%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL023-2 : 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 : 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 08:24:52 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : CNFRefutation 0.09s
% 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_260,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_260]) ).
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_261,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_21]) ).
cnf(c_262,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_20,c_261]) ).
cnf(c_22,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_262]) ).
fof(goals_17,axiom,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)),
file('theBenchmark.p',goals_17) ).
cnf(c_29,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_17]) ).
cnf(c_263,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_29]) ).
cnf(c_264,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_263]) ).
cnf(c_265,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_264]) ).
cnf(c_266,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_265]) ).
cnf(c_267,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_266]) ).
cnf(c_30,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_267]) ).
cnf(c_33,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_34,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_268,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_36,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_268]) ).
cnf(c_269,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_20,c_5]) ).
cnf(c_61,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_22,c_269]) ).
cnf(c_66,plain,
join(top,zero) = top,
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_270,plain,
join(top,A) = join(top,join(zero,A)),
inference(paramod,[status(thm)],[c_66,c_3]) ).
cnf(c_103,plain,
join(top,join(zero,A)) = join(top,A),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,plain,
join(top,top) = join(top,complement(zero)),
inference(paramod,[status(thm)],[c_20,c_103]) ).
cnf(c_108,plain,
join(top,complement(zero)) = join(top,top),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_272,plain,
join(complement(join(top,top)),complement(join(complement(zero),complement(top)))) = zero,
inference(paramod,[status(thm)],[c_108,c_33]) ).
cnf(c_273,plain,
join(complement(join(top,top)),complement(join(complement(zero),zero))) = zero,
inference(paramod,[status(thm)],[c_22,c_272]) ).
cnf(c_274,plain,
join(complement(join(top,top)),complement(join(zero,complement(zero)))) = zero,
inference(paramod,[status(thm)],[c_1,c_273]) ).
cnf(c_275,plain,
join(complement(join(top,top)),complement(top)) = zero,
inference(paramod,[status(thm)],[c_20,c_274]) ).
cnf(c_276,plain,
join(complement(join(top,top)),zero) = zero,
inference(paramod,[status(thm)],[c_22,c_275]) ).
cnf(c_124,plain,
join(zero,complement(join(top,top))) = zero,
inference(paramod,[status(thm)],[c_1,c_276]) ).
cnf(c_277,plain,
join(zero,A) = join(zero,join(complement(join(top,top)),A)),
inference(paramod,[status(thm)],[c_124,c_3]) ).
cnf(c_126,plain,
join(zero,join(complement(join(top,top)),A)) = join(zero,A),
inference(copy,[status(thm)],[c_277]) ).
cnf(c_278,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_124,c_103]) ).
cnf(c_279,plain,
top = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_66,c_278]) ).
cnf(c_128,plain,
join(top,complement(join(top,top))) = top,
inference(copy,[status(thm)],[c_279]) ).
cnf(c_280,plain,
join(complement(top),complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_128,c_33]) ).
cnf(c_281,plain,
join(zero,complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_22,c_280]) ).
cnf(c_282,plain,
join(zero,complement(join(complement(join(top,top)),zero))) = join(top,top),
inference(paramod,[status(thm)],[c_22,c_281]) ).
cnf(c_283,plain,
join(zero,complement(join(zero,complement(join(top,top))))) = join(top,top),
inference(paramod,[status(thm)],[c_1,c_282]) ).
cnf(c_284,plain,
join(zero,complement(zero)) = join(top,top),
inference(paramod,[status(thm)],[c_124,c_283]) ).
cnf(c_285,plain,
top = join(top,top),
inference(paramod,[status(thm)],[c_20,c_284]) ).
cnf(c_132,plain,
join(top,top) = top,
inference(copy,[status(thm)],[c_285]) ).
cnf(c_286,plain,
join(zero,join(complement(top),A)) = join(zero,A),
inference(paramod,[status(thm)],[c_132,c_126]) ).
cnf(c_134,plain,
join(zero,join(zero,A)) = join(zero,A),
inference(paramod,[status(thm)],[c_22,c_286]) ).
cnf(c_287,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_20,c_34]) ).
cnf(c_288,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_287]) ).
cnf(c_289,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_22,c_288]) ).
cnf(c_149,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_289]) ).
cnf(c_155,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_149,c_61]) ).
cnf(c_156,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_155,c_149]) ).
cnf(c_290,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_155,c_5]) ).
cnf(c_159,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_155,c_290]) ).
cnf(c_291,plain,
join(zero,complement(A)) = join(zero,complement(join(A,A))),
inference(paramod,[status(thm)],[c_156,c_134]) ).
cnf(c_187,plain,
join(zero,complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_156,c_291]) ).
cnf(c_292,plain,
join(zero,join(zero,complement(join(A,A)))) = complement(A),
inference(paramod,[status(thm)],[c_156,c_134]) ).
cnf(c_293,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_187,c_292]) ).
cnf(c_188,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_187,c_293]) ).
cnf(c_294,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_188,c_155]) ).
cnf(c_295,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_155,c_294]) ).
cnf(c_237,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_295]) ).
cnf(c_296,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_237,c_36]) ).
cnf(c_297,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_296]) ).
cnf(c_298,plain,
complement(complement(A)) = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_159,c_297]) ).
cnf(c_299,plain,
A = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_155,c_298]) ).
cnf(c_300,plain,
A = join(A,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_1,c_299]) ).
cnf(c_255,plain,
join(A,complement(join(complement(A),B))) = A,
inference(copy,[status(thm)],[c_300]) ).
cnf(c_301,plain,
composition(sk1,complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(paramod,[status(thm)],[c_255,c_30]) ).
cnf(c_259,plain,
$false,
inference(copy,[status(thm)],[c_301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:36:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 88173 was started by sandbox on n016,
% 0.09/0.36 % Sat Sep 26 05:36:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.45
% 0.09/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.45
% 0.09/0.45 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.09/0.45 % Length of proof is 35.
% 0.09/0.45 % Level of proof is 14.
% 0.09/0.45 % Maximum clause weight is 60.000.
% 0.09/0.45 % Given clauses 46.
% 0.09/0.45
% 0.09/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------