%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 : Unsatisfiable 0.13s 5.74s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 12
% Syntax : Number of formulae : 139 ( 116 unt; 0 def)
% Number of atoms : 162 ( 161 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 47 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 156 ( 7 sgn 19 !; 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_465,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_465]) ).
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_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(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_466,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_467,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_466]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_467]) ).
fof(goals_14,axiom,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2)) ),
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2)) ),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_468,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(complement(join(complement(sk1),complement(sk2)))),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2)) ),
inference(paramod,[status(thm)],[c_6,c_20]) ).
cnf(c_469,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(converse(complement(join(complement(sk1),complement(sk2)))),complement(join(complement(converse(sk1)),complement(converse(sk2))))) != meet(converse(sk1),converse(sk2)) ),
inference(paramod,[status(thm)],[c_6,c_468]) ).
cnf(c_470,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != meet(converse(sk1),converse(sk2)) ),
inference(paramod,[status(thm)],[c_1,c_469]) ).
cnf(c_471,plain,
( join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_6,c_470]) ).
cnf(c_472,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_6,c_471]) ).
cnf(c_473,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != converse(meet(sk1,sk2))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_6,c_472]) ).
cnf(c_21,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_6,c_473]) ).
cnf(c_24,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_25,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_474,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_28,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_474]) ).
cnf(c_475,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_35,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_475]) ).
cnf(c_476,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_477,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_476]) ).
cnf(c_36,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_477]) ).
cnf(c_478,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_38,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_478]) ).
cnf(c_479,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_28]) ).
cnf(c_54,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_479]) ).
cnf(c_480,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_54,c_9]) ).
cnf(c_56,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_480]) ).
cnf(c_60,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_54,c_15]) ).
cnf(c_61,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_56,c_54]) ).
cnf(c_62,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_61,c_60]) ).
cnf(c_63,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_62,c_36]) ).
cnf(c_481,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_482,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_481]) ).
cnf(c_483,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_482]) ).
cnf(c_66,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_483]) ).
cnf(c_67,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_66,c_35]) ).
cnf(c_68,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_66]) ).
cnf(c_69,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_67,c_63]) ).
cnf(c_70,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_69,c_68]) ).
cnf(c_484,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_5]) ).
cnf(c_85,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_484]) ).
cnf(c_485,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_67,c_24]) ).
cnf(c_87,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_67,c_485]) ).
cnf(c_486,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_70,c_17]) ).
cnf(c_487,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_486]) ).
cnf(c_92,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_487]) ).
cnf(c_488,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_70,c_67]) ).
cnf(c_489,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_67,c_488]) ).
cnf(c_93,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_489]) ).
cnf(c_490,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_92,c_1]) ).
cnf(c_107,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_490]) ).
cnf(c_491,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_92,c_12]) ).
cnf(c_109,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_491]) ).
cnf(c_492,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_93,c_3]) ).
cnf(c_111,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_492]) ).
cnf(c_133,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_109]) ).
cnf(c_136,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_133,c_107]) ).
cnf(c_138,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_136,c_38]) ).
cnf(c_159,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_11,c_138]) ).
cnf(c_493,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_85,c_111]) ).
cnf(c_494,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_493]) ).
cnf(c_213,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_85,c_494]) ).
cnf(c_495,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_87,c_85]) ).
cnf(c_496,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_67,c_495]) ).
cnf(c_497,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_67,c_496]) ).
cnf(c_498,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_1,c_497]) ).
cnf(c_499,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_3,c_498]) ).
cnf(c_500,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_213,c_499]) ).
cnf(c_232,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_67,c_500]) ).
cnf(c_501,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_87,c_87]) ).
cnf(c_502,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_67,c_501]) ).
cnf(c_503,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_67,c_502]) ).
cnf(c_504,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_503]) ).
cnf(c_505,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_504]) ).
cnf(c_506,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_232,c_505]) ).
cnf(c_507,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_111,c_506]) ).
cnf(c_234,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_67,c_507]) ).
cnf(c_508,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_138,c_234]) ).
cnf(c_509,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_19,c_508]) ).
cnf(c_510,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_1,c_509]) ).
cnf(c_511,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_69,c_510]) ).
cnf(c_512,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_1,c_511]) ).
cnf(c_363,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_512]) ).
cnf(c_513,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_159,c_234]) ).
cnf(c_514,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_19,c_513]) ).
cnf(c_515,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_1,c_514]) ).
cnf(c_516,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_69,c_515]) ).
cnf(c_517,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_516]) ).
cnf(c_367,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_517]) ).
cnf(c_518,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_363,c_12]) ).
cnf(c_519,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_11,c_518]) ).
cnf(c_520,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_11,c_519]) ).
cnf(c_521,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_1,c_520]) ).
cnf(c_522,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_367,c_521]) ).
cnf(c_413,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_522]) ).
cnf(c_433,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_413,c_11]) ).
cnf(c_523,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(converse(join(complement(sk1),complement(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_21]) ).
cnf(c_524,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(join(converse(complement(sk1)),converse(complement(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_12,c_523]) ).
cnf(c_525,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(join(complement(converse(sk1)),converse(complement(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_524]) ).
cnf(c_526,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(join(complement(converse(sk1)),complement(converse(sk2))))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_525]) ).
cnf(c_527,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_93,c_526]) ).
cnf(c_528,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(converse(join(complement(sk1),complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_527]) ).
cnf(c_529,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(join(converse(complement(sk1)),converse(complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_12,c_528]) ).
cnf(c_530,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(join(complement(converse(sk1)),converse(complement(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_529]) ).
cnf(c_531,plain,
( join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),complement(join(complement(converse(sk1)),complement(converse(sk2))))) != converse(complement(join(complement(sk1),complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_530]) ).
cnf(c_532,plain,
( complement(join(complement(converse(sk1)),complement(converse(sk2)))) != converse(complement(join(complement(sk1),complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_93,c_531]) ).
cnf(c_533,plain,
( complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(converse(join(complement(sk1),complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_532]) ).
cnf(c_534,plain,
( complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(converse(complement(sk1)),converse(complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_12,c_533]) ).
cnf(c_535,plain,
( complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),converse(complement(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_534]) ).
cnf(c_536,plain,
( complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2))))
| complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))) ),
inference(paramod,[status(thm)],[c_433,c_535]) ).
cnf(c_537,plain,
complement(join(complement(converse(sk1)),complement(converse(sk2)))) != complement(join(complement(converse(sk1)),complement(converse(sk2)))),
inference(copy,[status(thm)],[c_536]) ).
cnf(c_464,plain,
$false,
inference(copy,[status(thm)],[c_537]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p
% 0.09/5.58 % Computer : n020.cluster.edu
% 0.09/5.58 % Model : x86_64 x86_64
% 0.09/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.58 % Memory : 8046.5625MB
% 0.09/5.58 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Sat Sep 26 05:25:55 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.58 % Process 711945 was started by sandbox on n020,
% 0.09/5.58 % Sat Sep 26 05:25:55 2026
% 0.09/5.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.58
% 0.09/5.58 % From the command line: assign(max_seconds, 300).
% 0.13/5.74
% 0.13/5.74 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.74
% 0.13/5.74 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.13/5.74 % Length of proof is 54.
% 0.13/5.74 % Level of proof is 18.
% 0.13/5.74 % Maximum clause weight is 61.000.
% 0.13/5.74 % Given clauses 108.
% 0.13/5.74
% 0.13/5.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------