%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL026-2 : 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 : n006.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 08:24:54 AM UTC 2026
% Result : Unsatisfiable 16.36s 2.80s
% Output : CNFRefutation 16.36s
% 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_2607,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_2607]) ).
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_2608,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_2609,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_2608]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_2609]) ).
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(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_15) ).
cnf(c_22,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_15]) ).
cnf(c_2610,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_22]) ).
cnf(c_2611,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_2610]) ).
cnf(c_2612,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_2611]) ).
cnf(c_2613,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_2612]) ).
cnf(c_2614,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_2613]) ).
cnf(c_2615,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_2614]) ).
cnf(c_23,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_2615]) ).
cnf(c_2616,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_2616]) ).
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_2617,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_30,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2617]) ).
cnf(c_2618,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_2619,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_12,c_2618]) ).
cnf(c_2620,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_2619]) ).
cnf(c_2621,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_2620]) ).
cnf(c_2622,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_2621]) ).
cnf(c_31,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_2622]) ).
cnf(c_2623,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_37,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_2623]) ).
cnf(c_2624,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_2625,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_2624]) ).
cnf(c_38,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_2625]) ).
cnf(c_2626,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_47,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_2626]) ).
cnf(c_2627,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_30]) ).
cnf(c_61,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_2627]) ).
cnf(c_2628,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_61,c_9]) ).
cnf(c_63,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2628]) ).
cnf(c_67,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_61,c_15]) ).
cnf(c_68,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_63,c_61]) ).
cnf(c_2629,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_68,c_47]) ).
cnf(c_70,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_68,c_2629]) ).
cnf(c_71,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_68,c_67]) ).
cnf(c_72,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_71,c_38]) ).
cnf(c_2630,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_2631,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2630]) ).
cnf(c_2632,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_2631]) ).
cnf(c_75,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_2632]) ).
cnf(c_76,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_75,c_37]) ).
cnf(c_77,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_76,c_75]) ).
cnf(c_78,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_76,c_72]) ).
cnf(c_79,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_78,c_77]) ).
cnf(c_2633,plain,
join(A,B) = join(B,join(A,composition(sk1,B))),
inference(paramod,[status(thm)],[c_70,c_25]) ).
cnf(c_101,plain,
join(A,join(B,composition(sk1,A))) = join(B,A),
inference(copy,[status(thm)],[c_2633]) ).
cnf(c_2634,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_31]) ).
cnf(c_2635,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_2634]) ).
cnf(c_103,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2635]) ).
cnf(c_2636,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_76,c_5]) ).
cnf(c_117,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_76,c_2636]) ).
cnf(c_2637,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_76,c_26]) ).
cnf(c_119,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_76,c_2637]) ).
cnf(c_2638,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_79,c_76]) ).
cnf(c_2639,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_76,c_2638]) ).
cnf(c_126,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2639]) ).
cnf(c_2640,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_126,c_3]) ).
cnf(c_132,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_2640]) ).
cnf(c_2641,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_103]) ).
cnf(c_393,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2641]) ).
cnf(c_2642,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_117,c_132]) ).
cnf(c_2643,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_2642]) ).
cnf(c_505,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_117,c_2643]) ).
cnf(c_521,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_505]) ).
cnf(c_2644,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_76,c_521]) ).
cnf(c_542,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_76,c_2644]) ).
cnf(c_2645,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_117,c_119]) ).
cnf(c_2646,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_76,c_2645]) ).
cnf(c_2647,plain,
join(A,complement(join(complement(join(A,complement(B))),join(A,B)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_76,c_2646]) ).
cnf(c_2648,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_2647]) ).
cnf(c_2649,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_2648]) ).
cnf(c_2650,plain,
join(A,complement(join(A,B))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_542,c_2649]) ).
cnf(c_600,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_76,c_2650]) ).
cnf(c_2651,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_11,c_393]) ).
cnf(c_2375,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_11,c_2651]) ).
cnf(c_2652,plain,
composition(A,top) = join(composition(A,B),composition(A,complement(B))),
inference(paramod,[status(thm)],[c_17,c_2375]) ).
cnf(c_2404,plain,
join(composition(A,B),composition(A,complement(B))) = composition(A,top),
inference(copy,[status(thm)],[c_2652]) ).
cnf(c_2653,plain,
join(complement(A),composition(sk1,top)) = join(composition(sk1,A),complement(A)),
inference(paramod,[status(thm)],[c_2404,c_101]) ).
cnf(c_2481,plain,
join(complement(A),composition(sk1,top)) = join(complement(A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_1,c_2653]) ).
cnf(c_2654,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_2481,c_119]) ).
cnf(c_2655,plain,
join(complement(join(complement(A),composition(sk1,top))),complement(join(composition(sk1,A),A))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_76,c_2654]) ).
cnf(c_2656,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_2655]) ).
cnf(c_2657,plain,
join(complement(join(complement(A),composition(sk1,top))),complement(A)) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_70,c_2656]) ).
cnf(c_2658,plain,
join(complement(A),complement(join(complement(A),composition(sk1,top)))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_1,c_2657]) ).
cnf(c_2659,plain,
join(complement(A),complement(composition(sk1,top))) = complement(composition(sk1,A)),
inference(paramod,[status(thm)],[c_600,c_2658]) ).
cnf(c_2509,plain,
complement(composition(sk1,A)) = join(complement(A),complement(composition(sk1,top))),
inference(copy,[status(thm)],[c_2659]) ).
cnf(c_2660,plain,
meet(A,composition(sk1,top)) = complement(complement(composition(sk1,A))),
inference(paramod,[status(thm)],[c_2509,c_6]) ).
cnf(c_2661,plain,
complement(join(complement(A),complement(composition(sk1,top)))) = complement(complement(composition(sk1,A))),
inference(paramod,[status(thm)],[c_6,c_2660]) ).
cnf(c_2662,plain,
complement(join(complement(A),complement(composition(sk1,top)))) = composition(sk1,A),
inference(paramod,[status(thm)],[c_76,c_2661]) ).
cnf(c_2559,plain,
composition(sk1,A) = complement(join(complement(A),complement(composition(sk1,top)))),
inference(copy,[status(thm)],[c_2662]) ).
cnf(c_2663,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_2509,c_23]) ).
cnf(c_2664,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_76,c_2663]) ).
cnf(c_2665,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_126,c_2664]) ).
cnf(c_2561,plain,
join(complement(join(complement(sk2),complement(composition(sk1,top)))),composition(sk1,sk2)) != composition(sk1,sk2),
inference(resolve,[status(thm)],[c_2559,c_2665]) ).
cnf(c_2666,plain,
join(complement(complement(composition(sk1,sk2))),composition(sk1,sk2)) != composition(sk1,sk2),
inference(paramod,[status(thm)],[c_2509,c_2561]) ).
cnf(c_2667,plain,
join(composition(sk1,sk2),composition(sk1,sk2)) != composition(sk1,sk2),
inference(paramod,[status(thm)],[c_76,c_2666]) ).
cnf(c_2668,plain,
composition(sk1,sk2) != composition(sk1,sk2),
inference(paramod,[status(thm)],[c_126,c_2667]) ).
cnf(c_2606,plain,
$false,
inference(copy,[status(thm)],[c_2668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL026-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n006.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 05:32:10 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 464325 was started by sandbox2 on n006,
% 0.18/0.43 % Sat Sep 26 05:32:10 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 16.36/2.80
% 16.36/2.80 % SZS status Unsatisfiable for theBenchmark
% 16.36/2.80
% 16.36/2.80 % Proof 1 at 1.72 (+ 0.60) seconds.
% 16.36/2.80 % Length of proof is 59.
% 16.36/2.80 % Level of proof is 18.
% 16.36/2.80 % Maximum clause weight is 49.000.
% 16.36/2.80 % Given clauses 389.
% 16.36/2.80
% 16.36/2.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------