%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL015-1 : 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 : n009.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 : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 82 unt; 0 def)
% Number of atoms : 82 ( 81 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 10 sgn 22 !; 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_186,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_186]) ).
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(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]) ).
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_187,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_188,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_187]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_188]) ).
fof(goals_14,axiom,
composition(top,top) != top,
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
composition(top,top) != top,
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_24,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_189,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_27,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_190,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_34,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_190]) ).
cnf(c_191,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_192,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_191]) ).
cnf(c_35,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_192]) ).
cnf(c_193,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_40,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_19,c_193]) ).
cnf(c_194,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_27]) ).
cnf(c_53,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_194]) ).
cnf(c_195,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_53,c_9]) ).
cnf(c_55,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_195]) ).
cnf(c_59,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_53,c_15]) ).
cnf(c_60,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_55,c_53]) ).
cnf(c_61,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_60,c_59]) ).
cnf(c_62,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_61,c_35]) ).
cnf(c_196,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_24]) ).
cnf(c_197,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_196]) ).
cnf(c_198,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_197]) ).
cnf(c_65,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_198]) ).
cnf(c_66,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_65,c_34]) ).
cnf(c_67,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_66,c_65]) ).
cnf(c_68,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_66,c_62]) ).
cnf(c_69,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_68,c_67]) ).
cnf(c_71,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_68,c_40]) ).
cnf(c_199,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_69,c_17]) ).
cnf(c_200,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_199]) ).
cnf(c_91,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_200]) ).
cnf(c_201,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_91,c_1]) ).
cnf(c_106,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_201]) ).
cnf(c_202,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_91,c_12]) ).
cnf(c_108,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_132,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_108]) ).
cnf(c_135,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_132,c_106]) ).
cnf(c_168,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_135,c_71]) ).
cnf(c_203,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_168,c_10]) ).
cnf(c_204,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_106,c_203]) ).
cnf(c_205,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_168,c_204]) ).
cnf(c_206,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_68,c_205]) ).
cnf(c_176,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_206]) ).
cnf(c_207,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_176,c_60]) ).
cnf(c_180,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_207]) ).
cnf(c_208,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_180,c_17]) ).
cnf(c_209,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_1,c_208]) ).
cnf(c_184,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_68,c_209]) ).
cnf(c_185,plain,
$false,
inference(resolve,[status(thm)],[c_184,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL015-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n009.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 05:27:29 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 3442421 was started by sandbox on n009,
% 0.17/0.43 % Sat Sep 26 05:27:29 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.17/0.50 % Length of proof is 45.
% 0.17/0.50 % Level of proof is 17.
% 0.17/0.50 % Maximum clause weight is 30.000.
% 0.17/0.50 % Given clauses 55.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------