%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL004+2 : 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 : n007.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 08:24:43 AM UTC 2026
% Result : Theorem 1.76s 0.70s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 117 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 155 ( 7 sgn 21 !; 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_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] : converse(complement(X0)) = complement(converse(X0)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : converse(complement(X0)) = complement(converse(X0)),
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_458,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_458]) ).
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_459,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_459]) ).
fof(nnf_17,plain,
? [X0] : converse(complement(X0)) != complement(converse(X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
converse(complement(sK0)) != complement(converse(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
converse(complement(sK0)) != complement(converse(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_43,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_44,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_460,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_47,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_460]) ).
cnf(c_461,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_54,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_461]) ).
cnf(c_462,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_463,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_462]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_463]) ).
cnf(c_464,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_57,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_464]) ).
cnf(c_465,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_47]) ).
cnf(c_73,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_465]) ).
cnf(c_466,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_73,c_24]) ).
cnf(c_75,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_466]) ).
cnf(c_79,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_30]) ).
cnf(c_80,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_75,c_73]) ).
cnf(c_81,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_80,c_79]) ).
cnf(c_82,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_81,c_55]) ).
cnf(c_467,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_44]) ).
cnf(c_468,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_467]) ).
cnf(c_469,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_468]) ).
cnf(c_85,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_469]) ).
cnf(c_86,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_85,c_54]) ).
cnf(c_87,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_86,c_85]) ).
cnf(c_88,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_86,c_82]) ).
cnf(c_89,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_88,c_87]) ).
cnf(c_470,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_86,c_21]) ).
cnf(c_104,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_86,c_470]) ).
cnf(c_471,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_86,c_43]) ).
cnf(c_106,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_86,c_471]) ).
cnf(c_472,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_89,c_31]) ).
cnf(c_473,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_19,c_472]) ).
cnf(c_111,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_473]) ).
cnf(c_474,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_89,c_86]) ).
cnf(c_475,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_86,c_474]) ).
cnf(c_112,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_475]) ).
cnf(c_476,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_111,c_18]) ).
cnf(c_126,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_476]) ).
cnf(c_477,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_111,c_27]) ).
cnf(c_128,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_477]) ).
cnf(c_478,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_112,c_19]) ).
cnf(c_130,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_478]) ).
cnf(c_152,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_128]) ).
cnf(c_155,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_152,c_126]) ).
cnf(c_157,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_155,c_57]) ).
cnf(c_178,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_26,c_157]) ).
cnf(c_479,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_104,c_130]) ).
cnf(c_480,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_479]) ).
cnf(c_234,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_104,c_480]) ).
cnf(c_481,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_106,c_104]) ).
cnf(c_482,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_86,c_481]) ).
cnf(c_483,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_86,c_482]) ).
cnf(c_484,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_483]) ).
cnf(c_485,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_484]) ).
cnf(c_486,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_234,c_485]) ).
cnf(c_253,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_86,c_486]) ).
cnf(c_487,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_106,c_106]) ).
cnf(c_488,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_86,c_487]) ).
cnf(c_489,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_86,c_488]) ).
cnf(c_490,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_489]) ).
cnf(c_491,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_490]) ).
cnf(c_492,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_253,c_491]) ).
cnf(c_493,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_130,c_492]) ).
cnf(c_255,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_86,c_493]) ).
cnf(c_494,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_157,c_255]) ).
cnf(c_495,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_33,c_494]) ).
cnf(c_496,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_18,c_495]) ).
cnf(c_497,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_88,c_496]) ).
cnf(c_498,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_18,c_497]) ).
cnf(c_386,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_498]) ).
cnf(c_499,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_178,c_255]) ).
cnf(c_500,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_33,c_499]) ).
cnf(c_501,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_18,c_500]) ).
cnf(c_502,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_88,c_501]) ).
cnf(c_503,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_502]) ).
cnf(c_390,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_503]) ).
cnf(c_504,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_386,c_27]) ).
cnf(c_505,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_26,c_504]) ).
cnf(c_506,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_26,c_505]) ).
cnf(c_507,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_18,c_506]) ).
cnf(c_508,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_390,c_507]) ).
cnf(c_436,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_508]) ).
cnf(c_456,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_436,c_26]) ).
cnf(c_457,plain,
$false,
inference(resolve,[status(thm)],[c_456,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL004+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 05:23:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2874209 was started by sandbox on n007,
% 0.10/0.36 % Sat Sep 26 05:23:08 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 1.76/0.70
% 1.76/0.70 % SZS status Theorem for theBenchmark
% 1.76/0.70
% 1.76/0.70 % Proof 1 at 0.14 (+ 0.05) seconds.
% 1.76/0.70 % Length of proof is 63.
% 1.76/0.70 % Level of proof is 19.
% 1.76/0.70 % Maximum clause weight is 30.000.
% 1.76/0.70 % Given clauses 111.
% 1.76/0.70
% 1.76/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------