%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.16s 5.48s
% Output : CNFRefutation 0.16s
% 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_15,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_16,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_17,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_18,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_15,c_17]) ).
cnf(c_19,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_22,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_23,plain,
join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_31,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_32,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_198,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_198]) ).
fof(nnf_14,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_14]) ).
cnf(c_34,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_199,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_19,c_34]) ).
cnf(c_200,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_19,c_199]) ).
cnf(c_201,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_19,c_200]) ).
cnf(c_202,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_19,c_201]) ).
cnf(c_203,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_15,c_202]) ).
cnf(c_204,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_23,c_203]) ).
cnf(c_35,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_204]) ).
cnf(c_38,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_39,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_205,plain,
join(join(A,complement(join(complement(B),C))),complement(join(complement(B),complement(C)))) = join(A,B),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_41,plain,
join(complement(join(complement(A),complement(B))),join(C,complement(join(complement(A),B)))) = join(C,A),
inference(paramod,[status(thm)],[c_15,c_205]) ).
cnf(c_206,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_18]) ).
cnf(c_66,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_206]) ).
cnf(c_71,plain,
join(top,zero) = top,
inference(paramod,[status(thm)],[c_33,c_31]) ).
cnf(c_207,plain,
join(top,A) = join(top,join(zero,A)),
inference(paramod,[status(thm)],[c_71,c_16]) ).
cnf(c_78,plain,
join(top,join(zero,A)) = join(top,A),
inference(copy,[status(thm)],[c_207]) ).
cnf(c_208,plain,
join(top,top) = join(top,complement(zero)),
inference(paramod,[status(thm)],[c_31,c_78]) ).
cnf(c_83,plain,
join(top,complement(zero)) = join(top,top),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_209,plain,
join(complement(join(top,top)),complement(join(complement(zero),complement(top)))) = zero,
inference(paramod,[status(thm)],[c_83,c_38]) ).
cnf(c_210,plain,
join(complement(join(top,top)),complement(join(complement(zero),zero))) = zero,
inference(paramod,[status(thm)],[c_33,c_209]) ).
cnf(c_211,plain,
join(complement(join(top,top)),complement(join(zero,complement(zero)))) = zero,
inference(paramod,[status(thm)],[c_15,c_210]) ).
cnf(c_212,plain,
join(complement(join(top,top)),complement(top)) = zero,
inference(paramod,[status(thm)],[c_31,c_211]) ).
cnf(c_213,plain,
join(complement(join(top,top)),zero) = zero,
inference(paramod,[status(thm)],[c_33,c_212]) ).
cnf(c_99,plain,
join(zero,complement(join(top,top))) = zero,
inference(paramod,[status(thm)],[c_15,c_213]) ).
cnf(c_214,plain,
join(zero,A) = join(zero,join(complement(join(top,top)),A)),
inference(paramod,[status(thm)],[c_99,c_16]) ).
cnf(c_101,plain,
join(zero,join(complement(join(top,top)),A)) = join(zero,A),
inference(copy,[status(thm)],[c_214]) ).
cnf(c_215,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_99,c_78]) ).
cnf(c_216,plain,
top = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_71,c_215]) ).
cnf(c_103,plain,
join(top,complement(join(top,top))) = top,
inference(copy,[status(thm)],[c_216]) ).
cnf(c_217,plain,
join(complement(top),complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_103,c_38]) ).
cnf(c_218,plain,
join(zero,complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_33,c_217]) ).
cnf(c_219,plain,
join(zero,complement(join(complement(join(top,top)),zero))) = join(top,top),
inference(paramod,[status(thm)],[c_33,c_218]) ).
cnf(c_220,plain,
join(zero,complement(join(zero,complement(join(top,top))))) = join(top,top),
inference(paramod,[status(thm)],[c_15,c_219]) ).
cnf(c_221,plain,
join(zero,complement(zero)) = join(top,top),
inference(paramod,[status(thm)],[c_99,c_220]) ).
cnf(c_222,plain,
top = join(top,top),
inference(paramod,[status(thm)],[c_31,c_221]) ).
cnf(c_107,plain,
join(top,top) = top,
inference(copy,[status(thm)],[c_222]) ).
cnf(c_223,plain,
join(zero,join(complement(top),A)) = join(zero,A),
inference(paramod,[status(thm)],[c_107,c_101]) ).
cnf(c_109,plain,
join(zero,join(zero,A)) = join(zero,A),
inference(paramod,[status(thm)],[c_33,c_223]) ).
cnf(c_224,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_39]) ).
cnf(c_225,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_224]) ).
cnf(c_226,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_225]) ).
cnf(c_124,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_226]) ).
cnf(c_130,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_124,c_66]) ).
cnf(c_131,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_130,c_124]) ).
cnf(c_227,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_130,c_18]) ).
cnf(c_133,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_130,c_227]) ).
cnf(c_228,plain,
join(zero,complement(A)) = join(zero,complement(join(A,A))),
inference(paramod,[status(thm)],[c_131,c_109]) ).
cnf(c_147,plain,
join(zero,complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_131,c_228]) ).
cnf(c_229,plain,
join(zero,join(zero,complement(join(A,A)))) = complement(A),
inference(paramod,[status(thm)],[c_131,c_109]) ).
cnf(c_230,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_147,c_229]) ).
cnf(c_148,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_147,c_230]) ).
cnf(c_231,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_148,c_130]) ).
cnf(c_232,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_130,c_231]) ).
cnf(c_181,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_232]) ).
cnf(c_233,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_181,c_41]) ).
cnf(c_234,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_15,c_233]) ).
cnf(c_235,plain,
complement(complement(A)) = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_133,c_234]) ).
cnf(c_236,plain,
A = join(complement(join(complement(A),B)),A),
inference(paramod,[status(thm)],[c_130,c_235]) ).
cnf(c_237,plain,
A = join(A,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_15,c_236]) ).
cnf(c_194,plain,
join(A,complement(join(complement(A),B))) = A,
inference(copy,[status(thm)],[c_237]) ).
cnf(c_238,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(paramod,[status(thm)],[c_194,c_35]) ).
cnf(c_197,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_238]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n014.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sat Sep 26 05:31:37 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.43 % Process 2257241 was started by sandbox on n014,
% 0.16/5.43 % Sat Sep 26 05:31:37 2026
% 0.16/5.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.44
% 0.16/5.44 % From the command line: assign(max_seconds, 300).
% 0.16/5.48
% 0.16/5.48 % SZS status Theorem for theBenchmark
% 0.16/5.48
% 0.16/5.48 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.16/5.48 % Length of proof is 41.
% 0.16/5.48 % Level of proof is 14.
% 0.16/5.48 % Maximum clause weight is 60.000.
% 0.16/5.48 % Given clauses 43.
% 0.16/5.48
% 0.16/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------