%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL050-4 : 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 : n018.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 08:25:09 AM UTC 2026
% Result : Unsatisfiable 23.56s 3.59s
% Output : CNFRefutation 23.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 14
% Syntax : Number of formulae : 164 ( 159 unt; 0 def)
% Number of atoms : 169 ( 168 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 224 ( 13 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(maddux3_a_kind_of_de_Morgan_3,axiom,
! [VAR_0,VAR_1] : VAR_0 = join(complement(join(complement(VAR_0),complement(VAR_1))),complement(join(complement(VAR_0),VAR_1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c_4,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c_5933,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_5933]) ).
fof(maddux4_definiton_of_meet_4,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c_6,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet_4]) ).
fof(composition_associativity_5,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(VAR_0,composition(VAR_1,VAR_2)) = composition(composition(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',composition_associativity_5) ).
cnf(c_7,plain,
composition(A,composition(B,C)) = composition(composition(A,B),C),
inference(clausify,[status(thm)],[composition_associativity_5]) ).
cnf(c_8,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(copy,[status(thm)],[c_7]) ).
fof(composition_identity_6,axiom,
! [VAR_0] : composition(VAR_0,one) = VAR_0,
file('theBenchmark.p',composition_identity_6) ).
cnf(c_9,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity_6]) ).
fof(composition_distributivity_7,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(join(VAR_0,VAR_1),VAR_2) = join(composition(VAR_0,VAR_2),composition(VAR_1,VAR_2)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c_10,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity_7]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_11,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_12,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
fof(converse_multiplicativity_10,axiom,
! [VAR_0,VAR_1] : converse(composition(VAR_0,VAR_1)) = composition(converse(VAR_1),converse(VAR_0)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c_13,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity_10]) ).
fof(converse_cancellativity_11,axiom,
! [VAR_0,VAR_1] : join(composition(converse(VAR_0),complement(composition(VAR_0,VAR_1))),complement(VAR_1)) = complement(VAR_1),
file('theBenchmark.p',converse_cancellativity_11) ).
cnf(c_14,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(clausify,[status(thm)],[converse_cancellativity_11]) ).
cnf(c_15,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_14]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_16,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_17,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_16]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_18,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_5934,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_5935,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_5934]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_5935]) ).
fof(goals_17,axiom,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
( join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(paramod,[status(thm)],[c_1,c_26]) ).
cnf(c_5936,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_29,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_5936]) ).
cnf(c_30,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_31,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_5937,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_32,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_5937]) ).
cnf(c_5938,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_38,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_5938]) ).
cnf(c_5939,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_40,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_5939]) ).
cnf(c_5940,plain,
converse(complement(A)) = join(converse(complement(A)),converse(composition(converse(B),complement(composition(B,A))))),
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_5941,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),converse(converse(B)))),
inference(paramod,[status(thm)],[c_13,c_5940]) ).
cnf(c_5942,plain,
converse(complement(A)) = join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)),
inference(paramod,[status(thm)],[c_11,c_5941]) ).
cnf(c_47,plain,
join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)),
inference(copy,[status(thm)],[c_5942]) ).
cnf(c_5943,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_50,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_5943]) ).
cnf(c_5944,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_53,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_5944]) ).
cnf(c_5945,plain,
join(A,B) = join(complement(join(C,complement(B))),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_30,c_29]) ).
cnf(c_97,plain,
join(complement(join(A,complement(B))),join(C,complement(join(complement(B),complement(A))))) = join(C,B),
inference(copy,[status(thm)],[c_5945]) ).
cnf(c_5946,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_5947,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_5946]) ).
cnf(c_5948,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_5947]) ).
cnf(c_106,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_5948]) ).
cnf(c_112,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_106,c_50]) ).
cnf(c_113,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_112,c_106]) ).
cnf(c_5949,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_38]) ).
cnf(c_122,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_5949]) ).
cnf(c_5950,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_122,c_9]) ).
cnf(c_131,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_5950]) ).
cnf(c_135,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_122,c_15]) ).
cnf(c_150,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_131,c_122]) ).
cnf(c_155,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_150,c_135]) ).
cnf(c_5951,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_155,c_5]) ).
cnf(c_5952,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_1,c_5951]) ).
cnf(c_5953,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_17,c_5952]) ).
cnf(c_5954,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_19,c_5953]) ).
cnf(c_217,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_112,c_5954]) ).
cnf(c_5955,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_155,c_32]) ).
cnf(c_5956,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_5,c_5955]) ).
cnf(c_220,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_5956]) ).
cnf(c_229,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_217,c_113]) ).
cnf(c_5957,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_229,c_5]) ).
cnf(c_5958,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_229,c_5957]) ).
cnf(c_5959,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_5958]) ).
cnf(c_273,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_5959]) ).
cnf(c_5960,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_273,c_3]) ).
cnf(c_306,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_5960]) ).
cnf(c_5961,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_273,c_32]) ).
cnf(c_5962,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_5961]) ).
cnf(c_5963,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_220,c_5962]) ).
cnf(c_309,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_5963]) ).
cnf(c_402,plain,
join(A,converse(complement(converse(A)))) = converse(top),
inference(paramod,[status(thm)],[c_11,c_53]) ).
cnf(c_406,plain,
join(one,converse(complement(one))) = converse(top),
inference(paramod,[status(thm)],[c_131,c_53]) ).
cnf(c_5964,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_17,c_306]) ).
cnf(c_451,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_5964]) ).
cnf(c_5965,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_53,c_306]) ).
cnf(c_452,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_53,c_5965]) ).
cnf(c_5966,plain,
join(one,converse(top)) = join(one,converse(complement(one))),
inference(paramod,[status(thm)],[c_406,c_306]) ).
cnf(c_453,plain,
join(one,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_406,c_5966]) ).
cnf(c_5967,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_451,c_1]) ).
cnf(c_455,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_5967]) ).
cnf(c_5968,plain,
composition(converse(top),A) = join(composition(one,A),composition(converse(top),A)),
inference(paramod,[status(thm)],[c_453,c_10]) ).
cnf(c_5969,plain,
composition(converse(top),A) = join(A,composition(converse(top),A)),
inference(paramod,[status(thm)],[c_150,c_5968]) ).
cnf(c_468,plain,
join(A,composition(converse(top),A)) = composition(converse(top),A),
inference(copy,[status(thm)],[c_5969]) ).
cnf(c_501,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_452]) ).
cnf(c_506,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_501,c_455]) ).
cnf(c_5970,plain,
join(A,composition(top,A)) = composition(converse(top),A),
inference(paramod,[status(thm)],[c_506,c_468]) ).
cnf(c_514,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_506,c_5970]) ).
cnf(c_519,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_506,c_402]) ).
cnf(c_525,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_506,c_53]) ).
cnf(c_5971,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_514,c_12]) ).
cnf(c_5972,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_5971]) ).
cnf(c_5973,plain,
composition(converse(A),top) = join(converse(A),converse(composition(top,A))),
inference(paramod,[status(thm)],[c_506,c_5972]) ).
cnf(c_5974,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_5973]) ).
cnf(c_5975,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),top)),
inference(paramod,[status(thm)],[c_506,c_5974]) ).
cnf(c_536,plain,
join(converse(A),composition(converse(A),top)) = composition(converse(A),top),
inference(copy,[status(thm)],[c_5975]) ).
cnf(c_539,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_514,c_455]) ).
cnf(c_5976,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_539,c_8]) ).
cnf(c_541,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_5976]) ).
cnf(c_5977,plain,
join(converse(complement(composition(top,A))),composition(converse(complement(composition(top,A))),top)) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_541,c_47]) ).
cnf(c_642,plain,
composition(converse(complement(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_536,c_5977]) ).
cnf(c_5978,plain,
join(A,composition(converse(converse(A)),top)) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_536]) ).
cnf(c_5979,plain,
join(A,composition(A,top)) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_5978]) ).
cnf(c_714,plain,
join(A,composition(A,top)) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_5979]) ).
cnf(c_5980,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != composition(complement(composition(sk1,top)),top) ),
inference(paramod,[status(thm)],[c_714,c_27]) ).
cnf(c_5981,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != composition(complement(composition(sk1,top)),top) ),
inference(paramod,[status(thm)],[c_714,c_5980]) ).
cnf(c_718,plain,
composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)),
inference(copy,[status(thm)],[c_5981]) ).
cnf(c_5982,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(complement(A)),C)))) = complement(A),
inference(paramod,[status(thm)],[c_309,c_40]) ).
cnf(c_5983,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(A,C)))) = complement(A),
inference(paramod,[status(thm)],[c_112,c_5982]) ).
cnf(c_881,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_40,c_5983]) ).
cnf(c_901,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_881]) ).
cnf(c_5984,plain,
join(complement(join(A,complement(B))),complement(complement(A))) = join(complement(complement(A)),B),
inference(paramod,[status(thm)],[c_901,c_97]) ).
cnf(c_5985,plain,
join(complement(join(A,complement(B))),A) = join(complement(complement(A)),B),
inference(paramod,[status(thm)],[c_112,c_5984]) ).
cnf(c_5986,plain,
join(A,complement(join(A,complement(B)))) = join(complement(complement(A)),B),
inference(paramod,[status(thm)],[c_1,c_5985]) ).
cnf(c_1169,plain,
join(A,complement(join(A,complement(B)))) = join(A,B),
inference(paramod,[status(thm)],[c_112,c_5986]) ).
cnf(c_2636,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_112,c_1169]) ).
cnf(c_2648,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_1,c_2636]) ).
cnf(c_5987,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_525,c_2648]) ).
cnf(c_5988,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_5987]) ).
cnf(c_5989,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_5988]) ).
cnf(c_5990,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_217,c_5989]) ).
cnf(c_5991,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_5990]) ).
cnf(c_2696,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_5991]) ).
cnf(c_5992,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_519,c_2648]) ).
cnf(c_5993,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_5992]) ).
cnf(c_5994,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_5993]) ).
cnf(c_5995,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_217,c_5994]) ).
cnf(c_5996,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_5995]) ).
cnf(c_2700,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_5996]) ).
cnf(c_5997,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_2696,c_12]) ).
cnf(c_5998,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_5997]) ).
cnf(c_5999,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_5998]) ).
cnf(c_6000,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_5999]) ).
cnf(c_6001,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_2700,c_6000]) ).
cnf(c_2840,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_6001]) ).
cnf(c_2859,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_2840,c_11]) ).
cnf(c_6002,plain,
composition(complement(converse(composition(top,A))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_2859,c_642]) ).
cnf(c_6003,plain,
composition(complement(composition(converse(A),converse(top))),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_13,c_6002]) ).
cnf(c_6004,plain,
composition(complement(composition(converse(A),top)),top) = converse(complement(composition(top,A))),
inference(paramod,[status(thm)],[c_506,c_6003]) ).
cnf(c_6005,plain,
composition(complement(composition(converse(A),top)),top) = complement(converse(composition(top,A))),
inference(paramod,[status(thm)],[c_2859,c_6004]) ).
cnf(c_6006,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),converse(top))),
inference(paramod,[status(thm)],[c_13,c_6005]) ).
cnf(c_2996,plain,
composition(complement(composition(converse(A),top)),top) = complement(composition(converse(A),top)),
inference(paramod,[status(thm)],[c_506,c_6006]) ).
cnf(c_6007,plain,
composition(complement(composition(A,top)),top) = complement(composition(converse(converse(A)),top)),
inference(paramod,[status(thm)],[c_11,c_2996]) ).
cnf(c_5931,plain,
composition(complement(composition(A,top)),top) = complement(composition(A,top)),
inference(paramod,[status(thm)],[c_11,c_6007]) ).
cnf(c_5932,plain,
$false,
inference(resolve,[status(thm)],[c_5931,c_718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n018.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Sat Sep 26 05:45:07 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.53 % Process 3853790 was started by sandbox on n018,
% 0.10/0.53 % Sat Sep 26 05:45:07 2026
% 0.10/0.53 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.53
% 0.10/0.53 % From the command line: assign(max_seconds, 300).
% 23.56/3.59
% 23.56/3.59 % SZS status Unsatisfiable for theBenchmark
% 23.56/3.59
% 23.56/3.59 % Proof 1 at 2.46 (+ 0.55) seconds.
% 23.56/3.59 % Length of proof is 75.
% 23.56/3.59 % Level of proof is 20.
% 23.56/3.59 % Maximum clause weight is 59.000.
% 23.56/3.59 % Given clauses 359.
% 23.56/3.59
% 23.56/3.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------