sk1)))))),
inference(paramod,[status(thm)],[c_19,c_5035]) ).
cnf(c_5037,plain,
complement(join(sk1,complement(composition(sk3,converse(sk2))))) = composition(zero,complement(join(complement(composition(converse(sk3),complement(sk1))),complement(converse(sk2))))),
inference(paramod,[status(thm)],[c_1,c_5036]) ).
cnf(c_1320,plain,
complement(join(sk1,complement(composition(sk3,converse(sk2))))) = zero,
inference(paramod,[status(thm)],[c_521,c_5037]) ).
cnf(c_5038,plain,
join(join(sk1,complement(composition(sk3,converse(sk2)))),zero) = top,
inference(paramod,[status(thm)],[c_1320,c_17]) ).
cnf(c_5039,plain,
join(zero,join(sk1,complement(composition(sk3,converse(sk2))))) = top,
inference(paramod,[status(thm)],[c_1,c_5038]) ).
cnf(c_5040,plain,
join(sk1,join(zero,complement(composition(sk3,converse(sk2))))) = top,
inference(paramod,[status(thm)],[c_31,c_5039]) ).
cnf(c_1520,plain,
join(sk1,complement(composition(sk3,converse(sk2)))) = top,
inference(paramod,[status(thm)],[c_232,c_5040]) ).
cnf(c_5041,plain,
join(complement(join(complement(A),B)),B) = join(B,A),
inference(paramod,[status(thm)],[c_535,c_119]) ).
cnf(c_4129,plain,
join(A,complement(join(complement(B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_1,c_5041]) ).
cnf(c_4215,plain,
join(A,complement(join(A,complement(B)))) = join(A,B),
inference(paramod,[status(thm)],[c_1,c_4129]) ).
cnf(c_5042,plain,
join(sk1,complement(top)) = join(sk1,composition(sk3,converse(sk2))),
inference(paramod,[status(thm)],[c_1520,c_4215]) ).
cnf(c_5043,plain,
join(sk1,zero) = join(sk1,composition(sk3,converse(sk2))),
inference(paramod,[status(thm)],[c_19,c_5042]) ).
cnf(c_5044,plain,
sk1 = join(sk1,composition(sk3,converse(sk2))),
inference(paramod,[status(thm)],[c_270,c_5043]) ).
cnf(c_4976,plain,
join(sk1,composition(sk3,converse(sk2))) = sk1,
inference(copy,[status(thm)],[c_5044]) ).
cnf(c_4977,plain,
$false,
inference(resolve,[status(thm)],[c_4976,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL044-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 05:41:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1334445 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 05:41:17 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 19.77/2.93
% 19.77/2.93 % SZS status Unsatisfiable for theBenchmark
% 19.77/2.93
% 19.77/2.93 % Proof 1 at 2.09 (+ 0.39) seconds.
% 19.77/2.93 % Length of proof is 75.
% 19.77/2.93 % Level of proof is 19.
% 19.77/2.93 % Maximum clause weight is 49.000.
% 19.77/2.93 % Given clauses 296.
% 19.77/2.93
% 19.77/2.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------