%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 84 unt; 0 def)
% Number of atoms : 84 ( 83 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 : 96 ( 9 sgn 22 !; 0 ?)
% 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_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,
composition(top,top) = top,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
composition(top,top) != top,
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_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_321,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_321]) ).
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_322,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_322]) ).
cnf(c_31,negated_conjecture,
composition(top,top) != top,
inference(clausify,[status(thm)],[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_323,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_42,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_323]) ).
cnf(c_324,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_54,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_324]) ).
cnf(c_325,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_326,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_325]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_326]) ).
cnf(c_327,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_57,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_327]) ).
cnf(c_328,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_27]) ).
cnf(c_60,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_30,c_328]) ).
cnf(c_329,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_42]) ).
cnf(c_72,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_329]) ).
cnf(c_330,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_72,c_21]) ).
cnf(c_74,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_330]) ).
cnf(c_78,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_72,c_27]) ).
cnf(c_79,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_74,c_72]) ).
cnf(c_80,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_79,c_78]) ).
cnf(c_81,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_80,c_55]) ).
cnf(c_331,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_35]) ).
cnf(c_332,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_331]) ).
cnf(c_333,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_332]) ).
cnf(c_114,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_333]) ).
cnf(c_120,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_114,c_54]) ).
cnf(c_126,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_120,c_81]) ).
cnf(c_130,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_126,c_60]) ).
cnf(c_334,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_120,c_80]) ).
cnf(c_335,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_120,c_334]) ).
cnf(c_136,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_120,c_335]) ).
cnf(c_336,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_136,c_16]) ).
cnf(c_141,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_336]) ).
cnf(c_337,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_28,c_141]) ).
cnf(c_209,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_337]) ).
cnf(c_338,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_57,c_141]) ).
cnf(c_210,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_57,c_338]) ).
cnf(c_339,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_209,c_15]) ).
cnf(c_213,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_339]) ).
cnf(c_230,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_210]) ).
cnf(c_235,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_230,c_213]) ).
cnf(c_250,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_235,c_130]) ).
cnf(c_340,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_250,c_22]) ).
cnf(c_341,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_213,c_340]) ).
cnf(c_342,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_250,c_341]) ).
cnf(c_343,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_126,c_342]) ).
cnf(c_293,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_343]) ).
cnf(c_344,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_293,c_79]) ).
cnf(c_304,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_344]) ).
cnf(c_345,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_304,c_28]) ).
cnf(c_346,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_15,c_345]) ).
cnf(c_319,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_126,c_346]) ).
cnf(c_320,plain,
$false,
inference(resolve,[status(thm)],[c_319,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL015+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:27:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 481147 was started by sandbox2 on n019,
% 0.10/0.37 % Sat Sep 26 05:27:48 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.45
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45
% 0.10/0.45 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.10/0.45 % Length of proof is 57.
% 0.10/0.45 % Level of proof is 16.
% 0.10/0.45 % Maximum clause weight is 14.000.
% 0.10/0.45 % Given clauses 62.
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------