%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL024-2 : 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 : n016.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 08:24:53 AM UTC 2026
% Result : Unsatisfiable 13.87s 7.26s
% Output : CNFRefutation 13.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 92 ( 92 unt; 0 def)
% Number of atoms : 92 ( 91 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 146 ( 5 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_1617,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_1617]) ).
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_1618,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1619,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1618]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1619]) ).
fof(goals_17,axiom,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_1620,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_6,c_26]) ).
cnf(c_1621,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_6,c_1620]) ).
cnf(c_1622,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_6,c_1621]) ).
cnf(c_1623,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3))))) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_1,c_1622]) ).
cnf(c_27,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3))))) != composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),
inference(paramod,[status(thm)],[c_6,c_1623]) ).
cnf(c_30,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_31,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1624,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_1624]) ).
cnf(c_1625,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_1626,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_12,c_1625]) ).
cnf(c_1627,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_1626]) ).
cnf(c_1628,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_1627]) ).
cnf(c_1629,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_1628]) ).
cnf(c_35,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_1629]) ).
cnf(c_1630,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_41,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1630]) ).
cnf(c_1631,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1632,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_1631]) ).
cnf(c_42,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1632]) ).
cnf(c_1633,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_60,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1633]) ).
cnf(c_1634,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_60,c_9]) ).
cnf(c_62,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1634]) ).
cnf(c_66,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_60,c_15]) ).
cnf(c_67,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_62,c_60]) ).
cnf(c_68,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_67,c_66]) ).
cnf(c_69,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_68,c_42]) ).
cnf(c_1635,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_31]) ).
cnf(c_1636,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1635]) ).
cnf(c_1637,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1636]) ).
cnf(c_72,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1637]) ).
cnf(c_73,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_72,c_41]) ).
cnf(c_74,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_73,c_72]) ).
cnf(c_75,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_73,c_69]) ).
cnf(c_76,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_75,c_74]) ).
cnf(c_1638,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_73,c_30]) ).
cnf(c_93,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_73,c_1638]) ).
cnf(c_1639,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_76,c_73]) ).
cnf(c_1640,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_73,c_1639]) ).
cnf(c_99,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1640]) ).
cnf(c_1641,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_35]) ).
cnf(c_1642,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_1641]) ).
cnf(c_101,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_1642]) ).
cnf(c_1643,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_99,c_3]) ).
cnf(c_117,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1643]) ).
cnf(c_1644,plain,
join(complement(join(A,B)),complement(B)) = join(complement(join(A,B)),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_93,c_117]) ).
cnf(c_1645,plain,
join(complement(B),complement(join(A,B))) = join(complement(join(A,B)),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_1,c_1644]) ).
cnf(c_241,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_93,c_1645]) ).
cnf(c_1646,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_73,c_241]) ).
cnf(c_301,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_73,c_1646]) ).
cnf(c_1647,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_101]) ).
cnf(c_313,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_1647]) ).
cnf(c_1648,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_11,c_313]) ).
cnf(c_1553,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_11,c_1648]) ).
cnf(c_1649,plain,
composition(A,B) = join(composition(A,B),composition(A,complement(join(C,complement(B))))),
inference(paramod,[status(thm)],[c_301,c_1553]) ).
cnf(c_1615,plain,
join(composition(A,B),composition(A,complement(join(C,complement(B))))) = composition(A,B),
inference(copy,[status(thm)],[c_1649]) ).
cnf(c_1616,plain,
$false,
inference(resolve,[status(thm)],[c_1615,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL024-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n016.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sat Sep 26 05:36:35 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.46 % Process 87395 was started by sandbox on n016,
% 0.19/5.46 % Sat Sep 26 05:36:35 2026
% 0.19/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/5.47
% 0.19/5.47 % From the command line: assign(max_seconds, 300).
% 13.87/7.26
% 13.87/7.26 % SZS status Unsatisfiable for theBenchmark
% 13.87/7.26
% 13.87/7.26 % Proof 1 at 1.30 (+ 0.45) seconds.
% 13.87/7.26 % Length of proof is 46.
% 13.87/7.26 % Level of proof is 14.
% 13.87/7.26 % Maximum clause weight is 48.000.
% 13.87/7.26 % Given clauses 286.
% 13.87/7.26
% 13.87/7.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------