%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL023-1 : 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 : n017.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 08:24:52 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.75s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 8
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 4 sgn 14 !; 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_187,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_187]) ).
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_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]) ).
cnf(c_11,plain,
join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
inference(copy,[status(thm)],[c_10]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_19,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_20,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_19]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_21,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_188,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_21]) ).
cnf(c_189,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_20,c_188]) ).
cnf(c_22,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_189]) ).
fof(goals_14,axiom,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)),
file('theBenchmark.p',goals_14) ).
cnf(c_23,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_190,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)),
inference(paramod,[status(thm)],[c_6,c_23]) ).
cnf(c_191,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)),
inference(paramod,[status(thm)],[c_6,c_190]) ).
cnf(c_192,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(sk1,complement(join(complement(sk2),complement(sk3))))) != composition(sk1,meet(sk2,sk3)),
inference(paramod,[status(thm)],[c_6,c_191]) ).
cnf(c_193,plain,
join(composition(sk1,complement(join(complement(sk2),complement(sk3)))),composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3))))) != composition(sk1,meet(sk2,sk3)),
inference(paramod,[status(thm)],[c_1,c_192]) ).
cnf(c_194,plain,
composition(join(sk1,complement(join(complement(sk1),complement(converse(sk2))))),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,meet(sk2,sk3)),
inference(paramod,[status(thm)],[c_11,c_193]) ).
cnf(c_24,plain,
composition(join(sk1,complement(join(complement(sk1),complement(converse(sk2))))),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(paramod,[status(thm)],[c_6,c_194]) ).
cnf(c_27,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_28,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_195,plain,
join(join(A,complement(join(complement(B),C))),complement(join(complement(B),complement(C)))) = join(A,B),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_30,plain,
join(complement(join(complement(A),complement(B))),join(C,complement(join(complement(A),B)))) = join(C,A),
inference(paramod,[status(thm)],[c_1,c_195]) ).
cnf(c_196,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_20,c_5]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_22,c_196]) ).
cnf(c_60,plain,
join(top,zero) = top,
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_197,plain,
join(top,A) = join(top,join(zero,A)),
inference(paramod,[status(thm)],[c_60,c_3]) ).
cnf(c_67,plain,
join(top,join(zero,A)) = join(top,A),
inference(copy,[status(thm)],[c_197]) ).
cnf(c_198,plain,
join(top,top) = join(top,complement(zero)),
inference(paramod,[status(thm)],[c_20,c_67]) ).
cnf(c_72,plain,
join(top,complement(zero)) = join(top,top),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_199,plain,
join(complement(join(top,top)),complement(join(complement(zero),complement(top)))) = zero,
inference(paramod,[status(thm)],[c_72,c_27]) ).
cnf(c_200,plain,
join(complement(join(top,top)),complement(join(complement(zero),zero))) = zero,
inference(paramod,[status(thm)],[c_22,c_199]) ).
cnf(c_201,plain,
join(complement(join(top,top)),complement(join(zero,complement(zero)))) = zero,
inference(paramod,[status(thm)],[c_1,c_200]) ).
cnf(c_202,plain,
join(complement(join(top,top)),complement(top)) = zero,
inference(paramod,[status(thm)],[c_20,c_201]) ).
cnf(c_203,plain,
join(complement(join(top,top)),zero) = zero,
inference(paramod,[status(thm)],[c_22,c_202]) ).
cnf(c_88,plain,
join(zero,complement(join(top,top))) = zero,
inference(paramod,[status(thm)],[c_1,c_203]) ).
cnf(c_204,plain,
join(zero,A) = join(zero,join(complement(join(top,top)),A)),
inference(paramod,[status(thm)],[c_88,c_3]) ).
cnf(c_90,plain,
join(zero,join(complement(join(top,top)),A)) = join(zero,A),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_205,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_88,c_67]) ).
cnf(c_206,plain,
top = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_60,c_205]) ).
cnf(c_92,plain,
join(top,complement(join(top,top))) = top,
inference(copy,[status(thm)],[c_206]) ).
cnf(c_207,plain,
join(complement(top),complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_92,c_27]) ).
cnf(c_208,plain,
join(zero,complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_22,c_207]) ).
cnf(c_209,plain,
join(zero,complement(join(complement(join(top,top)),zero))) = join(top,top),
inference(paramod,[status(thm)],[c_22,c_208]) ).
cnf(c_210,plain,
join(zero,complement(join(zero,complement(join(top,top))))) = join(top,top),
inference(paramod,[status(thm)],[c_1,c_209]) ).
cnf(c_211,plain,
join(zero,complement(zero)) = join(top,top),
inference(paramod,[status(thm)],[c_88,c_210]) ).
cnf(c_212,plain,
top = join(top,top),
inference(paramod,[status(thm)],[c_20,c_211]) ).
cnf(c_96,plain,
join(top,top) = top,
inference(copy,[status(thm)],[c_212]) ).
cnf(c_213,plain,
join(zero,join(complement(top),A)) = join(zero,A),
inference(paramod,[status(thm)],[c_96,c_90]) ).
cnf(c_98,plain,
join(zero,join(zero,A)) = join(zero,A),
inference(paramod,[status(thm)],[c_22,c_213]) ).
cnf(c_214,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_20,c_28]) ).
cnf(c_215,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_214]) ).
cnf(c_216,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_22,c_215]) ).
cnf(c_113,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_216]) ).
cnf(c_119,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_113,c_55]) ).
cnf(c_120,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_119,c_113]) ).
cnf(c_217,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_119,c_5]) ).
cnf(c_122,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_119,c_217]) ).
cnf(c_218,plain,
join(zero,complement(A)) = join(zero,complement(join(A,A))),
inference(paramod,[status(thm)],[c_120,c_98]) ).
cnf(c_136,plain,
join(zero,complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_120,c_218]) ).
cnf(c_219,plain,
join(zero,join(zero,complement(join(A,A)))) = complement(A),
inference(paramod,[status(thm)],[c_120,c_98]) ).
cnf(c_220,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_136,c_219]) ).
cnf(c_137,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_136,c_220]) ).
cnf(c_221,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_137,c_119]) ).
cnf(c_222,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_119,c_221]) ).
cnf(c_170,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_222]) ).
cnf(c_223,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_170,c_30]) ).
cnf(c_224,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_1,c_223]) ).
cnf(c_225,plain,
complement(complement(A)) = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_122,c_224]) ).
cnf(c_226,plain,
A = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_119,c_225]) ).
cnf(c_227,plain,
A = join(A,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_1,c_226]) ).
cnf(c_183,plain,
join(A,complement(join(complement(A),B))) = A,
inference(copy,[status(thm)],[c_227]) ).
cnf(c_228,plain,
composition(sk1,complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(paramod,[status(thm)],[c_183,c_24]) ).
cnf(c_186,plain,
$false,
inference(copy,[status(thm)],[c_228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL023-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.65 % Computer : n017.cluster.edu
% 0.18/0.65 % Model : x86_64 x86_64
% 0.18/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.65 % Memory : 8046.5625MB
% 0.18/0.65 % OS : Linux 6.8.0-71-generic
% 0.18/0.65 % CPULimit : 300
% 0.18/0.65 % WCLimit : 300
% 0.18/0.65 % DateTime : Sat Sep 26 05:26:49 UTC 2026
% 0.18/0.66 % CPUTime :
% 0.18/0.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.66 % Process 4127053 was started by sandbox2 on n017,
% 0.18/0.66 % Sat Sep 26 05:26:49 2026
% 0.18/0.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.67
% 0.18/0.67 % From the command line: assign(max_seconds, 300).
% 0.22/0.75
% 0.22/0.75 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.75
% 0.22/0.75 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.22/0.75 % Length of proof is 35.
% 0.22/0.75 % Level of proof is 14.
% 0.22/0.75 % Maximum clause weight is 60.000.
% 0.22/0.75 % Given clauses 43.
% 0.22/0.75
% 0.22/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------