%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL042-1 : 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 : 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 08:25:05 AM UTC 2026
% Result : Unsatisfiable 6.88s 1.35s
% Output : CNFRefutation 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 14
% Syntax : Number of formulae : 202 ( 202 unt; 0 def)
% Number of atoms : 202 ( 201 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 : 295 ( 13 sgn 23 !; 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_2041,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_2041]) ).
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_2042,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_2043,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_2042]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_2043]) ).
fof(goals_14,axiom,
! [VAR_0] : meet(composition(sk1,VAR_0),composition(sk1,complement(VAR_0))) = zero,
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
meet(composition(sk1,A),composition(sk1,complement(A))) = zero,
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_21,plain,
complement(join(complement(composition(sk1,A)),complement(composition(sk1,complement(A))))) = zero,
inference(paramod,[status(thm)],[c_6,c_20]) ).
fof(goals_15,axiom,
join(composition(converse(sk1),sk1),one) != one,
file('theBenchmark.p',goals_15) ).
cnf(c_22,plain,
join(composition(converse(sk1),sk1),one) != one,
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_23,plain,
join(one,composition(converse(sk1),sk1)) != one,
inference(paramod,[status(thm)],[c_1,c_22]) ).
cnf(c_2044,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_25,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_2044]) ).
cnf(c_26,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_27,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_2045,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_28,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_2045]) ).
cnf(c_2046,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_2047,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_2046]) ).
cnf(c_2048,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_2047]) ).
cnf(c_30,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_2048]) ).
cnf(c_2049,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_34,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2049]) ).
cnf(c_2050,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_2051,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_12,c_2050]) ).
cnf(c_2052,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_2051]) ).
cnf(c_2053,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_2052]) ).
cnf(c_2054,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_2053]) ).
cnf(c_35,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_2054]) ).
cnf(c_2055,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_36,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_2055]) ).
cnf(c_2056,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_2056]) ).
cnf(c_2057,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_48,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_2057]) ).
cnf(c_2058,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_49,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_2058]) ).
cnf(c_2059,plain,
join(complement(join(zero,A)),complement(join(complement(top),complement(A)))) = top,
inference(paramod,[status(thm)],[c_19,c_5]) ).
cnf(c_50,plain,
join(complement(join(zero,A)),complement(join(zero,complement(A)))) = top,
inference(paramod,[status(thm)],[c_19,c_2059]) ).
cnf(c_2060,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_52,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_2060]) ).
cnf(c_2061,plain,
join(complement(join(zero,A)),complement(join(complement(join(complement(composition(sk1,B)),complement(composition(sk1,complement(B))))),complement(A)))) = join(complement(composition(sk1,B)),complement(composition(sk1,complement(B)))),
inference(paramod,[status(thm)],[c_21,c_5]) ).
cnf(c_2062,plain,
join(complement(join(zero,A)),complement(join(zero,complement(A)))) = join(complement(composition(sk1,B)),complement(composition(sk1,complement(B)))),
inference(paramod,[status(thm)],[c_21,c_2061]) ).
cnf(c_2063,plain,
top = join(complement(composition(sk1,B)),complement(composition(sk1,complement(B)))),
inference(paramod,[status(thm)],[c_50,c_2062]) ).
cnf(c_54,plain,
join(complement(composition(sk1,A)),complement(composition(sk1,complement(A)))) = top,
inference(copy,[status(thm)],[c_2063]) ).
cnf(c_2064,plain,
join(complement(join(complement(composition(sk1,A)),composition(sk1,complement(A)))),zero) = composition(sk1,A),
inference(paramod,[status(thm)],[c_21,c_5]) ).
cnf(c_56,plain,
join(zero,complement(join(complement(composition(sk1,A)),composition(sk1,complement(A))))) = composition(sk1,A),
inference(paramod,[status(thm)],[c_1,c_2064]) ).
cnf(c_2065,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_2066,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2065]) ).
cnf(c_2067,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_2066]) ).
cnf(c_82,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2067]) ).
cnf(c_2068,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_27,c_27]) ).
cnf(c_2069,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_2068]) ).
cnf(c_2070,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_2069]) ).
cnf(c_87,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_2070]) ).
cnf(c_88,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_82,c_46]) ).
cnf(c_89,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_82]) ).
cnf(c_2071,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_97,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_2071]) ).
cnf(c_2072,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_97,c_9]) ).
cnf(c_99,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2072]) ).
cnf(c_103,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_97,c_15]) ).
cnf(c_104,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_99,c_97]) ).
cnf(c_105,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_104,c_103]) ).
cnf(c_109,plain,
join(complement(join(A,B)),complement(join(complement(join(complement(A),C)),complement(join(complement(join(complement(A),complement(C))),B))))) = join(complement(A),C),
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_2073,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_26,c_28]) ).
cnf(c_2074,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_1,c_2073]) ).
cnf(c_125,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_88,c_2074]) ).
cnf(c_2075,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_30,c_25]) ).
cnf(c_139,plain,
join(complement(A),join(B,complement(join(complement(A),join(complement(C),complement(join(complement(A),C))))))) = join(B,join(complement(A),C)),
inference(copy,[status(thm)],[c_2075]) ).
cnf(c_2076,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_30,c_26]) ).
cnf(c_2077,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_88,c_2076]) ).
cnf(c_141,plain,
join(complement(join(complement(A),B)),complement(join(A,complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_1,c_2077]) ).
cnf(c_2078,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_105,c_5]) ).
cnf(c_2079,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_1,c_2078]) ).
cnf(c_2080,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_17,c_2079]) ).
cnf(c_2081,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_19,c_2080]) ).
cnf(c_165,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_88,c_2081]) ).
cnf(c_2082,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_105,c_28]) ).
cnf(c_2083,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_5,c_2082]) ).
cnf(c_168,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_2083]) ).
cnf(c_177,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_165,c_89]) ).
cnf(c_178,plain,
complement(join(complement(composition(sk1,A)),composition(sk1,complement(A)))) = composition(sk1,A),
inference(paramod,[status(thm)],[c_165,c_56]) ).
cnf(c_179,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_165,c_52]) ).
cnf(c_181,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_168,c_87]) ).
cnf(c_2084,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_177,c_5]) ).
cnf(c_2085,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_177,c_2084]) ).
cnf(c_2086,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_2085]) ).
cnf(c_208,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2086]) ).
cnf(c_2087,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_35]) ).
cnf(c_2088,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_2087]) ).
cnf(c_220,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2088]) ).
cnf(c_2089,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_208,c_3]) ).
cnf(c_239,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_2089]) ).
cnf(c_2090,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_208,c_28]) ).
cnf(c_2091,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_2090]) ).
cnf(c_2092,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_168,c_2091]) ).
cnf(c_242,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_2092]) ).
cnf(c_2093,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_242,c_141]) ).
cnf(c_2094,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_2093]) ).
cnf(c_2095,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_181,c_2094]) ).
cnf(c_244,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_2095]) ).
cnf(c_247,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_244,c_139]) ).
cnf(c_2096,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_5]) ).
cnf(c_260,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_2096]) ).
cnf(c_325,plain,
join(one,converse(complement(one))) = converse(top),
inference(paramod,[status(thm)],[c_99,c_49]) ).
cnf(c_2097,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_239]) ).
cnf(c_365,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_2097]) ).
cnf(c_2098,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_49,c_239]) ).
cnf(c_366,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_49,c_2098]) ).
cnf(c_2099,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_365,c_1]) ).
cnf(c_369,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_2099]) ).
cnf(c_389,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_104,c_48]) ).
cnf(c_400,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_366]) ).
cnf(c_405,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_400,c_369]) ).
cnf(c_414,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_405,c_325]) ).
cnf(c_2100,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_389,c_12]) ).
cnf(c_2101,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_13,c_2100]) ).
cnf(c_2102,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_405,c_2101]) ).
cnf(c_2103,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_13,c_2102]) ).
cnf(c_563,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_2103]) ).
cnf(c_2104,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(complement(A)),C)))) = complement(A),
inference(paramod,[status(thm)],[c_242,c_36]) ).
cnf(c_2105,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(A,C)))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_2104]) ).
cnf(c_754,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_36,c_2105]) ).
cnf(c_759,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_754]) ).
cnf(c_2106,plain,
join(complement(join(composition(sk1,A),B)),complement(join(complement(join(complement(composition(sk1,A)),composition(sk1,complement(A)))),complement(join(complement(top),B))))) = join(complement(composition(sk1,A)),composition(sk1,complement(A))),
inference(paramod,[status(thm)],[c_54,c_109]) ).
cnf(c_2107,plain,
join(complement(join(composition(sk1,A),B)),complement(join(composition(sk1,A),complement(join(complement(top),B))))) = join(complement(composition(sk1,A)),composition(sk1,complement(A))),
inference(paramod,[status(thm)],[c_178,c_2106]) ).
cnf(c_2108,plain,
join(complement(join(composition(sk1,A),B)),complement(join(composition(sk1,A),complement(join(zero,B))))) = join(complement(composition(sk1,A)),composition(sk1,complement(A))),
inference(paramod,[status(thm)],[c_19,c_2107]) ).
cnf(c_2109,plain,
join(complement(join(composition(sk1,A),B)),complement(join(composition(sk1,A),complement(B)))) = join(complement(composition(sk1,A)),composition(sk1,complement(A))),
inference(paramod,[status(thm)],[c_165,c_2108]) ).
cnf(c_2110,plain,
complement(composition(sk1,A)) = join(complement(composition(sk1,A)),composition(sk1,complement(A))),
inference(paramod,[status(thm)],[c_260,c_2109]) ).
cnf(c_827,plain,
join(complement(composition(sk1,A)),composition(sk1,complement(A))) = complement(composition(sk1,A)),
inference(copy,[status(thm)],[c_2110]) ).
cnf(c_2111,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_125,c_36]) ).
cnf(c_2112,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_247,c_2111]) ).
cnf(c_2113,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_25,c_2112]) ).
cnf(c_2114,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_36,c_2113]) ).
cnf(c_2115,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_88,c_2114]) ).
cnf(c_1010,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_2115]) ).
cnf(c_1031,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_1,c_1010]) ).
cnf(c_2116,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_414,c_1010]) ).
cnf(c_2117,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_19,c_2116]) ).
cnf(c_2118,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_2117]) ).
cnf(c_2119,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_165,c_2118]) ).
cnf(c_1042,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_2119]) ).
cnf(c_2120,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1042,c_12]) ).
cnf(c_2121,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_11,c_2120]) ).
cnf(c_2122,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_11,c_2121]) ).
cnf(c_2123,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_2122]) ).
cnf(c_2124,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1042,c_2123]) ).
cnf(c_1058,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_2124]) ).
cnf(c_1060,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_1058,c_563]) ).
cnf(c_2125,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_1060]) ).
cnf(c_2126,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_2125]) ).
cnf(c_1265,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_2126]) ).
cnf(c_2127,plain,
join(A,complement(composition(A,top))) = join(complement(composition(A,complement(one))),A),
inference(paramod,[status(thm)],[c_1265,c_1031]) ).
cnf(c_2128,plain,
join(A,complement(composition(A,top))) = join(A,complement(composition(A,complement(one)))),
inference(paramod,[status(thm)],[c_1,c_2127]) ).
cnf(c_1291,plain,
join(A,complement(composition(A,complement(one)))) = join(A,complement(composition(A,top))),
inference(copy,[status(thm)],[c_2128]) ).
cnf(c_2129,plain,
join(complement(sk1),composition(sk1,complement(one))) = complement(composition(sk1,one)),
inference(paramod,[status(thm)],[c_9,c_827]) ).
cnf(c_1417,plain,
join(complement(sk1),composition(sk1,complement(one))) = complement(sk1),
inference(paramod,[status(thm)],[c_9,c_2129]) ).
cnf(c_2130,plain,
join(complement(composition(sk1,complement(one))),complement(complement(sk1))) = complement(composition(sk1,complement(one))),
inference(paramod,[status(thm)],[c_1417,c_759]) ).
cnf(c_2131,plain,
join(complement(composition(sk1,complement(one))),sk1) = complement(composition(sk1,complement(one))),
inference(paramod,[status(thm)],[c_88,c_2130]) ).
cnf(c_2132,plain,
join(sk1,complement(composition(sk1,complement(one)))) = complement(composition(sk1,complement(one))),
inference(paramod,[status(thm)],[c_1,c_2131]) ).
cnf(c_2133,plain,
join(sk1,complement(composition(sk1,top))) = complement(composition(sk1,complement(one))),
inference(paramod,[status(thm)],[c_1291,c_2132]) ).
cnf(c_1427,plain,
complement(composition(sk1,complement(one))) = join(sk1,complement(composition(sk1,top))),
inference(copy,[status(thm)],[c_2133]) ).
cnf(c_2134,plain,
join(complement(complement(one)),composition(converse(sk1),join(sk1,complement(composition(sk1,top))))) = complement(complement(one)),
inference(paramod,[status(thm)],[c_1427,c_15]) ).
cnf(c_2135,plain,
join(one,composition(converse(sk1),join(sk1,complement(composition(sk1,top))))) = complement(complement(one)),
inference(paramod,[status(thm)],[c_88,c_2134]) ).
cnf(c_1432,plain,
join(one,composition(converse(sk1),join(sk1,complement(composition(sk1,top))))) = one,
inference(paramod,[status(thm)],[c_88,c_2135]) ).
cnf(c_2136,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_220]) ).
cnf(c_1683,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2136]) ).
cnf(c_2137,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_11,c_1683]) ).
cnf(c_2005,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_11,c_2137]) ).
cnf(c_2138,plain,
join(one,join(composition(converse(sk1),sk1),composition(converse(sk1),complement(composition(sk1,top))))) = one,
inference(paramod,[status(thm)],[c_2005,c_1432]) ).
cnf(c_2139,plain,
join(one,join(composition(converse(sk1),sk1),zero)) = one,
inference(paramod,[status(thm)],[c_179,c_2138]) ).
cnf(c_2140,plain,
join(one,join(zero,composition(converse(sk1),sk1))) = one,
inference(paramod,[status(thm)],[c_1,c_2139]) ).
cnf(c_2039,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(paramod,[status(thm)],[c_165,c_2140]) ).
cnf(c_2040,plain,
$false,
inference(resolve,[status(thm)],[c_2039,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL042-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:40:02 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1332764 was started by sandbox on n005,
% 0.09/0.38 % Sat Sep 26 05:40:02 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 6.88/1.35
% 6.88/1.35 % SZS status Unsatisfiable for theBenchmark
% 6.88/1.35
% 6.88/1.35 % Proof 1 at 0.72 (+ 0.20) seconds.
% 6.88/1.35 % Length of proof is 88.
% 6.88/1.35 % Level of proof is 22.
% 6.88/1.35 % Maximum clause weight is 93.000.
% 6.88/1.35 % Given clauses 182.
% 6.88/1.35
% 6.88/1.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------