%------------------------------------------------------------------------------
% 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/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 08:24:52 AM UTC 2026
% Result : Theorem 0.57s 0.47s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% 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 : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 91 ( 4 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_20,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_21,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_22,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_34,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_35,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_274,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_35]) ).
cnf(c_36,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_34,c_274]) ).
fof(nnf_17,plain,
? [X0,X1,X2] : composition(X0,meet(X1,X2)) != join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
composition(sK0,meet(sK1,sK2)) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_43,negated_conjecture,
composition(sK0,meet(sK1,sK2)) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_275,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(paramod,[status(thm)],[c_22,c_43]) ).
cnf(c_276,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(paramod,[status(thm)],[c_22,c_275]) ).
cnf(c_277,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2)))),composition(sK0,meet(sK1,sK2))),
inference(paramod,[status(thm)],[c_22,c_276]) ).
cnf(c_278,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2)))),composition(sK0,complement(join(complement(sK1),complement(sK2))))),
inference(paramod,[status(thm)],[c_22,c_277]) ).
cnf(c_279,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(sK0,complement(join(complement(sK1),complement(sK2)))),composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2))))),
inference(paramod,[status(thm)],[c_18,c_278]) ).
cnf(c_280,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != composition(join(sK0,complement(join(complement(sK0),complement(converse(sK1))))),complement(join(complement(sK1),complement(sK2)))),
inference(paramod,[status(thm)],[c_26,c_279]) ).
cnf(c_44,negated_conjecture,
composition(join(sK0,complement(join(complement(sK0),complement(converse(sK1))))),complement(join(complement(sK1),complement(sK2)))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(copy,[status(thm)],[c_280]) ).
cnf(c_47,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_48,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_281,plain,
join(join(A,complement(join(complement(B),C))),complement(join(complement(B),complement(C)))) = join(A,B),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_50,plain,
join(complement(join(complement(A),complement(B))),join(C,complement(join(complement(A),B)))) = join(C,A),
inference(paramod,[status(thm)],[c_18,c_281]) ).
cnf(c_282,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_34,c_21]) ).
cnf(c_75,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_36,c_282]) ).
cnf(c_80,plain,
join(top,zero) = top,
inference(paramod,[status(thm)],[c_36,c_34]) ).
cnf(c_283,plain,
join(top,A) = join(top,join(zero,A)),
inference(paramod,[status(thm)],[c_80,c_19]) ).
cnf(c_117,plain,
join(top,join(zero,A)) = join(top,A),
inference(copy,[status(thm)],[c_283]) ).
cnf(c_284,plain,
join(top,top) = join(top,complement(zero)),
inference(paramod,[status(thm)],[c_34,c_117]) ).
cnf(c_122,plain,
join(top,complement(zero)) = join(top,top),
inference(copy,[status(thm)],[c_284]) ).
cnf(c_285,plain,
join(complement(join(top,top)),complement(join(complement(zero),complement(top)))) = zero,
inference(paramod,[status(thm)],[c_122,c_47]) ).
cnf(c_286,plain,
join(complement(join(top,top)),complement(join(complement(zero),zero))) = zero,
inference(paramod,[status(thm)],[c_36,c_285]) ).
cnf(c_287,plain,
join(complement(join(top,top)),complement(join(zero,complement(zero)))) = zero,
inference(paramod,[status(thm)],[c_18,c_286]) ).
cnf(c_288,plain,
join(complement(join(top,top)),complement(top)) = zero,
inference(paramod,[status(thm)],[c_34,c_287]) ).
cnf(c_289,plain,
join(complement(join(top,top)),zero) = zero,
inference(paramod,[status(thm)],[c_36,c_288]) ).
cnf(c_138,plain,
join(zero,complement(join(top,top))) = zero,
inference(paramod,[status(thm)],[c_18,c_289]) ).
cnf(c_290,plain,
join(zero,A) = join(zero,join(complement(join(top,top)),A)),
inference(paramod,[status(thm)],[c_138,c_19]) ).
cnf(c_140,plain,
join(zero,join(complement(join(top,top)),A)) = join(zero,A),
inference(copy,[status(thm)],[c_290]) ).
cnf(c_291,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_138,c_117]) ).
cnf(c_292,plain,
top = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_80,c_291]) ).
cnf(c_142,plain,
join(top,complement(join(top,top))) = top,
inference(copy,[status(thm)],[c_292]) ).
cnf(c_293,plain,
join(complement(top),complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_142,c_47]) ).
cnf(c_294,plain,
join(zero,complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_36,c_293]) ).
cnf(c_295,plain,
join(zero,complement(join(complement(join(top,top)),zero))) = join(top,top),
inference(paramod,[status(thm)],[c_36,c_294]) ).
cnf(c_296,plain,
join(zero,complement(join(zero,complement(join(top,top))))) = join(top,top),
inference(paramod,[status(thm)],[c_18,c_295]) ).
cnf(c_297,plain,
join(zero,complement(zero)) = join(top,top),
inference(paramod,[status(thm)],[c_138,c_296]) ).
cnf(c_298,plain,
top = join(top,top),
inference(paramod,[status(thm)],[c_34,c_297]) ).
cnf(c_146,plain,
join(top,top) = top,
inference(copy,[status(thm)],[c_298]) ).
cnf(c_299,plain,
join(zero,join(complement(top),A)) = join(zero,A),
inference(paramod,[status(thm)],[c_146,c_140]) ).
cnf(c_148,plain,
join(zero,join(zero,A)) = join(zero,A),
inference(paramod,[status(thm)],[c_36,c_299]) ).
cnf(c_300,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_34,c_48]) ).
cnf(c_301,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_300]) ).
cnf(c_302,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_36,c_301]) ).
cnf(c_163,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_302]) ).
cnf(c_169,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_163,c_75]) ).
cnf(c_170,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_169,c_163]) ).
cnf(c_303,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_169,c_21]) ).
cnf(c_173,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_169,c_303]) ).
cnf(c_304,plain,
join(zero,complement(A)) = join(zero,complement(join(A,A))),
inference(paramod,[status(thm)],[c_170,c_148]) ).
cnf(c_201,plain,
join(zero,complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_170,c_304]) ).
cnf(c_305,plain,
join(zero,join(zero,complement(join(A,A)))) = complement(A),
inference(paramod,[status(thm)],[c_170,c_148]) ).
cnf(c_306,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_201,c_305]) ).
cnf(c_202,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_201,c_306]) ).
cnf(c_307,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_202,c_169]) ).
cnf(c_308,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_169,c_307]) ).
cnf(c_251,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_308]) ).
cnf(c_309,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_251,c_50]) ).
cnf(c_310,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_18,c_309]) ).
cnf(c_311,plain,
complement(complement(A)) = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_173,c_310]) ).
cnf(c_312,plain,
A = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_169,c_311]) ).
cnf(c_313,plain,
A = join(A,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_18,c_312]) ).
cnf(c_269,plain,
join(A,complement(join(complement(A),B))) = A,
inference(copy,[status(thm)],[c_313]) ).
cnf(c_314,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(paramod,[status(thm)],[c_269,c_44]) ).
cnf(c_273,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_314]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:36:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 88193 was started by sandbox2 on n016,
% 0.09/0.37 % Sat Sep 26 05:36:44 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.57/0.47
% 0.57/0.47 % SZS status Theorem for theBenchmark
% 0.57/0.47
% 0.57/0.47 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.57/0.47 % Length of proof is 41.
% 0.57/0.47 % Level of proof is 14.
% 0.57/0.47 % Maximum clause weight is 60.000.
% 0.57/0.47 % Given clauses 46.
% 0.57/0.47
% 0.57/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------