%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL005+3 : 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 : n012.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 08:24:44 AM UTC 2026
% Result : Theorem 0.07s 0.41s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 12
% Syntax : Number of formulae : 123 ( 123 unt; 0 def)
% Number of atoms : 123 ( 122 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 158 ( 7 sgn 23 !; 2 ?)
% 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(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,X1] : converse(meet(X0,X1)) = meet(converse(X0),converse(X1)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] : converse(meet(X0,X1)) = meet(converse(X0),converse(X1)),
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_24,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_26,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_27,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_28,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_29,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_489,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_30,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_489]) ).
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_490,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_490]) ).
fof(nnf_17,plain,
? [X0,X1] : converse(meet(X0,X1)) != meet(converse(X0),converse(X1)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
converse(meet(sK0,sK1)) != meet(converse(sK0),converse(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
converse(meet(sK0,sK1)) != meet(converse(sK0),converse(sK1)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_491,negated_conjecture,
converse(complement(join(complement(sK0),complement(sK1)))) != meet(converse(sK0),converse(sK1)),
inference(paramod,[status(thm)],[c_22,c_40]) ).
cnf(c_41,negated_conjecture,
converse(complement(join(complement(sK0),complement(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))),
inference(paramod,[status(thm)],[c_22,c_491]) ).
cnf(c_44,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_45,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_492,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_48,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_492]) ).
cnf(c_493,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_493]) ).
cnf(c_494,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_495,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_494]) ).
cnf(c_56,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_495]) ).
cnf(c_496,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_58,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_496]) ).
cnf(c_497,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_48]) ).
cnf(c_74,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_497]) ).
cnf(c_498,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_74,c_24]) ).
cnf(c_76,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_498]) ).
cnf(c_80,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_74,c_30]) ).
cnf(c_81,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_76,c_74]) ).
cnf(c_82,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_81,c_80]) ).
cnf(c_83,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_82,c_56]) ).
cnf(c_499,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_45]) ).
cnf(c_500,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_499]) ).
cnf(c_501,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_500]) ).
cnf(c_86,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_501]) ).
cnf(c_87,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_86,c_55]) ).
cnf(c_88,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_89,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_87,c_83]) ).
cnf(c_90,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_89,c_88]) ).
cnf(c_502,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_21]) ).
cnf(c_105,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_502]) ).
cnf(c_503,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_44]) ).
cnf(c_107,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_503]) ).
cnf(c_504,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_90,c_31]) ).
cnf(c_505,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_19,c_504]) ).
cnf(c_112,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_505]) ).
cnf(c_506,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_90,c_87]) ).
cnf(c_507,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_87,c_506]) ).
cnf(c_113,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_507]) ).
cnf(c_508,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_112,c_18]) ).
cnf(c_127,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_508]) ).
cnf(c_509,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_112,c_27]) ).
cnf(c_129,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_509]) ).
cnf(c_510,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_113,c_19]) ).
cnf(c_131,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_510]) ).
cnf(c_153,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_129]) ).
cnf(c_156,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_153,c_127]) ).
cnf(c_158,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_156,c_58]) ).
cnf(c_179,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_26,c_158]) ).
cnf(c_511,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_105,c_131]) ).
cnf(c_512,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_511]) ).
cnf(c_235,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_105,c_512]) ).
cnf(c_513,plain,
join(complement(complement(A)),complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_107,c_105]) ).
cnf(c_514,plain,
join(A,complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_87,c_513]) ).
cnf(c_515,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_87,c_514]) ).
cnf(c_516,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_18,c_515]) ).
cnf(c_517,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_19,c_516]) ).
cnf(c_518,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_235,c_517]) ).
cnf(c_254,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_87,c_518]) ).
cnf(c_519,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_107,c_107]) ).
cnf(c_520,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_87,c_519]) ).
cnf(c_521,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_87,c_520]) ).
cnf(c_522,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_521]) ).
cnf(c_523,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_19,c_522]) ).
cnf(c_524,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_254,c_523]) ).
cnf(c_525,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_131,c_524]) ).
cnf(c_256,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_87,c_525]) ).
cnf(c_526,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_158,c_256]) ).
cnf(c_527,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_33,c_526]) ).
cnf(c_528,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_18,c_527]) ).
cnf(c_529,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_89,c_528]) ).
cnf(c_530,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_18,c_529]) ).
cnf(c_387,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_530]) ).
cnf(c_531,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_179,c_256]) ).
cnf(c_532,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_33,c_531]) ).
cnf(c_533,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_18,c_532]) ).
cnf(c_534,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_89,c_533]) ).
cnf(c_535,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_534]) ).
cnf(c_391,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_535]) ).
cnf(c_536,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_387,c_27]) ).
cnf(c_537,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_26,c_536]) ).
cnf(c_538,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_26,c_537]) ).
cnf(c_539,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_538]) ).
cnf(c_540,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_391,c_539]) ).
cnf(c_437,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_540]) ).
cnf(c_457,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_437,c_26]) ).
cnf(c_541,negated_conjecture,
complement(converse(join(complement(sK0),complement(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))),
inference(paramod,[status(thm)],[c_457,c_41]) ).
cnf(c_542,negated_conjecture,
complement(join(converse(complement(sK0)),converse(complement(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))),
inference(paramod,[status(thm)],[c_27,c_541]) ).
cnf(c_543,negated_conjecture,
complement(join(complement(converse(sK0)),converse(complement(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))),
inference(paramod,[status(thm)],[c_457,c_542]) ).
cnf(c_544,negated_conjecture,
complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))),
inference(paramod,[status(thm)],[c_457,c_543]) ).
cnf(c_488,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL005+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 05:24:36 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.31 % Process 3983686 was started by sandbox2 on n012,
% 0.04/0.31 % Sat Sep 26 05:24:36 2026
% 0.04/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.32
% 0.04/0.32 % From the command line: assign(max_seconds, 300).
% 0.07/0.41
% 0.07/0.41 % SZS status Theorem for theBenchmark
% 0.07/0.41
% 0.07/0.41 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.07/0.41 % Length of proof is 64.
% 0.07/0.41 % Level of proof is 19.
% 0.07/0.41 % Maximum clause weight is 30.000.
% 0.07/0.41 % Given clauses 111.
% 0.07/0.41
% 0.07/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
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