%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL043-2 : 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 : n009.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 51.43s 7.87s
% Output : CNFRefutation 51.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 15
% Syntax : Number of formulae : 163 ( 163 unt; 0 def)
% Number of atoms : 163 ( 162 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 : 11 ( 3 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 : 202 ( 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_8411,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_8411]) ).
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_8412,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_8413,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_8412]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_8413]) ).
fof(modular_law_2_16,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(composition(VAR_0,VAR_1),VAR_2),meet(composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),VAR_1),VAR_2)) = meet(composition(meet(VAR_0,composition(VAR_2,converse(VAR_1))),VAR_1),VAR_2),
file('theBenchmark.p',modular_law_2_16) ).
cnf(c_24,plain,
join(meet(composition(A,B),C),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(clausify,[status(thm)],[modular_law_2_16]) ).
cnf(c_8414,plain,
join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_6,c_24]) ).
cnf(c_8415,plain,
join(complement(join(complement(composition(A,B)),complement(C))),meet(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_6,c_8414]) ).
cnf(c_8416,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)),complement(C)))) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_6,c_8415]) ).
cnf(c_8417,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = meet(composition(meet(A,composition(C,converse(B))),B),C),
inference(paramod,[status(thm)],[c_1,c_8416]) ).
cnf(c_8418,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = meet(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B),C),
inference(paramod,[status(thm)],[c_6,c_8417]) ).
cnf(c_8419,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = complement(join(complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)),complement(C))),
inference(paramod,[status(thm)],[c_6,c_8418]) ).
cnf(c_25,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)))),
inference(paramod,[status(thm)],[c_1,c_8419]) ).
fof(goals_17,axiom,
join(composition(sk1,converse(sk2)),sk3) = sk3,
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(composition(sk1,converse(sk2)),sk3) = sk3,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
join(sk3,composition(sk1,converse(sk2))) = sk3,
inference(paramod,[status(thm)],[c_1,c_26]) ).
fof(goals_18,axiom,
join(composition(complement(sk3),sk2),complement(sk1)) != complement(sk1),
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
join(composition(complement(sk3),sk2),complement(sk1)) != complement(sk1),
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_29,plain,
join(complement(sk1),composition(complement(sk3),sk2)) != complement(sk1),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_8420,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_8420]) ).
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_8421,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_8421]) ).
cnf(c_8422,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_8422]) ).
cnf(c_8423,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_8423]) ).
cnf(c_8424,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_8425,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_8424]) ).
cnf(c_53,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_8425]) ).
cnf(c_8426,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_8426]) ).
cnf(c_8427,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_8427]) ).
cnf(c_8428,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_118,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_8428]) ).
cnf(c_8429,plain,
join(A,top) = join(B,join(A,complement(B))),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_120,plain,
join(A,join(B,complement(A))) = join(B,top),
inference(copy,[status(thm)],[c_8429]) ).
cnf(c_8430,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_40]) ).
cnf(c_131,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_8430]) ).
cnf(c_8431,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_131,c_9]) ).
cnf(c_140,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_8431]) ).
cnf(c_144,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_131,c_15]) ).
cnf(c_162,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_140,c_131]) ).
cnf(c_167,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_162,c_144]) ).
cnf(c_168,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_167,c_53]) ).
cnf(c_8432,plain,
converse(A) = join(converse(zero),converse(complement(complement(A)))),
inference(paramod,[status(thm)],[c_168,c_12]) ).
cnf(c_185,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(copy,[status(thm)],[c_8432]) ).
cnf(c_8433,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_33]) ).
cnf(c_8434,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_8433]) ).
cnf(c_8435,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_8434]) ).
cnf(c_210,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_8435]) ).
cnf(c_218,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_210,c_52]) ).
cnf(c_229,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_218,c_185]) ).
cnf(c_231,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_218,c_168]) ).
cnf(c_244,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_231,c_58]) ).
cnf(c_8436,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_218,c_5]) ).
cnf(c_246,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_218,c_8436]) ).
cnf(c_248,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_19,c_218]) ).
cnf(c_8437,plain,
join(complement(join(complement(composition(complement(A),B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(A,complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(complement(complement(A)),complement(composition(C,converse(B))))),B)))),
inference(paramod,[status(thm)],[c_218,c_25]) ).
cnf(c_255,plain,
join(complement(join(complement(composition(complement(A),B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(A,complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(A,complement(composition(C,converse(B))))),B)))),
inference(paramod,[status(thm)],[c_218,c_8437]) ).
cnf(c_8438,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_218,c_167]) ).
cnf(c_8439,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_218,c_8438]) ).
cnf(c_257,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_218,c_8439]) ).
cnf(c_8440,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_231,c_1]) ).
cnf(c_268,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_8440]) ).
cnf(c_8441,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_257,c_3]) ).
cnf(c_269,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_8441]) ).
cnf(c_8442,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_257,c_34]) ).
cnf(c_8443,plain,
complement(complement(A)) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_246,c_8442]) ).
cnf(c_8444,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_218,c_8443]) ).
cnf(c_291,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_8444]) ).
cnf(c_8445,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_257,c_34]) ).
cnf(c_8446,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_8445]) ).
cnf(c_8447,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_291,c_8446]) ).
cnf(c_292,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_8447]) ).
cnf(c_8448,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_229]) ).
cnf(c_309,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_11,c_8448]) ).
cnf(c_8449,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_309,c_268]) ).
cnf(c_314,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_8449]) ).
cnf(c_8450,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_269]) ).
cnf(c_372,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_8450]) ).
cnf(c_8451,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_55,c_269]) ).
cnf(c_373,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_55,c_8451]) ).
cnf(c_375,plain,
join(A,join(B,complement(A))) = top,
inference(paramod,[status(thm)],[c_372,c_120]) ).
cnf(c_8452,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_372,c_1]) ).
cnf(c_376,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_8452]) ).
cnf(c_408,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_373]) ).
cnf(c_413,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_408,c_376]) ).
cnf(c_432,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_413,c_244]) ).
cnf(c_448,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_218,c_375]) ).
cnf(c_8453,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_432,c_10]) ).
cnf(c_8454,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_376,c_8453]) ).
cnf(c_8455,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_432,c_8454]) ).
cnf(c_8456,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_231,c_8455]) ).
cnf(c_478,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_8456]) ).
cnf(c_8457,plain,
join(complement(composition(sk1,converse(sk2))),sk3) = top,
inference(paramod,[status(thm)],[c_27,c_448]) ).
cnf(c_483,plain,
join(sk3,complement(composition(sk1,converse(sk2)))) = top,
inference(paramod,[status(thm)],[c_1,c_8457]) ).
cnf(c_8458,plain,
converse(zero) = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_478,c_13]) ).
cnf(c_8459,plain,
zero = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_314,c_8458]) ).
cnf(c_489,plain,
composition(converse(complement(composition(top,top))),converse(A)) = zero,
inference(copy,[status(thm)],[c_8459]) ).
cnf(c_8460,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_478,c_162]) ).
cnf(c_491,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_8460]) ).
cnf(c_8461,plain,
composition(converse(zero),converse(A)) = zero,
inference(paramod,[status(thm)],[c_491,c_489]) ).
cnf(c_494,plain,
composition(zero,converse(A)) = zero,
inference(paramod,[status(thm)],[c_314,c_8461]) ).
cnf(c_515,plain,
composition(zero,A) = zero,
inference(paramod,[status(thm)],[c_11,c_494]) ).
cnf(c_529,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_292]) ).
cnf(c_8462,plain,
join(complement(join(complement(A),B)),B) = join(B,A),
inference(paramod,[status(thm)],[c_529,c_118]) ).
cnf(c_3996,plain,
join(A,complement(join(complement(B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_1,c_8462]) ).
cnf(c_4078,plain,
join(A,complement(join(A,complement(B)))) = join(A,B),
inference(paramod,[status(thm)],[c_1,c_3996]) ).
cnf(c_4744,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_218,c_4078]) ).
cnf(c_8463,plain,
join(complement(join(complement(composition(complement(sk3),sk2)),complement(sk1))),complement(join(complement(sk1),complement(composition(complement(top),sk2))))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_483,c_255]) ).
cnf(c_8464,plain,
join(complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))),complement(join(complement(sk1),complement(composition(complement(top),sk2))))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_1,c_8463]) ).
cnf(c_8465,plain,
join(complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))),complement(join(complement(sk1),complement(composition(zero,sk2))))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_19,c_8464]) ).
cnf(c_8466,plain,
join(complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))),complement(join(complement(sk1),complement(zero)))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_515,c_8465]) ).
cnf(c_8467,plain,
join(complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))),complement(join(complement(sk1),top))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_248,c_8466]) ).
cnf(c_8468,plain,
join(complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))),complement(join(top,complement(sk1)))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_1,c_8467]) ).
cnf(c_8469,plain,
join(complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))),complement(top)) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_376,c_8468]) ).
cnf(c_8470,plain,
join(complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))),zero) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_19,c_8469]) ).
cnf(c_8471,plain,
join(zero,complement(join(complement(sk1),complement(composition(complement(sk3),sk2))))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_1,c_8470]) ).
cnf(c_8472,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = complement(join(complement(sk1),complement(composition(complement(join(sk3,complement(composition(sk1,converse(sk2))))),sk2)))),
inference(paramod,[status(thm)],[c_231,c_8471]) ).
cnf(c_8473,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = complement(join(complement(sk1),complement(composition(complement(top),sk2)))),
inference(paramod,[status(thm)],[c_483,c_8472]) ).
cnf(c_8474,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = complement(join(complement(sk1),complement(composition(zero,sk2)))),
inference(paramod,[status(thm)],[c_19,c_8473]) ).
cnf(c_8475,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = complement(join(complement(sk1),complement(zero))),
inference(paramod,[status(thm)],[c_515,c_8474]) ).
cnf(c_8476,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = complement(join(complement(sk1),top)),
inference(paramod,[status(thm)],[c_248,c_8475]) ).
cnf(c_8477,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = complement(join(top,complement(sk1))),
inference(paramod,[status(thm)],[c_1,c_8476]) ).
cnf(c_8478,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = complement(top),
inference(paramod,[status(thm)],[c_376,c_8477]) ).
cnf(c_8367,plain,
complement(join(complement(sk1),complement(composition(complement(sk3),sk2)))) = zero,
inference(paramod,[status(thm)],[c_19,c_8478]) ).
cnf(c_8479,plain,
join(complement(sk1),zero) = join(complement(sk1),complement(complement(composition(complement(sk3),sk2)))),
inference(paramod,[status(thm)],[c_8367,c_4744]) ).
cnf(c_8480,plain,
join(zero,complement(sk1)) = join(complement(sk1),complement(complement(composition(complement(sk3),sk2)))),
inference(paramod,[status(thm)],[c_1,c_8479]) ).
cnf(c_8481,plain,
complement(sk1) = join(complement(sk1),complement(complement(composition(complement(sk3),sk2)))),
inference(paramod,[status(thm)],[c_231,c_8480]) ).
cnf(c_8482,plain,
complement(sk1) = join(complement(sk1),composition(complement(sk3),sk2)),
inference(paramod,[status(thm)],[c_218,c_8481]) ).
cnf(c_8409,plain,
join(complement(sk1),composition(complement(sk3),sk2)) = complement(sk1),
inference(copy,[status(thm)],[c_8482]) ).
cnf(c_8410,plain,
$false,
inference(resolve,[status(thm)],[c_8409,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL043-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n009.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 05:40:44 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3483082 was started by sandbox2 on n009,
% 0.19/0.45 % Sat Sep 26 05:40:44 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 51.43/7.87
% 51.43/7.87 % SZS status Unsatisfiable for theBenchmark
% 51.43/7.87
% 51.43/7.87 % Proof 1 at 6.31 (+ 1.05) seconds.
% 51.43/7.87 % Length of proof is 76.
% 51.43/7.87 % Level of proof is 18.
% 51.43/7.87 % Maximum clause weight is 42.000.
% 51.43/7.87 % Given clauses 455.
% 51.43/7.87
% 51.43/7.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------