%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL026-4 : 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 19.59s 2.97s
% Output : CNFRefutation 19.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 135 ( 123 unt; 0 def)
% Number of atoms : 147 ( 146 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 28 ~; 12 |; 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 : 191 ( 4 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_2688,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_2688]) ).
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_2689,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_2690,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_2689]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_2690]) ).
fof(goals_17,axiom,
join(sk1,one) = one,
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(sk1,one) = one,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
join(one,sk1) = one,
inference(paramod,[status(thm)],[c_1,c_26]) ).
fof(goals_18,axiom,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2) ),
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2) ),
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_2691,plain,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),complement(join(complement(composition(sk1,top)),complement(sk2)))) != meet(composition(sk1,top),sk2) ),
inference(paramod,[status(thm)],[c_6,c_28]) ).
cnf(c_2692,plain,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != meet(composition(sk1,top),sk2) ),
inference(paramod,[status(thm)],[c_1,c_2691]) ).
cnf(c_2693,plain,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != meet(composition(sk1,top),sk2) ),
inference(paramod,[status(thm)],[c_1,c_2692]) ).
cnf(c_2694,plain,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != complement(join(complement(composition(sk1,top)),complement(sk2))) ),
inference(paramod,[status(thm)],[c_6,c_2693]) ).
cnf(c_2695,plain,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != complement(join(complement(sk2),complement(composition(sk1,top)))) ),
inference(paramod,[status(thm)],[c_1,c_2694]) ).
cnf(c_2696,plain,
( join(complement(join(complement(composition(sk1,top)),complement(sk2))),composition(sk1,sk2)) != composition(sk1,sk2)
| join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != complement(join(complement(sk2),complement(composition(sk1,top)))) ),
inference(paramod,[status(thm)],[c_6,c_2695]) ).
cnf(c_29,plain,
( join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != composition(sk1,sk2)
| join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != complement(join(complement(sk2),complement(composition(sk1,top)))) ),
inference(paramod,[status(thm)],[c_1,c_2696]) ).
cnf(c_2697,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_31,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_2697]) ).
cnf(c_32,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_33,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_2698,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_36,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2698]) ).
cnf(c_2699,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_2700,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_12,c_2699]) ).
cnf(c_2701,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_13,c_2700]) ).
cnf(c_2702,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_13,c_2701]) ).
cnf(c_2703,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),join(converse(A),converse(C))),
inference(paramod,[status(thm)],[c_12,c_2702]) ).
cnf(c_37,plain,
composition(converse(A),join(converse(B),converse(C))) = join(composition(converse(A),converse(B)),composition(converse(A),converse(C))),
inference(copy,[status(thm)],[c_2703]) ).
cnf(c_2704,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_43,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_2704]) ).
cnf(c_2705,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_2706,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_2705]) ).
cnf(c_44,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_2706]) ).
cnf(c_2707,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_27,c_10]) ).
cnf(c_53,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_2707]) ).
cnf(c_2708,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_36]) ).
cnf(c_67,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_2708]) ).
cnf(c_2709,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_67,c_9]) ).
cnf(c_69,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2709]) ).
cnf(c_73,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_67,c_15]) ).
cnf(c_74,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_69,c_67]) ).
cnf(c_2710,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_74,c_53]) ).
cnf(c_76,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_74,c_2710]) ).
cnf(c_77,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_74,c_73]) ).
cnf(c_78,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_77,c_44]) ).
cnf(c_2711,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_33]) ).
cnf(c_2712,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2711]) ).
cnf(c_2713,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_2712]) ).
cnf(c_81,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2713]) ).
cnf(c_82,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_81,c_43]) ).
cnf(c_83,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_82,c_81]) ).
cnf(c_84,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_82,c_78]) ).
cnf(c_85,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_84,c_83]) ).
cnf(c_2714,plain,
join(A,B) = join(B,join(A,composition(sk1,B))),
inference(paramod,[status(thm)],[c_76,c_31]) ).
cnf(c_107,plain,
join(A,join(B,composition(sk1,A))) = join(B,A),
inference(copy,[status(thm)],[c_2714]) ).
cnf(c_2715,plain,
composition(A,join(converse(B),converse(C))) = join(composition(converse(converse(A)),converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_11,c_37]) ).
cnf(c_2716,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_11,c_2715]) ).
cnf(c_109,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2716]) ).
cnf(c_2717,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_82,c_5]) ).
cnf(c_123,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_82,c_2717]) ).
cnf(c_2718,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_82,c_32]) ).
cnf(c_125,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_82,c_2718]) ).
cnf(c_2719,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_85,c_82]) ).
cnf(c_2720,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_82,c_2719]) ).
cnf(c_132,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2720]) ).
cnf(c_2721,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_132,c_3]) ).
cnf(c_138,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_2721]) ).
cnf(c_2722,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_109]) ).
cnf(c_401,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2722]) ).
cnf(c_2723,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_123,c_138]) ).
cnf(c_2724,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_2723]) ).
cnf(c_513,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_123,c_2724]) ).
cnf(c_529,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_513]) ).
cnf(c_2725,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_82,c_529]) ).
cnf(c_550,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_82,c_2725]) ).
cnf(c_2726,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_123,c_125]) ).
cnf(c_2727,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(A,B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_82,c_2726]) ).
cnf(c_2728,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_82,c_2727]) ).
cnf(c_2729,plain,
join(A,complement(join(join(A,B),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_2728]) ).
cnf(c_2730,plain,
join(A,complement(join(A,join(B,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_2729]) ).
cnf(c_2731,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_550,c_2730]) ).
cnf(c_608,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_82,c_2731]) ).
cnf(c_2732,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_11,c_401]) ).
cnf(c_2424,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_11,c_2732]) ).
cnf(c_2733,plain,
composition(A,top) = join(composition(A,B),composition(A,complement(B))),
inference(paramod,[status(thm)],[c_17,c_2424]) ).
cnf(c_2458,plain,
join(composition(A,B),composition(A,complement(B))) = composition(A,top),
inference(copy,[status(thm)],[c_2733]) ).
cnf(c_2734,plain,
join(complement(A),composition(sk1,top)) = join(composition(sk1,A),complement(A)),
inference(paramod,[status(thm)],[c_2458,c_107]) ).
cnf(c_2534,plain,
join(complement(A),composition(sk1,top)) = join(complement(A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_1,c_2734]) ).
cnf(c_2735,plain,
join(complement(join(complement(A),composition(sk1,top))),complement(join(composition(sk1,A),complement(complement(A))))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_2534,c_125]) ).
cnf(c_2736,plain,
join(complement(join(complement(A),composition(sk1,top))),complement(join(composition(sk1,A),A))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_82,c_2735]) ).
cnf(c_2737,plain,
join(complement(join(complement(A),composition(sk1,top))),complement(join(A,composition(sk1,A)))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_1,c_2736]) ).
cnf(c_2738,plain,
join(complement(join(complement(A),composition(sk1,top))),complement(A)) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_76,c_2737]) ).
cnf(c_2739,plain,
join(complement(A),complement(join(complement(A),composition(sk1,top)))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_1,c_2738]) ).
cnf(c_2740,plain,
join(complement(A),complement(composition(sk1,top))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_608,c_2739]) ).
cnf(c_2565,plain,
complement(composition(sk1,A)) = join(complement(A),complement(composition(sk1,top))),
inference(copy,[status(thm)],[c_2740]) ).
cnf(c_2741,plain,
meet(A,composition(sk1,top)) = complement(complement(composition(sk1,A))),
inference(paramod,[status(thm)],[c_2565,c_6]) ).
cnf(c_2742,plain,
complement(join(complement(A),complement(composition(sk1,top)))) = complement(complement(composition(sk1,A))),
inference(paramod,[status(thm)],[c_6,c_2741]) ).
cnf(c_2743,plain,
complement(join(complement(A),complement(composition(sk1,top)))) = composition(sk1,A),
inference(paramod,[status(thm)],[c_82,c_2742]) ).
cnf(c_2610,plain,
composition(sk1,A) = complement(join(complement(A),complement(composition(sk1,top)))),
inference(copy,[status(thm)],[c_2743]) ).
cnf(c_2744,plain,
( join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != composition(sk1,sk2)
| join(complement(complement(composition(sk1,sk2))),composition(sk1,sk2)) != complement(join(complement(sk2),complement(composition(sk1,top)))) ),
inference(paramod,[status(thm)],[c_2565,c_29]) ).
cnf(c_2745,plain,
( join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),composition(sk1,sk2)) != complement(join(complement(sk2),complement(composition(sk1,top)))) ),
inference(paramod,[status(thm)],[c_82,c_2744]) ).
cnf(c_2746,plain,
( join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != composition(sk1,sk2)
| composition(sk1,sk2) != complement(join(complement(sk2),complement(composition(sk1,top)))) ),
inference(paramod,[status(thm)],[c_132,c_2745]) ).
cnf(c_2612,plain,
join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != composition(sk1,sk2),
inference(resolve,[status(thm)],[c_2610,c_2746]) ).
cnf(c_2747,plain,
join(complement(complement(composition(sk1,sk2))),composition(sk1,sk2)) != composition(sk1,sk2),
inference(paramod,[status(thm)],[c_2565,c_2612]) ).
cnf(c_2748,plain,
join(composition(sk1,sk2),composition(sk1,sk2)) != composition(sk1,sk2),
inference(paramod,[status(thm)],[c_82,c_2747]) ).
cnf(c_2749,plain,
composition(sk1,sk2) != composition(sk1,sk2),
inference(paramod,[status(thm)],[c_132,c_2748]) ).
cnf(c_2687,plain,
$false,
inference(copy,[status(thm)],[c_2749]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL026-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n020.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 05:33:18 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.42 % Process 742549 was started by sandbox2 on n020,
% 0.14/0.42 % Sat Sep 26 05:33:18 2026
% 0.14/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.42
% 0.14/0.42 % From the command line: assign(max_seconds, 300).
% 19.59/2.97
% 19.59/2.97 % SZS status Unsatisfiable for theBenchmark
% 19.59/2.97
% 19.59/2.97 % Proof 1 at 1.85 (+ 0.65) seconds.
% 19.59/2.97 % Length of proof is 59.
% 19.59/2.97 % Level of proof is 18.
% 19.59/2.97 % Maximum clause weight is 49.000.
% 19.59/2.97 % Given clauses 399.
% 19.59/2.97
% 19.59/2.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------