%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL010+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 : 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 08:24:47 AM UTC 2026
% Result : Theorem 0.20s 10.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 14
% Syntax : Number of formulae : 126 ( 122 unt; 0 def)
% Number of atoms : 130 ( 129 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 159 ( 10 sgn 31 !; 3 ?)
% 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(dedekind_law,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('theBenchmark.p',dedekind_law) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
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_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
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_509,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_509]) ).
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_510,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_32]) ).
cnf(c_511,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_510]) ).
cnf(c_33,plain,
zero = complement(top),
inference(copy,[status(thm)],[c_511]) ).
cnf(c_34,plain,
composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(clausify,[status(thm)],[dedekind_law]) ).
cnf(c_512,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_34]) ).
cnf(c_513,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_512]) ).
cnf(c_514,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_513]) ).
cnf(c_515,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_514]) ).
cnf(c_516,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B)))))),
inference(paramod,[status(thm)],[c_22,c_515]) ).
cnf(c_35,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C))))),
inference(copy,[status(thm)],[c_516]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( meet(X1,composition(converse(X0),X2)) != zero
& meet(composition(X0,X1),X2) = zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( meet(sK1,composition(converse(sK0),sK2)) != zero
& meet(composition(sK0,sK1),sK2) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
meet(composition(sK0,sK1),sK2) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_517,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),complement(sK2))) = zero,
inference(paramod,[status(thm)],[c_22,c_40]) ).
cnf(c_518,negated_conjecture,
complement(join(complement(sK2),complement(composition(sK0,sK1)))) = zero,
inference(paramod,[status(thm)],[c_18,c_517]) ).
cnf(c_41,negated_conjecture,
complement(join(complement(sK2),complement(composition(sK0,sK1)))) = complement(top),
inference(paramod,[status(thm)],[c_33,c_518]) ).
cnf(c_42,negated_conjecture,
meet(sK1,composition(converse(sK0),sK2)) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_519,negated_conjecture,
complement(join(complement(sK1),complement(composition(converse(sK0),sK2)))) != zero,
inference(paramod,[status(thm)],[c_22,c_42]) ).
cnf(c_43,negated_conjecture,
complement(join(complement(sK1),complement(composition(converse(sK0),sK2)))) != complement(top),
inference(paramod,[status(thm)],[c_33,c_519]) ).
cnf(c_520,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_45,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_19,c_520]) ).
cnf(c_47,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_521,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_54,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_521]) ).
cnf(c_522,plain,
top = join(A,join(B,complement(join(A,B)))),
inference(paramod,[status(thm)],[c_31,c_19]) ).
cnf(c_65,plain,
join(A,join(B,complement(join(A,B)))) = top,
inference(copy,[status(thm)],[c_522]) ).
cnf(c_66,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_523,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_69,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_523]) ).
cnf(c_524,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C)))))) = composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(converse(A)),C))))),
inference(paramod,[status(thm)],[c_26,c_35]) ).
cnf(c_76,plain,
join(complement(join(complement(composition(converse(A),B)),complement(C))),composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C)))))) = composition(complement(join(complement(converse(A)),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(A,C))))),
inference(paramod,[status(thm)],[c_26,c_524]) ).
cnf(c_525,plain,
join(complement(join(complement(top),A)),complement(join(complement(join(complement(sK2),complement(composition(sK0,sK1)))),complement(A)))) = join(complement(sK2),complement(composition(sK0,sK1))),
inference(paramod,[status(thm)],[c_41,c_21]) ).
cnf(c_526,plain,
join(complement(join(complement(top),A)),complement(join(complement(top),complement(A)))) = join(complement(sK2),complement(composition(sK0,sK1))),
inference(paramod,[status(thm)],[c_41,c_525]) ).
cnf(c_527,plain,
top = join(complement(sK2),complement(composition(sK0,sK1))),
inference(paramod,[status(thm)],[c_21,c_526]) ).
cnf(c_88,plain,
join(complement(sK2),complement(composition(sK0,sK1))) = top,
inference(copy,[status(thm)],[c_527]) ).
cnf(c_528,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_529,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_528]) ).
cnf(c_113,plain,
join(complement(top),complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_529]) ).
cnf(c_119,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_113,c_66]) ).
cnf(c_120,plain,
join(complement(top),complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_119,c_113]) ).
cnf(c_530,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_54]) ).
cnf(c_124,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_530]) ).
cnf(c_531,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_124,c_24]) ).
cnf(c_133,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_531]) ).
cnf(c_137,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_124,c_30]) ).
cnf(c_152,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_133,c_124]) ).
cnf(c_157,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_152,c_137]) ).
cnf(c_532,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_157,c_21]) ).
cnf(c_533,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_18,c_532]) ).
cnf(c_534,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_31,c_533]) ).
cnf(c_161,plain,
join(complement(top),A) = A,
inference(paramod,[status(thm)],[c_119,c_534]) ).
cnf(c_164,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_161,c_120]) ).
cnf(c_535,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_164,c_21]) ).
cnf(c_536,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_164,c_535]) ).
cnf(c_537,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_21,c_536]) ).
cnf(c_232,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_537]) ).
cnf(c_538,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_232,c_19]) ).
cnf(c_235,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_538]) ).
cnf(c_539,plain,
join(A,converse(top)) = join(converse(B),join(A,converse(complement(B)))),
inference(paramod,[status(thm)],[c_69,c_45]) ).
cnf(c_259,plain,
join(converse(A),join(B,converse(complement(A)))) = join(B,converse(top)),
inference(copy,[status(thm)],[c_539]) ).
cnf(c_260,plain,
join(one,converse(complement(one))) = converse(top),
inference(paramod,[status(thm)],[c_133,c_69]) ).
cnf(c_540,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_31,c_235]) ).
cnf(c_345,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_540]) ).
cnf(c_541,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_69,c_235]) ).
cnf(c_346,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_69,c_541]) ).
cnf(c_542,plain,
join(one,converse(top)) = join(one,converse(complement(one))),
inference(paramod,[status(thm)],[c_260,c_235]) ).
cnf(c_347,plain,
join(one,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_260,c_542]) ).
cnf(c_543,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_345,c_18]) ).
cnf(c_352,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_543]) ).
cnf(c_544,plain,
composition(converse(top),A) = join(composition(one,A),composition(converse(top),A)),
inference(paramod,[status(thm)],[c_347,c_25]) ).
cnf(c_545,plain,
composition(converse(top),A) = join(A,composition(converse(top),A)),
inference(paramod,[status(thm)],[c_152,c_544]) ).
cnf(c_362,plain,
join(A,composition(converse(top),A)) = composition(converse(top),A),
inference(copy,[status(thm)],[c_545]) ).
cnf(c_366,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_346]) ).
cnf(c_368,plain,
join(converse(A),join(B,converse(complement(A)))) = converse(top),
inference(paramod,[status(thm)],[c_366,c_259]) ).
cnf(c_546,plain,
join(converse(A),join(converse(complement(A)),complement(converse(top)))) = top,
inference(paramod,[status(thm)],[c_69,c_65]) ).
cnf(c_547,plain,
join(converse(A),join(complement(converse(top)),converse(complement(A)))) = top,
inference(paramod,[status(thm)],[c_18,c_546]) ).
cnf(c_386,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_368,c_547]) ).
cnf(c_548,plain,
join(A,composition(top,A)) = composition(converse(top),A),
inference(paramod,[status(thm)],[c_386,c_362]) ).
cnf(c_390,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_386,c_548]) ).
cnf(c_417,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_390,c_352]) ).
cnf(c_549,plain,
join(complement(top),composition(converse(top),complement(top))) = complement(top),
inference(paramod,[status(thm)],[c_417,c_30]) ).
cnf(c_550,plain,
join(complement(top),composition(top,complement(top))) = complement(top),
inference(paramod,[status(thm)],[c_386,c_549]) ).
cnf(c_419,plain,
composition(top,complement(top)) = complement(top),
inference(paramod,[status(thm)],[c_390,c_550]) ).
cnf(c_551,plain,
composition(join(top,A),complement(top)) = join(complement(top),composition(A,complement(top))),
inference(paramod,[status(thm)],[c_419,c_25]) ).
cnf(c_552,plain,
composition(top,complement(top)) = join(complement(top),composition(A,complement(top))),
inference(paramod,[status(thm)],[c_352,c_551]) ).
cnf(c_553,plain,
complement(top) = join(complement(top),composition(A,complement(top))),
inference(paramod,[status(thm)],[c_419,c_552]) ).
cnf(c_554,plain,
complement(top) = composition(A,complement(top)),
inference(paramod,[status(thm)],[c_161,c_553]) ).
cnf(c_426,plain,
composition(A,complement(top)) = complement(top),
inference(copy,[status(thm)],[c_554]) ).
cnf(c_555,plain,
join(complement(join(complement(composition(converse(sK0),sK2)),complement(sK1))),composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(top))) = composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(join(complement(sK2),complement(composition(sK0,sK1))))),
inference(paramod,[status(thm)],[c_88,c_76]) ).
cnf(c_556,plain,
join(complement(join(complement(sK1),complement(composition(converse(sK0),sK2)))),composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(top))) = composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(join(complement(sK2),complement(composition(sK0,sK1))))),
inference(paramod,[status(thm)],[c_18,c_555]) ).
cnf(c_557,plain,
join(complement(join(complement(sK1),complement(composition(converse(sK0),sK2)))),complement(top)) = composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(join(complement(sK2),complement(composition(sK0,sK1))))),
inference(paramod,[status(thm)],[c_426,c_556]) ).
cnf(c_558,plain,
join(complement(top),complement(join(complement(sK1),complement(composition(converse(sK0),sK2))))) = composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(join(complement(sK2),complement(composition(sK0,sK1))))),
inference(paramod,[status(thm)],[c_18,c_557]) ).
cnf(c_559,plain,
complement(join(complement(sK1),complement(composition(converse(sK0),sK2)))) = composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(join(complement(sK2),complement(composition(sK0,sK1))))),
inference(paramod,[status(thm)],[c_161,c_558]) ).
cnf(c_560,plain,
complement(join(complement(sK1),complement(composition(converse(sK0),sK2)))) = composition(complement(join(complement(converse(sK0)),complement(composition(sK1,converse(sK2))))),complement(top)),
inference(paramod,[status(thm)],[c_88,c_559]) ).
cnf(c_507,plain,
complement(join(complement(sK1),complement(composition(converse(sK0),sK2)))) = complement(top),
inference(paramod,[status(thm)],[c_426,c_560]) ).
cnf(c_508,plain,
$false,
inference(resolve,[status(thm)],[c_507,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.43 % Computer : n019.cluster.edu
% 0.13/10.43 % Model : x86_64 x86_64
% 0.13/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.43 % Memory : 8046.5625MB
% 0.13/10.43 % OS : Linux 6.8.0-71-generic
% 0.13/10.43 % CPULimit : 300
% 0.13/10.43 % WCLimit : 300
% 0.13/10.43 % DateTime : Sat Sep 26 05:26:59 UTC 2026
% 0.13/10.43 % CPUTime :
% 0.13/10.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/10.43 % Process 479624 was started by sandbox on n019,
% 0.13/10.43 % Sat Sep 26 05:26:59 2026
% 0.13/10.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/10.44
% 0.13/10.44 % From the command line: assign(max_seconds, 300).
% 0.20/10.59
% 0.20/10.59 % SZS status Theorem for theBenchmark
% 0.20/10.59
% 0.20/10.59 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.20/10.59 % Length of proof is 71.
% 0.20/10.59 % Level of proof is 20.
% 0.20/10.59 % Maximum clause weight is 89.000.
% 0.20/10.59 % Given clauses 75.
% 0.20/10.59
% 0.20/10.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------