%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL050-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:25:08 AM UTC 2026
% Result : Unsatisfiable 9.23s 1.67s
% Output : CNFRefutation 9.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 14
% Syntax : Number of formulae : 172 ( 172 unt; 0 def)
% Number of atoms : 172 ( 171 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 : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 253 ( 9 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_6375,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_6375]) ).
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_6376,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_6377,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_6376]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_6377]) ).
fof(goals_14,axiom,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_21,plain,
composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_6378,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_23,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_6378]) ).
cnf(c_24,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_25,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_6379,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_26,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_6379]) ).
cnf(c_6380,plain,
join(complement(join(complement(join(complement(A),B)),join(complement(A),complement(B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_6381,plain,
join(complement(join(join(complement(A),complement(B)),complement(join(complement(A),B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_1,c_6380]) ).
cnf(c_6382,plain,
join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_3,c_6381]) ).
cnf(c_28,plain,
join(complement(A),complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))) = join(complement(A),B),
inference(paramod,[status(thm)],[c_1,c_6382]) ).
cnf(c_6383,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_32,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_6383]) ).
cnf(c_6384,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_34,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_6384]) ).
cnf(c_6385,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_6386,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_6385]) ).
cnf(c_6387,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_6386]) ).
cnf(c_41,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_6387]) ).
cnf(c_6388,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_44,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_6388]) ).
cnf(c_6389,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_47,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_6389]) ).
cnf(c_6390,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_6391,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_6390]) ).
cnf(c_6392,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_6391]) ).
cnf(c_75,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_6392]) ).
cnf(c_6393,plain,
join(complement(join(complement(join(complement(A),complement(B))),join(complement(B),A))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_25,c_25]) ).
cnf(c_6394,plain,
join(complement(join(join(complement(B),A),complement(join(complement(A),complement(B))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_1,c_6393]) ).
cnf(c_6395,plain,
join(complement(join(complement(B),join(A,complement(join(complement(A),complement(B)))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_3,c_6394]) ).
cnf(c_80,plain,
join(complement(A),complement(join(complement(A),join(B,complement(join(complement(B),complement(A))))))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_1,c_6395]) ).
cnf(c_81,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_75,c_44]) ).
cnf(c_82,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_81,c_75]) ).
cnf(c_6396,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_32]) ).
cnf(c_90,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_6396]) ).
cnf(c_6397,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_90,c_9]) ).
cnf(c_92,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_6397]) ).
cnf(c_96,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_90,c_15]) ).
cnf(c_97,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_92,c_90]) ).
cnf(c_98,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_97,c_96]) ).
cnf(c_6398,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_24,c_26]) ).
cnf(c_6399,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_1,c_6398]) ).
cnf(c_118,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_81,c_6399]) ).
cnf(c_6400,plain,
join(A,join(complement(B),C)) = join(complement(B),join(A,complement(join(complement(B),join(complement(C),complement(join(complement(B),C))))))),
inference(paramod,[status(thm)],[c_28,c_23]) ).
cnf(c_131,plain,
join(complement(A),join(B,complement(join(complement(A),join(complement(C),complement(join(complement(A),C))))))) = join(B,join(complement(A),C)),
inference(copy,[status(thm)],[c_6400]) ).
cnf(c_6401,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(complement(A))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_6402,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),A))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_81,c_6401]) ).
cnf(c_133,plain,
join(complement(join(complement(A),B)),complement(join(A,complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_1,c_6402]) ).
cnf(c_6403,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_98,c_5]) ).
cnf(c_6404,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_1,c_6403]) ).
cnf(c_6405,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_17,c_6404]) ).
cnf(c_6406,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_19,c_6405]) ).
cnf(c_157,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_81,c_6406]) ).
cnf(c_6407,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_98,c_26]) ).
cnf(c_6408,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_5,c_6407]) ).
cnf(c_160,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_6408]) ).
cnf(c_169,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_157,c_82]) ).
cnf(c_172,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_160,c_80]) ).
cnf(c_6409,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_169,c_5]) ).
cnf(c_6410,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_169,c_6409]) ).
cnf(c_6411,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_6410]) ).
cnf(c_199,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_6411]) ).
cnf(c_6412,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_199,c_3]) ).
cnf(c_230,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_6412]) ).
cnf(c_6413,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_199,c_26]) ).
cnf(c_6414,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_6413]) ).
cnf(c_6415,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_160,c_6414]) ).
cnf(c_233,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_6415]) ).
cnf(c_6416,plain,
join(complement(join(complement(A),B)),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_233,c_133]) ).
cnf(c_6417,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_1,c_6416]) ).
cnf(c_6418,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_172,c_6417]) ).
cnf(c_235,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_6418]) ).
cnf(c_238,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_235,c_131]) ).
cnf(c_312,plain,
join(A,converse(complement(converse(A)))) = converse(top),
inference(paramod,[status(thm)],[c_11,c_47]) ).
cnf(c_316,plain,
join(one,converse(complement(one))) = converse(top),
inference(paramod,[status(thm)],[c_92,c_47]) ).
cnf(c_6419,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_230]) ).
cnf(c_356,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_6419]) ).
cnf(c_6420,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_47,c_230]) ).
cnf(c_357,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_47,c_6420]) ).
cnf(c_6421,plain,
join(one,converse(top)) = join(one,converse(complement(one))),
inference(paramod,[status(thm)],[c_316,c_230]) ).
cnf(c_358,plain,
join(one,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_316,c_6421]) ).
cnf(c_6422,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_356,c_1]) ).
cnf(c_360,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_6422]) ).
cnf(c_6423,plain,
composition(converse(top),A) = join(composition(one,A),composition(converse(top),A)),
inference(paramod,[status(thm)],[c_358,c_10]) ).
cnf(c_6424,plain,
composition(converse(top),A) = join(A,composition(converse(top),A)),
inference(paramod,[status(thm)],[c_97,c_6423]) ).
cnf(c_367,plain,
join(A,composition(converse(top),A)) = composition(converse(top),A),
inference(copy,[status(thm)],[c_6424]) ).
cnf(c_407,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_357]) ).
cnf(c_412,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_407,c_360]) ).
cnf(c_6425,plain,
join(A,composition(top,A)) = composition(converse(top),A),
inference(paramod,[status(thm)],[c_412,c_367]) ).
cnf(c_418,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_412,c_6425]) ).
cnf(c_423,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_412,c_312]) ).
cnf(c_427,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_412,c_47]) ).
cnf(c_6426,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_418,c_12]) ).
cnf(c_6427,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_6426]) ).
cnf(c_6428,plain,
composition(converse(A),top) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_412,c_6427]) ).
cnf(c_6429,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_6428]) ).
cnf(c_6430,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_412,c_6429]) ).
cnf(c_436,plain,
join(converse(A),composition(converse(A),top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_6430]) ).
cnf(c_439,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_418,c_360]) ).
cnf(c_6431,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_439,c_8]) ).
cnf(c_441,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_6431]) ).
cnf(c_6432,plain,
join(converse(complement(composition(top,A))),composition(converse(complement(composition(top,A))),top)) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_441,c_41]) ).
cnf(c_548,plain,
composition(converse(complement(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_436,c_6432]) ).
cnf(c_6433,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(C),complement(A))))) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_118,c_34]) ).
cnf(c_6434,plain,
join(composition(converse(B),complement(composition(B,A))),join(complement(A),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_238,c_6433]) ).
cnf(c_6435,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_23,c_6434]) ).
cnf(c_6436,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_34,c_6435]) ).
cnf(c_6437,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_81,c_6436]) ).
cnf(c_985,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_6437]) ).
cnf(c_6438,plain,
join(converse(complement(A)),complement(top)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_427,c_985]) ).
cnf(c_6439,plain,
join(converse(complement(A)),zero) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_19,c_6438]) ).
cnf(c_6440,plain,
join(zero,converse(complement(A))) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_6439]) ).
cnf(c_6441,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_157,c_6440]) ).
cnf(c_1038,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_6441]) ).
cnf(c_6442,plain,
join(converse(complement(converse(A))),complement(top)) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_423,c_985]) ).
cnf(c_6443,plain,
join(converse(complement(converse(A))),zero) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_19,c_6442]) ).
cnf(c_6444,plain,
join(zero,converse(complement(converse(A)))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_6443]) ).
cnf(c_6445,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_157,c_6444]) ).
cnf(c_1043,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_6445]) ).
cnf(c_6446,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_1038,c_12]) ).
cnf(c_6447,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_6446]) ).
cnf(c_6448,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_6447]) ).
cnf(c_6449,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_6448]) ).
cnf(c_6450,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_1043,c_6449]) ).
cnf(c_1084,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_6450]) ).
cnf(c_1090,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_1084,c_11]) ).
cnf(c_6451,plain,
composition(complement(converse(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_1090,c_548]) ).
cnf(c_6452,plain,
composition(complement(composition(converse(A),converse(top))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_6451]) ).
cnf(c_6453,plain,
composition(complement(composition(converse(A),top)),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_412,c_6452]) ).
cnf(c_6454,plain,
composition(complement(composition(converse(A),top)),top) = complement(converse(composition(top,A))),
inference(paramod,[status(thm)],[c_1090,c_6453]) ).
cnf(c_6455,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_6454]) ).
cnf(c_1121,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),top)),
inference(paramod,[status(thm)],[c_412,c_6455]) ).
cnf(c_6456,plain,
composition(complement(composition(A,top)),top) = complement(composition(converse(converse(A)),top)),
inference(paramod,[status(thm)],[c_11,c_1121]) ).
cnf(c_6373,plain,
composition(complement(composition(A,top)),top) = complement(composition(A,top)),
inference(paramod,[status(thm)],[c_11,c_6456]) ).
cnf(c_6374,plain,
$false,
inference(resolve,[status(thm)],[c_6373,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050-1 : 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 : n019.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 05:42:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 519540 was started by sandbox on n019,
% 0.10/0.36 % Sat Sep 26 05:42:18 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 9.23/1.67
% 9.23/1.67 % SZS status Unsatisfiable for theBenchmark
% 9.23/1.67
% 9.23/1.67 % Proof 1 at 1.07 (+ 0.22) seconds.
% 9.23/1.67 % Length of proof is 76.
% 9.23/1.67 % Level of proof is 19.
% 9.23/1.67 % Maximum clause weight is 93.000.
% 9.23/1.67 % Given clauses 353.
% 9.23/1.67
% 9.23/1.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------