%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL005+2 : 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 : n017.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 2.04s 0.68s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 12
% Syntax : Number of formulae : 141 ( 113 unt; 0 def)
% Number of atoms : 169 ( 168 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 82 ( 54 ~; 26 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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] :
( join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1))
& join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( join(meet(converse(X0),converse(X1)),converse(meet(X0,X1))) = converse(meet(X0,X1))
& join(converse(meet(X0,X1)),meet(converse(X0),converse(X1))) = meet(converse(X0),converse(X1)) ),
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_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_476,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_476]) ).
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_477,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_477]) ).
fof(nnf_14,plain,
? [X0,X1] :
( converse(meet(X0,X1)) != join(meet(converse(X0),converse(X1)),converse(meet(X0,X1)))
| meet(converse(X0),converse(X1)) != join(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)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1)))
| meet(converse(sK0),converse(sK1)) != join(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_14]) ).
cnf(c_31,negated_conjecture,
( converse(meet(sK0,sK1)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1)))
| meet(converse(sK0),converse(sK1)) != join(converse(meet(sK0,sK1)),meet(converse(sK0),converse(sK1))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_478,negated_conjecture,
( converse(meet(sK0,sK1)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1)))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(converse(meet(sK0,sK1)),meet(converse(sK0),converse(sK1))) ),
inference(paramod,[status(thm)],[c_19,c_31]) ).
cnf(c_479,negated_conjecture,
( converse(meet(sK0,sK1)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1)))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(converse(complement(join(complement(sK0),complement(sK1)))),meet(converse(sK0),converse(sK1))) ),
inference(paramod,[status(thm)],[c_19,c_478]) ).
cnf(c_480,negated_conjecture,
( converse(meet(sK0,sK1)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1)))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(converse(complement(join(complement(sK0),complement(sK1)))),complement(join(complement(converse(sK0)),complement(converse(sK1))))) ),
inference(paramod,[status(thm)],[c_19,c_479]) ).
cnf(c_481,negated_conjecture,
( converse(meet(sK0,sK1)) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1)))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) ),
inference(paramod,[status(thm)],[c_15,c_480]) ).
cnf(c_482,negated_conjecture,
( converse(complement(join(complement(sK0),complement(sK1)))) != join(meet(converse(sK0),converse(sK1)),converse(meet(sK0,sK1)))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) ),
inference(paramod,[status(thm)],[c_19,c_481]) ).
cnf(c_483,negated_conjecture,
( converse(complement(join(complement(sK0),complement(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(meet(sK0,sK1)))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) ),
inference(paramod,[status(thm)],[c_19,c_482]) ).
cnf(c_484,negated_conjecture,
( converse(complement(join(complement(sK0),complement(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1)))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) ),
inference(paramod,[status(thm)],[c_19,c_483]) ).
cnf(c_485,negated_conjecture,
( converse(complement(join(complement(sK0),complement(sK1)))) != join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1)))))
| join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(copy,[status(thm)],[c_484]) ).
cnf(c_32,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(copy,[status(thm)],[c_485]) ).
cnf(c_35,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_36,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_486,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_39,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_486]) ).
cnf(c_487,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_487]) ).
cnf(c_488,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_489,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_488]) ).
cnf(c_47,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_489]) ).
cnf(c_490,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_49,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_490]) ).
cnf(c_491,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_39]) ).
cnf(c_65,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_491]) ).
cnf(c_492,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_65,c_21]) ).
cnf(c_67,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_492]) ).
cnf(c_71,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_65,c_27]) ).
cnf(c_72,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_67,c_65]) ).
cnf(c_73,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_72,c_71]) ).
cnf(c_74,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_73,c_47]) ).
cnf(c_493,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_36]) ).
cnf(c_494,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_493]) ).
cnf(c_495,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_494]) ).
cnf(c_77,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_495]) ).
cnf(c_78,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_77,c_46]) ).
cnf(c_79,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_78,c_77]) ).
cnf(c_80,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_78,c_74]) ).
cnf(c_81,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_80,c_79]) ).
cnf(c_496,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_78,c_18]) ).
cnf(c_96,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_78,c_496]) ).
cnf(c_497,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_78,c_35]) ).
cnf(c_98,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_78,c_497]) ).
cnf(c_498,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_81,c_28]) ).
cnf(c_499,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_16,c_498]) ).
cnf(c_103,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_499]) ).
cnf(c_500,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_81,c_78]) ).
cnf(c_501,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_78,c_500]) ).
cnf(c_104,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_501]) ).
cnf(c_502,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_103,c_15]) ).
cnf(c_118,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_502]) ).
cnf(c_503,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_103,c_24]) ).
cnf(c_120,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_503]) ).
cnf(c_504,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_104,c_16]) ).
cnf(c_122,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_504]) ).
cnf(c_144,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_120]) ).
cnf(c_147,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_144,c_118]) ).
cnf(c_149,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_147,c_49]) ).
cnf(c_170,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_23,c_149]) ).
cnf(c_505,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_96,c_122]) ).
cnf(c_506,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_505]) ).
cnf(c_224,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_506]) ).
cnf(c_507,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_98,c_96]) ).
cnf(c_508,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_78,c_507]) ).
cnf(c_509,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_78,c_508]) ).
cnf(c_510,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_15,c_509]) ).
cnf(c_511,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_16,c_510]) ).
cnf(c_512,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_224,c_511]) ).
cnf(c_243,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_78,c_512]) ).
cnf(c_513,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_98,c_98]) ).
cnf(c_514,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_78,c_513]) ).
cnf(c_515,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_78,c_514]) ).
cnf(c_516,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_515]) ).
cnf(c_517,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_16,c_516]) ).
cnf(c_518,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_243,c_517]) ).
cnf(c_519,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_122,c_518]) ).
cnf(c_245,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_78,c_519]) ).
cnf(c_520,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_149,c_245]) ).
cnf(c_521,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_30,c_520]) ).
cnf(c_522,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_15,c_521]) ).
cnf(c_523,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_80,c_522]) ).
cnf(c_524,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_523]) ).
cnf(c_374,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_524]) ).
cnf(c_525,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_170,c_245]) ).
cnf(c_526,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_30,c_525]) ).
cnf(c_527,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_15,c_526]) ).
cnf(c_528,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_80,c_527]) ).
cnf(c_529,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_528]) ).
cnf(c_378,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_529]) ).
cnf(c_530,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_374,c_24]) ).
cnf(c_531,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_23,c_530]) ).
cnf(c_532,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_23,c_531]) ).
cnf(c_533,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_532]) ).
cnf(c_534,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_378,c_533]) ).
cnf(c_424,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_534]) ).
cnf(c_444,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_424,c_23]) ).
cnf(c_535,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(converse(join(complement(sK0),complement(sK1))))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_32]) ).
cnf(c_536,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(join(converse(complement(sK0)),converse(complement(sK1))))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_24,c_535]) ).
cnf(c_537,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(join(complement(converse(sK0)),converse(complement(sK1))))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_536]) ).
cnf(c_538,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(join(complement(converse(sK0)),complement(converse(sK1))))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_537]) ).
cnf(c_539,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),converse(complement(join(complement(sK0),complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_104,c_538]) ).
cnf(c_540,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(converse(join(complement(sK0),complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_539]) ).
cnf(c_541,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(join(converse(complement(sK0)),converse(complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_24,c_540]) ).
cnf(c_542,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(join(complement(converse(sK0)),converse(complement(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_541]) ).
cnf(c_543,negated_conjecture,
( join(complement(join(complement(converse(sK0)),complement(converse(sK1)))),complement(join(complement(converse(sK0)),complement(converse(sK1))))) != converse(complement(join(complement(sK0),complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_542]) ).
cnf(c_544,negated_conjecture,
( complement(join(complement(converse(sK0)),complement(converse(sK1)))) != converse(complement(join(complement(sK0),complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_104,c_543]) ).
cnf(c_545,negated_conjecture,
( complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(converse(join(complement(sK0),complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_544]) ).
cnf(c_546,negated_conjecture,
( complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(converse(complement(sK0)),converse(complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_24,c_545]) ).
cnf(c_547,negated_conjecture,
( complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),converse(complement(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_546]) ).
cnf(c_548,negated_conjecture,
( complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1))))
| complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))) ),
inference(paramod,[status(thm)],[c_444,c_547]) ).
cnf(c_549,negated_conjecture,
complement(join(complement(converse(sK0)),complement(converse(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))),
inference(copy,[status(thm)],[c_548]) ).
cnf(c_475,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL005+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n017.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:20:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 4106713 was started by sandbox2 on n017,
% 0.09/0.38 % Sat Sep 26 05:20:19 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 2.04/0.68
% 2.04/0.68 % SZS status Theorem for theBenchmark
% 2.04/0.68
% 2.04/0.68 % Proof 1 at 0.12 (+ 0.06) seconds.
% 2.04/0.68 % Length of proof is 64.
% 2.04/0.68 % Level of proof is 19.
% 2.04/0.68 % Maximum clause weight is 61.000.
% 2.04/0.68 % Given clauses 108.
% 2.04/0.68
% 2.04/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------