%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL004-2 : 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 : 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 08:24:43 AM UTC 2026
% Result : Unsatisfiable 0.95s 0.69s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 117 unt; 0 def)
% Number of atoms : 117 ( 116 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 : 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_444,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_444]) ).
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_445,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_446,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_445]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_446]) ).
fof(goals_17,axiom,
converse(complement(sk1)) != complement(converse(sk1)),
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
converse(complement(sk1)) != complement(converse(sk1)),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_29,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_30,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_447,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_33,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_447]) ).
cnf(c_448,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_40,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_448]) ).
cnf(c_449,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_450,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_449]) ).
cnf(c_41,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_450]) ).
cnf(c_451,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_43,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_451]) ).
cnf(c_452,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_33]) ).
cnf(c_59,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_452]) ).
cnf(c_453,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_59,c_9]) ).
cnf(c_61,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_453]) ).
cnf(c_65,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_59,c_15]) ).
cnf(c_66,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_67,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_66,c_65]) ).
cnf(c_68,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_67,c_41]) ).
cnf(c_454,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_30]) ).
cnf(c_455,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_454]) ).
cnf(c_456,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_455]) ).
cnf(c_71,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_456]) ).
cnf(c_72,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_71,c_40]) ).
cnf(c_73,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_72,c_71]) ).
cnf(c_74,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_72,c_68]) ).
cnf(c_75,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_74,c_73]) ).
cnf(c_457,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_72,c_5]) ).
cnf(c_90,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_72,c_457]) ).
cnf(c_458,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_72,c_29]) ).
cnf(c_92,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_72,c_458]) ).
cnf(c_459,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_75,c_17]) ).
cnf(c_460,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_459]) ).
cnf(c_97,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_460]) ).
cnf(c_461,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_75,c_72]) ).
cnf(c_462,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_72,c_461]) ).
cnf(c_98,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_462]) ).
cnf(c_463,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_97,c_1]) ).
cnf(c_112,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_463]) ).
cnf(c_464,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_97,c_12]) ).
cnf(c_114,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_464]) ).
cnf(c_465,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_98,c_3]) ).
cnf(c_116,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_465]) ).
cnf(c_138,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_114]) ).
cnf(c_141,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_138,c_112]) ).
cnf(c_143,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_141,c_43]) ).
cnf(c_164,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_143]) ).
cnf(c_466,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_90,c_116]) ).
cnf(c_467,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_466]) ).
cnf(c_220,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_90,c_467]) ).
cnf(c_468,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_92,c_90]) ).
cnf(c_469,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_72,c_468]) ).
cnf(c_470,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_72,c_469]) ).
cnf(c_471,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_470]) ).
cnf(c_472,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_471]) ).
cnf(c_473,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_220,c_472]) ).
cnf(c_239,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_72,c_473]) ).
cnf(c_474,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_92,c_92]) ).
cnf(c_475,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_72,c_474]) ).
cnf(c_476,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_72,c_475]) ).
cnf(c_477,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_476]) ).
cnf(c_478,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_477]) ).
cnf(c_479,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_239,c_478]) ).
cnf(c_480,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_116,c_479]) ).
cnf(c_241,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_72,c_480]) ).
cnf(c_481,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_143,c_241]) ).
cnf(c_482,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_481]) ).
cnf(c_483,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_482]) ).
cnf(c_484,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_74,c_483]) ).
cnf(c_485,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_484]) ).
cnf(c_372,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_485]) ).
cnf(c_486,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_164,c_241]) ).
cnf(c_487,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_486]) ).
cnf(c_488,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_487]) ).
cnf(c_489,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_74,c_488]) ).
cnf(c_490,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_489]) ).
cnf(c_376,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_490]) ).
cnf(c_491,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_372,c_12]) ).
cnf(c_492,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_491]) ).
cnf(c_493,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_492]) ).
cnf(c_494,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_493]) ).
cnf(c_495,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_376,c_494]) ).
cnf(c_422,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_495]) ).
cnf(c_442,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_422,c_11]) ).
cnf(c_443,plain,
$false,
inference(resolve,[status(thm)],[c_442,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL004-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n016.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 05:29:59 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 68900 was started by sandbox2 on n016,
% 0.15/0.43 % Sat Sep 26 05:29:59 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.95/0.69
% 0.95/0.69 % SZS status Unsatisfiable for theBenchmark
% 0.95/0.69
% 0.95/0.69 % Proof 1 at 0.19 (+ 0.05) seconds.
% 0.95/0.69 % Length of proof is 53.
% 0.95/0.69 % Level of proof is 18.
% 0.95/0.69 % Maximum clause weight is 30.000.
% 0.95/0.69 % Given clauses 111.
% 0.95/0.69
% 0.95/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------