%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL005-3 : 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 : n016.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 08:24:45 AM UTC 2026
% Result : Unsatisfiable 0.97s 0.70s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 12
% Syntax : Number of formulae : 123 ( 123 unt; 0 def)
% Number of atoms : 123 ( 122 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 156 ( 7 sgn 19 !; 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_475,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_475]) ).
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(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_476,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_477,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_476]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_477]) ).
fof(goals_17,axiom,
converse(meet(sk1,sk2)) != meet(converse(sk1),converse(sk2)),
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
converse(meet(sk1,sk2)) != meet(converse(sk1),converse(sk2)),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_478,plain,
converse(complement(join(complement(sk1),complement(sk2)))) != meet(converse(sk1),converse(sk2)),
inference(paramod,[status(thm)],[c_6,c_26]) ).
cnf(c_27,plain,
converse(complement(join(complement(sk1),complement(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))),
inference(paramod,[status(thm)],[c_6,c_478]) ).
cnf(c_30,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_31,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_479,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_479]) ).
cnf(c_480,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_41,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_480]) ).
cnf(c_481,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_482,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_481]) ).
cnf(c_42,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_482]) ).
cnf(c_483,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_44,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_483]) ).
cnf(c_484,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_60,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_484]) ).
cnf(c_485,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_60,c_9]) ).
cnf(c_62,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_485]) ).
cnf(c_66,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_60,c_15]) ).
cnf(c_67,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_62,c_60]) ).
cnf(c_68,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_67,c_66]) ).
cnf(c_69,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_68,c_42]) ).
cnf(c_486,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_487,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_486]) ).
cnf(c_488,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_487]) ).
cnf(c_72,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_488]) ).
cnf(c_73,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_72,c_41]) ).
cnf(c_74,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_72]) ).
cnf(c_75,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_73,c_69]) ).
cnf(c_76,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_75,c_74]) ).
cnf(c_489,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_5]) ).
cnf(c_91,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_489]) ).
cnf(c_490,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_73,c_30]) ).
cnf(c_93,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_73,c_490]) ).
cnf(c_491,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_76,c_17]) ).
cnf(c_492,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_491]) ).
cnf(c_98,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_492]) ).
cnf(c_493,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_76,c_73]) ).
cnf(c_494,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_73,c_493]) ).
cnf(c_99,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_494]) ).
cnf(c_495,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_98,c_1]) ).
cnf(c_113,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_495]) ).
cnf(c_496,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_98,c_12]) ).
cnf(c_115,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_496]) ).
cnf(c_497,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_99,c_3]) ).
cnf(c_117,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_497]) ).
cnf(c_139,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_115]) ).
cnf(c_142,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_139,c_113]) ).
cnf(c_144,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_142,c_44]) ).
cnf(c_165,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_144]) ).
cnf(c_498,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_91,c_117]) ).
cnf(c_499,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_498]) ).
cnf(c_221,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_91,c_499]) ).
cnf(c_500,plain,
join(complement(complement(A)),complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_93,c_91]) ).
cnf(c_501,plain,
join(A,complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_73,c_500]) ).
cnf(c_502,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_73,c_501]) ).
cnf(c_503,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_1,c_502]) ).
cnf(c_504,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_3,c_503]) ).
cnf(c_505,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_221,c_504]) ).
cnf(c_240,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_73,c_505]) ).
cnf(c_506,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_93,c_93]) ).
cnf(c_507,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_73,c_506]) ).
cnf(c_508,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_73,c_507]) ).
cnf(c_509,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_508]) ).
cnf(c_510,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_509]) ).
cnf(c_511,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_240,c_510]) ).
cnf(c_512,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_117,c_511]) ).
cnf(c_242,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_73,c_512]) ).
cnf(c_513,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_144,c_242]) ).
cnf(c_514,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_513]) ).
cnf(c_515,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_514]) ).
cnf(c_516,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_75,c_515]) ).
cnf(c_517,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_516]) ).
cnf(c_373,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_517]) ).
cnf(c_518,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_165,c_242]) ).
cnf(c_519,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_518]) ).
cnf(c_520,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_519]) ).
cnf(c_521,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_75,c_520]) ).
cnf(c_522,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_521]) ).
cnf(c_377,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_522]) ).
cnf(c_523,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_373,c_12]) ).
cnf(c_524,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_523]) ).
cnf(c_525,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_524]) ).
cnf(c_526,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_525]) ).
cnf(c_527,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_377,c_526]) ).
cnf(c_423,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_527]) ).
cnf(c_443,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_423,c_11]) ).
cnf(c_528,plain,
complement(converse(join(complement(sk1),complement(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))),
inference(paramod,[status(thm)],[c_443,c_27]) ).
cnf(c_529,plain,
complement(join(converse(complement(sk1)),converse(complement(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))),
inference(paramod,[status(thm)],[c_12,c_528]) ).
cnf(c_530,plain,
complement(join(complement(converse(sk1)),converse(complement(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))),
inference(paramod,[status(thm)],[c_443,c_529]) ).
cnf(c_531,plain,
complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))),
inference(paramod,[status(thm)],[c_443,c_530]) ).
cnf(c_474,plain,
$false,
inference(copy,[status(thm)],[c_531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL005-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n016.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 05:29:46 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 68497 was started by sandbox2 on n016,
% 0.16/0.43 % Sat Sep 26 05:29:46 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.97/0.70
% 0.97/0.70 % SZS status Unsatisfiable for theBenchmark
% 0.97/0.70
% 0.97/0.70 % Proof 1 at 0.17 (+ 0.07) seconds.
% 0.97/0.70 % Length of proof is 54.
% 0.97/0.70 % Level of proof is 18.
% 0.97/0.70 % Maximum clause weight is 30.000.
% 0.97/0.70 % Given clauses 111.
% 0.97/0.70
% 0.97/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
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