%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL027-2 : 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 : 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 08:24:55 AM UTC 2026
% Result : Unsatisfiable 5.34s 1.18s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 14
% Syntax : Number of formulae : 184 ( 155 unt; 0 def)
% Number of atoms : 213 ( 212 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 88 ( 59 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 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 : 220 ( 12 sgn 22 !; 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_2698,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_2698]) ).
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(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_2699,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_2700,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_2699]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_2700]) ).
fof(goals_14,axiom,
join(sk1,one) = one,
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
join(sk1,one) = one,
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_21,plain,
join(one,sk1) = one,
inference(paramod,[status(thm)],[c_1,c_20]) ).
fof(goals_15,axiom,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(meet(complement(sk1),one),meet(complement(composition(sk1,top)),one)) != meet(complement(composition(sk1,top)),one) ),
file('theBenchmark.p',goals_15) ).
cnf(c_22,plain,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(meet(complement(sk1),one),meet(complement(composition(sk1,top)),one)) != meet(complement(composition(sk1,top)),one) ),
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_2701,plain,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(complement(sk1)),complement(one))),meet(complement(composition(sk1,top)),one)) != meet(complement(composition(sk1,top)),one) ),
inference(paramod,[status(thm)],[c_6,c_22]) ).
cnf(c_2702,plain,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),meet(complement(composition(sk1,top)),one)) != meet(complement(composition(sk1,top)),one) ),
inference(paramod,[status(thm)],[c_1,c_2701]) ).
cnf(c_2703,plain,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(complement(composition(sk1,top))),complement(one)))) != meet(complement(composition(sk1,top)),one) ),
inference(paramod,[status(thm)],[c_6,c_2702]) ).
cnf(c_2704,plain,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != meet(complement(composition(sk1,top)),one) ),
inference(paramod,[status(thm)],[c_1,c_2703]) ).
cnf(c_2705,plain,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(complement(composition(sk1,top))),complement(one))) ),
inference(paramod,[status(thm)],[c_6,c_2704]) ).
cnf(c_2706,plain,
( join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_1,c_2705]) ).
cnf(c_2707,plain,
( join(complement(join(complement(complement(composition(sk1,top))),complement(one))),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_6,c_2706]) ).
cnf(c_2708,plain,
( join(complement(join(complement(one),complement(complement(composition(sk1,top))))),meet(complement(sk1),one)) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_1,c_2707]) ).
cnf(c_2709,plain,
( join(complement(join(complement(one),complement(complement(composition(sk1,top))))),complement(join(complement(complement(sk1)),complement(one)))) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_6,c_2708]) ).
cnf(c_2710,plain,
( join(complement(join(complement(one),complement(complement(composition(sk1,top))))),complement(join(complement(one),complement(complement(sk1))))) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_1,c_2709]) ).
cnf(c_2711,plain,
( join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != meet(complement(sk1),one)
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_1,c_2710]) ).
cnf(c_2712,plain,
( join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(complement(sk1)),complement(one)))
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_6,c_2711]) ).
cnf(c_23,plain,
( join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_1,c_2712]) ).
cnf(c_2713,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_25,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_2713]) ).
cnf(c_26,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_27,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_2714,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_28,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_2714]) ).
cnf(c_2715,plain,
join(complement(join(complement(join(complement(A),B)),join(complement(A),complement(B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_2716,plain,
join(complement(join(join(complement(A),complement(B)),complement(join(complement(A),B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_1,c_2715]) ).
cnf(c_2717,plain,
join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_3,c_2716]) ).
cnf(c_30,plain,
join(complement(A),complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))) = join(complement(A),B),
inference(paramod,[status(thm)],[c_1,c_2717]) ).
cnf(c_2718,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_34,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2718]) ).
cnf(c_2719,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_36,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_2719]) ).
cnf(c_2720,plain,
join(top,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_3]) ).
cnf(c_44,plain,
join(A,join(complement(A),B)) = join(top,B),
inference(copy,[status(thm)],[c_2720]) ).
cnf(c_2721,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_2721]) ).
cnf(c_2722,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_48,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_2722]) ).
cnf(c_2723,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_49,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_2723]) ).
cnf(c_2724,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_56,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_2724]) ).
cnf(c_2725,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_2726,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2725]) ).
cnf(c_2727,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_2726]) ).
cnf(c_82,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2727]) ).
cnf(c_2728,plain,
join(complement(join(complement(join(complement(A),complement(B))),join(complement(B),A))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_27,c_27]) ).
cnf(c_2729,plain,
join(complement(join(join(complement(B),A),complement(join(complement(A),complement(B))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_1,c_2728]) ).
cnf(c_2730,plain,
join(complement(join(complement(B),join(A,complement(join(complement(A),complement(B)))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_3,c_2729]) ).
cnf(c_87,plain,
join(complement(A),complement(join(complement(A),join(B,complement(join(complement(B),complement(A))))))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_1,c_2730]) ).
cnf(c_88,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_82,c_46]) ).
cnf(c_89,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_88,c_82]) ).
cnf(c_2731,plain,
( join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(complement(one),sk1)),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_88,c_23]) ).
cnf(c_2732,plain,
( join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_1,c_2731]) ).
cnf(c_2733,plain,
( join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) ),
inference(paramod,[status(thm)],[c_88,c_2732]) ).
cnf(c_2734,plain,
( join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_88,c_2733]) ).
cnf(c_2735,plain,
( join(complement(join(complement(one),sk1)),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_88,c_2734]) ).
cnf(c_2736,plain,
( join(complement(join(sk1,complement(one))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_1,c_2735]) ).
cnf(c_2737,plain,
( join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),complement(complement(sk1))))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_88,c_2736]) ).
cnf(c_2738,plain,
( join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),sk1))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_88,c_2737]) ).
cnf(c_91,plain,
( join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(sk1,complement(one)))
| join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_1,c_2738]) ).
cnf(c_2739,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_98,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_2739]) ).
cnf(c_2740,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_98,c_9]) ).
cnf(c_100,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2740]) ).
cnf(c_104,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_98,c_15]) ).
cnf(c_105,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_100,c_98]) ).
cnf(c_2741,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_105,c_56]) ).
cnf(c_107,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_105,c_2741]) ).
cnf(c_108,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_105,c_104]) ).
cnf(c_2742,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_26,c_28]) ).
cnf(c_2743,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_1,c_2742]) ).
cnf(c_128,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_88,c_2743]) ).
cnf(c_2744,plain,
join(A,join(complement(B),C)) = join(complement(B),join(A,complement(join(complement(B),join(complement(C),complement(join(complement(B),C))))))),
inference(paramod,[status(thm)],[c_30,c_25]) ).
cnf(c_141,plain,
join(complement(A),join(B,complement(join(complement(A),join(complement(C),complement(join(complement(A),C))))))) = join(B,join(complement(A),C)),
inference(copy,[status(thm)],[c_2744]) ).
cnf(c_2745,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(complement(A))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_30,c_26]) ).
cnf(c_2746,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),A))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_88,c_2745]) ).
cnf(c_143,plain,
join(complement(join(complement(A),B)),complement(join(A,complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_1,c_2746]) ).
cnf(c_2747,plain,
join(A,B) = join(B,join(A,composition(sk1,B))),
inference(paramod,[status(thm)],[c_107,c_25]) ).
cnf(c_168,plain,
join(A,join(B,composition(sk1,A))) = join(B,A),
inference(copy,[status(thm)],[c_2747]) ).
cnf(c_2748,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_108,c_5]) ).
cnf(c_2749,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_1,c_2748]) ).
cnf(c_2750,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_17,c_2749]) ).
cnf(c_2751,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_19,c_2750]) ).
cnf(c_179,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_88,c_2751]) ).
cnf(c_2752,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_108,c_28]) ).
cnf(c_2753,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_5,c_2752]) ).
cnf(c_182,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_2753]) ).
cnf(c_191,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_179,c_89]) ).
cnf(c_194,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_182,c_87]) ).
cnf(c_2754,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_191,c_5]) ).
cnf(c_2755,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_191,c_2754]) ).
cnf(c_2756,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_2755]) ).
cnf(c_257,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2756]) ).
cnf(c_2757,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_257,c_28]) ).
cnf(c_2758,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_1,c_2757]) ).
cnf(c_2759,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_182,c_2758]) ).
cnf(c_261,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_1,c_2759]) ).
cnf(c_2760,plain,
join(complement(join(complement(A),B)),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_261,c_143]) ).
cnf(c_2761,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_1,c_2760]) ).
cnf(c_2762,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_194,c_2761]) ).
cnf(c_263,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_2762]) ).
cnf(c_266,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_263,c_141]) ).
cnf(c_2763,plain,
join(A,complement(A)) = join(top,complement(A)),
inference(paramod,[status(thm)],[c_257,c_44]) ).
cnf(c_2764,plain,
top = join(top,complement(A)),
inference(paramod,[status(thm)],[c_17,c_2763]) ).
cnf(c_412,plain,
join(top,complement(A)) = top,
inference(copy,[status(thm)],[c_2764]) ).
cnf(c_2765,plain,
join(A,join(complement(A),top)) = top,
inference(paramod,[status(thm)],[c_257,c_44]) ).
cnf(c_2766,plain,
join(A,join(top,complement(A))) = top,
inference(paramod,[status(thm)],[c_1,c_2765]) ).
cnf(c_413,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_412,c_2766]) ).
cnf(c_438,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_105,c_48]) ).
cnf(c_2767,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_413,c_1]) ).
cnf(c_443,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_2767]) ).
cnf(c_2768,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_413,c_12]) ).
cnf(c_445,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_2768]) ).
cnf(c_460,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_11,c_445]) ).
cnf(c_463,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_460,c_443]) ).
cnf(c_472,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_463,c_49]) ).
cnf(c_623,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_100,c_472]) ).
cnf(c_2769,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_438,c_12]) ).
cnf(c_2770,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_13,c_2769]) ).
cnf(c_2771,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_463,c_2770]) ).
cnf(c_2772,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_13,c_2771]) ).
cnf(c_821,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_2772]) ).
cnf(c_2773,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(C),complement(A))))) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_128,c_36]) ).
cnf(c_2774,plain,
join(composition(converse(B),complement(composition(B,A))),join(complement(A),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_266,c_2773]) ).
cnf(c_2775,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_25,c_2774]) ).
cnf(c_2776,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_36,c_2775]) ).
cnf(c_2777,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_88,c_2776]) ).
cnf(c_1179,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_2777]) ).
cnf(c_2778,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_623,c_1179]) ).
cnf(c_2779,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_19,c_2778]) ).
cnf(c_2780,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_2779]) ).
cnf(c_2781,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_179,c_2780]) ).
cnf(c_1258,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_2781]) ).
cnf(c_2782,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1258,c_12]) ).
cnf(c_2783,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_11,c_2782]) ).
cnf(c_2784,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_11,c_2783]) ).
cnf(c_2785,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_1,c_2784]) ).
cnf(c_2786,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1258,c_2785]) ).
cnf(c_1470,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_2786]) ).
cnf(c_1478,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_1470,c_821]) ).
cnf(c_2787,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_1478]) ).
cnf(c_2788,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_11,c_2787]) ).
cnf(c_2659,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_11,c_2788]) ).
cnf(c_2690,plain,
join(complement(one),composition(sk1,top)) = join(sk1,complement(one)),
inference(paramod,[status(thm)],[c_2659,c_168]) ).
cnf(c_2789,plain,
( join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(sk1,complement(one)))
| join(complement(join(sk1,complement(one))),complement(join(sk1,complement(one)))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_2690,c_91]) ).
cnf(c_2790,plain,
( join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(sk1,complement(one)))
| complement(join(sk1,complement(one))) != complement(join(complement(one),composition(sk1,top))) ),
inference(paramod,[status(thm)],[c_257,c_2789]) ).
cnf(c_2791,plain,
( join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(sk1,complement(one)))
| complement(join(sk1,complement(one))) != complement(join(sk1,complement(one))) ),
inference(paramod,[status(thm)],[c_2690,c_2790]) ).
cnf(c_2792,plain,
( join(complement(join(sk1,complement(one))),complement(join(sk1,complement(one)))) != complement(join(sk1,complement(one)))
| complement(join(sk1,complement(one))) != complement(join(sk1,complement(one))) ),
inference(paramod,[status(thm)],[c_2690,c_2791]) ).
cnf(c_2793,plain,
( complement(join(sk1,complement(one))) != complement(join(sk1,complement(one)))
| complement(join(sk1,complement(one))) != complement(join(sk1,complement(one))) ),
inference(paramod,[status(thm)],[c_257,c_2792]) ).
cnf(c_2794,plain,
complement(join(sk1,complement(one))) != complement(join(sk1,complement(one))),
inference(copy,[status(thm)],[c_2793]) ).
cnf(c_2697,plain,
$false,
inference(copy,[status(thm)],[c_2794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL027-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n020.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 05:33:34 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.41 % Process 743862 was started by sandbox2 on n020,
% 0.16/0.41 % Sat Sep 26 05:33:34 2026
% 0.16/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.42
% 0.16/0.42 % From the command line: assign(max_seconds, 300).
% 5.34/1.18
% 5.34/1.18 % SZS status Unsatisfiable for theBenchmark
% 5.34/1.18
% 5.34/1.18 % Proof 1 at 0.58 (+ 0.16) seconds.
% 5.34/1.18 % Length of proof is 73.
% 5.34/1.18 % Level of proof is 21.
% 5.34/1.18 % Maximum clause weight is 117.000.
% 5.34/1.18 % Given clauses 219.
% 5.34/1.18
% 5.34/1.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------