%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL018-1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:24:51 AM UTC 2026
% Result : Unsatisfiable 0.45s 0.61s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 14
% Syntax : Number of formulae : 126 ( 126 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 117 ( 10 sgn 22 !; 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_275,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_275]) ).
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_276,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_277,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_276]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_277]) ).
fof(goals_14,axiom,
composition(sk1,top) = sk1,
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
composition(sk1,top) = sk1,
inference(clausify,[status(thm)],[goals_14]) ).
fof(goals_15,axiom,
composition(complement(sk1),top) != complement(sk1),
file('theBenchmark.p',goals_15) ).
cnf(c_21,plain,
composition(complement(sk1),top) != complement(sk1),
inference(clausify,[status(thm)],[goals_15]) ).
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_278,plain,
converse(A) = join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_27,plain,
join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))) = converse(A),
inference(copy,[status(thm)],[c_278]) ).
cnf(c_279,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_28,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_280,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_35,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_280]) ).
cnf(c_281,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_282,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_281]) ).
cnf(c_36,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_282]) ).
cnf(c_283,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_37,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_283]) ).
cnf(c_284,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_41,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_284]) ).
cnf(c_285,plain,
join(complement(top),composition(converse(sk1),complement(sk1))) = complement(top),
inference(paramod,[status(thm)],[c_20,c_15]) ).
cnf(c_286,plain,
join(zero,composition(converse(sk1),complement(sk1))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_285]) ).
cnf(c_45,plain,
join(zero,composition(converse(sk1),complement(sk1))) = zero,
inference(paramod,[status(thm)],[c_19,c_286]) ).
cnf(c_287,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_28]) ).
cnf(c_57,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_287]) ).
cnf(c_288,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_57,c_9]) ).
cnf(c_59,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_288]) ).
cnf(c_63,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_57,c_15]) ).
cnf(c_64,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_59,c_57]) ).
cnf(c_65,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_64,c_63]) ).
cnf(c_66,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_65,c_36]) ).
cnf(c_289,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_290,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_289]) ).
cnf(c_291,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_290]) ).
cnf(c_69,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_291]) ).
cnf(c_70,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_69,c_35]) ).
cnf(c_71,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_70,c_69]) ).
cnf(c_72,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_70,c_66]) ).
cnf(c_73,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_72,c_71]) ).
cnf(c_75,plain,
composition(converse(sk1),complement(sk1)) = zero,
inference(paramod,[status(thm)],[c_72,c_45]) ).
cnf(c_76,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_72,c_41]) ).
cnf(c_292,plain,
join(converse(complement(top)),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_293,plain,
join(converse(zero),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_19,c_292]) ).
cnf(c_294,plain,
join(converse(zero),converse(complement(join(complement(A),complement(A))))) = converse(A),
inference(paramod,[status(thm)],[c_70,c_293]) ).
cnf(c_295,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(paramod,[status(thm)],[c_65,c_294]) ).
cnf(c_78,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_70,c_295]) ).
cnf(c_296,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_72,c_1]) ).
cnf(c_81,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_296]) ).
cnf(c_83,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_72,c_17]) ).
cnf(c_297,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_70,c_24]) ).
cnf(c_91,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_70,c_297]) ).
cnf(c_298,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_73,c_17]) ).
cnf(c_299,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_298]) ).
cnf(c_96,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_299]) ).
cnf(c_300,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_96,c_1]) ).
cnf(c_111,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_300]) ).
cnf(c_301,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_96,c_12]) ).
cnf(c_113,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_301]) ).
cnf(c_302,plain,
converse(zero) = composition(converse(complement(sk1)),converse(converse(sk1))),
inference(paramod,[status(thm)],[c_75,c_13]) ).
cnf(c_303,plain,
converse(zero) = composition(converse(complement(sk1)),sk1),
inference(paramod,[status(thm)],[c_11,c_302]) ).
cnf(c_121,plain,
composition(converse(complement(sk1)),sk1) = converse(zero),
inference(copy,[status(thm)],[c_303]) ).
cnf(c_304,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_78]) ).
cnf(c_132,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_11,c_304]) ).
cnf(c_305,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_132,c_81]) ).
cnf(c_138,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_305]) ).
cnf(c_140,plain,
composition(converse(complement(sk1)),sk1) = zero,
inference(paramod,[status(thm)],[c_138,c_121]) ).
cnf(c_145,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_113]) ).
cnf(c_148,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_145,c_111]) ).
cnf(c_161,plain,
join(sk1,composition(complement(sk1),top)) = composition(top,top),
inference(paramod,[status(thm)],[c_20,c_37]) ).
cnf(c_306,plain,
join(complement(sk1),composition(converse(converse(complement(sk1))),complement(zero))) = complement(sk1),
inference(paramod,[status(thm)],[c_140,c_15]) ).
cnf(c_307,plain,
join(complement(sk1),composition(complement(sk1),complement(zero))) = complement(sk1),
inference(paramod,[status(thm)],[c_11,c_306]) ).
cnf(c_168,plain,
join(complement(sk1),composition(complement(sk1),top)) = complement(sk1),
inference(paramod,[status(thm)],[c_83,c_307]) ).
cnf(c_196,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_148,c_76]) ).
cnf(c_308,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_196,c_10]) ).
cnf(c_309,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_111,c_308]) ).
cnf(c_310,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_196,c_309]) ).
cnf(c_311,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_72,c_310]) ).
cnf(c_199,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_311]) ).
cnf(c_312,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_199,c_64]) ).
cnf(c_216,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_312]) ).
cnf(c_313,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_216,c_17]) ).
cnf(c_314,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_1,c_313]) ).
cnf(c_226,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_72,c_314]) ).
cnf(c_227,plain,
join(sk1,composition(complement(sk1),top)) = top,
inference(paramod,[status(thm)],[c_226,c_161]) ).
cnf(c_315,plain,
join(complement(top),complement(join(composition(complement(sk1),top),complement(sk1)))) = complement(composition(complement(sk1),top)),
inference(paramod,[status(thm)],[c_227,c_91]) ).
cnf(c_316,plain,
join(zero,complement(join(composition(complement(sk1),top),complement(sk1)))) = complement(composition(complement(sk1),top)),
inference(paramod,[status(thm)],[c_19,c_315]) ).
cnf(c_317,plain,
join(zero,complement(join(complement(sk1),composition(complement(sk1),top)))) = complement(composition(complement(sk1),top)),
inference(paramod,[status(thm)],[c_1,c_316]) ).
cnf(c_318,plain,
join(zero,complement(complement(sk1))) = complement(composition(complement(sk1),top)),
inference(paramod,[status(thm)],[c_168,c_317]) ).
cnf(c_319,plain,
join(zero,sk1) = complement(composition(complement(sk1),top)),
inference(paramod,[status(thm)],[c_70,c_318]) ).
cnf(c_320,plain,
join(sk1,zero) = complement(composition(complement(sk1),top)),
inference(paramod,[status(thm)],[c_1,c_319]) ).
cnf(c_321,plain,
sk1 = complement(composition(complement(sk1),top)),
inference(paramod,[status(thm)],[c_81,c_320]) ).
cnf(c_265,plain,
complement(composition(complement(sk1),top)) = sk1,
inference(copy,[status(thm)],[c_321]) ).
cnf(c_322,plain,
complement(sk1) = composition(complement(sk1),top),
inference(paramod,[status(thm)],[c_265,c_70]) ).
cnf(c_273,plain,
composition(complement(sk1),top) = complement(sk1),
inference(copy,[status(thm)],[c_322]) ).
cnf(c_274,plain,
$false,
inference(resolve,[status(thm)],[c_273,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL018-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42 % Computer : n020.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Sat Sep 26 05:30:04 UTC 2026
% 0.09/0.42 % CPUTime :
% 0.09/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.43 % Process 725192 was started by sandbox on n020,
% 0.09/0.43 % Sat Sep 26 05:30:04 2026
% 0.09/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.43
% 0.09/0.43 % From the command line: assign(max_seconds, 300).
% 0.45/0.61
% 0.45/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.45/0.61
% 0.45/0.61 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.45/0.61 % Length of proof is 64.
% 0.45/0.61 % Level of proof is 20.
% 0.45/0.61 % Maximum clause weight is 30.000.
% 0.45/0.61 % Given clauses 81.
% 0.45/0.61
% 0.45/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
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