%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL013+1 : 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 : n001.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 08:24:49 AM UTC 2026
% Result : Theorem 0.09s 0.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 105 ( 99 unt; 0 def)
% Number of atoms : 111 ( 110 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 2 &)
% ( 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 : 122 ( 20 sgn 27 !; 1 ?)
% 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_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('theBenchmark.p',composition_associativity) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
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(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
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] :
( composition(zero,X0) = zero
& composition(X0,zero) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( composition(zero,X0) = zero
& composition(X0,zero) = zero ),
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_20,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(clausify,[status(thm)],[composition_associativity]) ).
cnf(c_21,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
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,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_24,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_26,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_208,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_15,c_26]) ).
cnf(c_27,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_28,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_29,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_209,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_30,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_28,c_209]) ).
fof(nnf_14,plain,
? [X0] :
( composition(zero,X0) != zero
| composition(X0,zero) != zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( composition(zero,sK0) != zero
| composition(sK0,zero) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
( composition(zero,sK0) != zero
| composition(sK0,zero) != zero ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_35,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_210,plain,
converse(A) = join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_18,c_24]) ).
cnf(c_37,plain,
join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))) = converse(A),
inference(copy,[status(thm)],[c_210]) ).
cnf(c_211,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_38,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_211]) ).
cnf(c_212,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_45,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_212]) ).
cnf(c_213,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_214,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_213]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_214]) ).
cnf(c_215,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_27]) ).
cnf(c_51,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_30,c_215]) ).
cnf(c_216,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_38]) ).
cnf(c_64,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_216]) ).
cnf(c_217,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_64,c_21]) ).
cnf(c_66,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_217]) ).
cnf(c_70,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_64,c_27]) ).
cnf(c_71,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_66,c_64]) ).
cnf(c_72,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_71,c_70]) ).
cnf(c_73,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_72,c_46]) ).
cnf(c_218,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_35]) ).
cnf(c_219,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_218]) ).
cnf(c_220,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_219]) ).
cnf(c_76,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_220]) ).
cnf(c_77,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_76,c_45]) ).
cnf(c_78,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_77,c_76]) ).
cnf(c_79,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_77,c_73]) ).
cnf(c_80,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_79,c_78]) ).
cnf(c_82,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_79,c_51]) ).
cnf(c_221,plain,
join(converse(complement(top)),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_28,c_37]) ).
cnf(c_222,plain,
join(converse(zero),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_30,c_221]) ).
cnf(c_223,plain,
join(converse(zero),converse(complement(join(complement(A),complement(A))))) = converse(A),
inference(paramod,[status(thm)],[c_77,c_222]) ).
cnf(c_224,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(paramod,[status(thm)],[c_72,c_223]) ).
cnf(c_84,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_77,c_224]) ).
cnf(c_225,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_79,c_15]) ).
cnf(c_87,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_225]) ).
cnf(c_226,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_80,c_28]) ).
cnf(c_227,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_16,c_226]) ).
cnf(c_102,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_227]) ).
cnf(c_228,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_102,c_15]) ).
cnf(c_117,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_228]) ).
cnf(c_229,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_102,c_24]) ).
cnf(c_119,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_230,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_84]) ).
cnf(c_128,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_23,c_230]) ).
cnf(c_231,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_128,c_87]) ).
cnf(c_133,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_231]) ).
cnf(c_143,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_119]) ).
cnf(c_146,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_143,c_117]) ).
cnf(c_179,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_146,c_82]) ).
cnf(c_232,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_179,c_22]) ).
cnf(c_233,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_117,c_232]) ).
cnf(c_234,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_179,c_233]) ).
cnf(c_235,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_79,c_234]) ).
cnf(c_187,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_235]) ).
cnf(c_236,plain,
zero = composition(A,composition(B,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_187,c_20]) ).
cnf(c_237,plain,
zero = composition(A,zero),
inference(paramod,[status(thm)],[c_187,c_236]) ).
cnf(c_189,plain,
composition(A,zero) = zero,
inference(copy,[status(thm)],[c_237]) ).
cnf(c_238,plain,
converse(zero) = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_187,c_25]) ).
cnf(c_239,plain,
zero = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_133,c_238]) ).
cnf(c_190,plain,
composition(converse(complement(composition(top,top))),converse(A)) = zero,
inference(copy,[status(thm)],[c_239]) ).
cnf(c_240,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_187,c_71]) ).
cnf(c_191,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_240]) ).
cnf(c_241,negated_conjecture,
( composition(zero,sK0) != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_189,c_31]) ).
cnf(c_192,negated_conjecture,
composition(zero,sK0) != zero,
inference(copy,[status(thm)],[c_241]) ).
cnf(c_242,plain,
composition(converse(zero),converse(A)) = zero,
inference(paramod,[status(thm)],[c_191,c_190]) ).
cnf(c_193,plain,
composition(zero,converse(A)) = zero,
inference(paramod,[status(thm)],[c_133,c_242]) ).
cnf(c_206,plain,
composition(zero,A) = zero,
inference(paramod,[status(thm)],[c_23,c_193]) ).
cnf(c_207,plain,
$false,
inference(resolve,[status(thm)],[c_206,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.39 % Computer : n001.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sat Sep 26 05:33:42 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.40 % Process 997702 was started by sandbox2 on n001,
% 0.09/0.40 % Sat Sep 26 05:33:42 2026
% 0.09/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 0.09/0.47
% 0.09/0.47 % SZS status Theorem for theBenchmark
% 0.09/0.47
% 0.09/0.47 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.09/0.47 % Length of proof is 67.
% 0.09/0.47 % Level of proof is 19.
% 0.09/0.47 % Maximum clause weight is 30.000.
% 0.09/0.47 % Given clauses 61.
% 0.09/0.47
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------