%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL028-1 : 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 : n017.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 08:24:57 AM UTC 2026
% Result : Unsatisfiable 3.77s 1.60s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 15
% Syntax : Number of formulae : 146 ( 146 unt; 0 def)
% Number of atoms : 146 ( 145 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 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 : 181 ( 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_1680,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_1680]) ).
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_1681,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1682,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1681]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1682]) ).
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(sk2,one) = one,
file('theBenchmark.p',goals_15) ).
cnf(c_22,plain,
join(sk2,one) = one,
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_23,plain,
join(one,sk2) = one,
inference(paramod,[status(thm)],[c_1,c_22]) ).
fof(goals_16,axiom,
composition(sk1,sk2) != meet(sk1,sk2),
file('theBenchmark.p',goals_16) ).
cnf(c_24,plain,
composition(sk1,sk2) != meet(sk1,sk2),
inference(clausify,[status(thm)],[goals_16]) ).
cnf(c_25,plain,
composition(sk1,sk2) != complement(join(complement(sk1),complement(sk2))),
inference(paramod,[status(thm)],[c_6,c_24]) ).
cnf(c_1683,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_27,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_1683]) ).
cnf(c_28,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_29,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1684,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_32,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1684]) ).
cnf(c_1685,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_39,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1685]) ).
cnf(c_1686,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1687,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_1686]) ).
cnf(c_40,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1687]) ).
cnf(c_1688,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_41,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_1688]) ).
cnf(c_1689,plain,
composition(one,A) = join(composition(one,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_49,plain,
join(composition(one,A),composition(sk1,A)) = composition(one,A),
inference(copy,[status(thm)],[c_1689]) ).
cnf(c_1690,plain,
converse(one) = join(converse(one),converse(sk2)),
inference(paramod,[status(thm)],[c_23,c_12]) ).
cnf(c_54,plain,
join(converse(one),converse(sk2)) = converse(one),
inference(copy,[status(thm)],[c_1690]) ).
cnf(c_1691,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_32]) ).
cnf(c_68,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1691]) ).
cnf(c_1692,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_68,c_9]) ).
cnf(c_70,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1692]) ).
cnf(c_74,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_68,c_15]) ).
cnf(c_75,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_70,c_68]) ).
cnf(c_1693,plain,
join(one,converse(sk2)) = converse(one),
inference(paramod,[status(thm)],[c_70,c_54]) ).
cnf(c_76,plain,
join(one,converse(sk2)) = one,
inference(paramod,[status(thm)],[c_70,c_1693]) ).
cnf(c_1694,plain,
join(A,composition(sk1,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_75,c_49]) ).
cnf(c_79,plain,
join(A,composition(sk1,A)) = A,
inference(paramod,[status(thm)],[c_75,c_1694]) ).
cnf(c_80,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_75,c_74]) ).
cnf(c_81,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_80,c_40]) ).
cnf(c_1695,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_29]) ).
cnf(c_1696,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1695]) ).
cnf(c_1697,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1696]) ).
cnf(c_84,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1697]) ).
cnf(c_85,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_84,c_39]) ).
cnf(c_86,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_85,c_84]) ).
cnf(c_87,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_85,c_81]) ).
cnf(c_88,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_1698,plain,
composition(one,A) = join(composition(one,A),composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_76,c_10]) ).
cnf(c_1699,plain,
A = join(composition(one,A),composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_75,c_1698]) ).
cnf(c_1700,plain,
A = join(A,composition(converse(sk2),A)),
inference(paramod,[status(thm)],[c_75,c_1699]) ).
cnf(c_104,plain,
join(A,composition(converse(sk2),A)) = A,
inference(copy,[status(thm)],[c_1700]) ).
cnf(c_1701,plain,
join(A,B) = join(B,join(A,composition(sk1,B))),
inference(paramod,[status(thm)],[c_79,c_27]) ).
cnf(c_133,plain,
join(A,join(B,composition(sk1,A))) = join(B,A),
inference(copy,[status(thm)],[c_1701]) ).
cnf(c_1702,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_85,c_5]) ).
cnf(c_137,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_85,c_1702]) ).
cnf(c_1703,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_85,c_28]) ).
cnf(c_139,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_85,c_1703]) ).
cnf(c_1704,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_88,c_17]) ).
cnf(c_1705,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_3,c_1704]) ).
cnf(c_154,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_17,c_1705]) ).
cnf(c_1706,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_88,c_85]) ).
cnf(c_1707,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_85,c_1706]) ).
cnf(c_155,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1707]) ).
cnf(c_1708,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_154,c_10]) ).
cnf(c_158,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1708]) ).
cnf(c_1709,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_155,c_3]) ).
cnf(c_161,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1709]) ).
cnf(c_1710,plain,
join(A,composition(top,B)) = join(composition(C,B),join(A,composition(complement(C),B))),
inference(paramod,[status(thm)],[c_41,c_27]) ).
cnf(c_178,plain,
join(composition(A,B),join(C,composition(complement(A),B))) = join(C,composition(top,B)),
inference(copy,[status(thm)],[c_1710]) ).
cnf(c_1711,plain,
converse(A) = join(converse(A),converse(composition(converse(sk2),A))),
inference(paramod,[status(thm)],[c_104,c_12]) ).
cnf(c_1712,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sk2)))),
inference(paramod,[status(thm)],[c_13,c_1711]) ).
cnf(c_1713,plain,
converse(A) = join(converse(A),composition(converse(A),sk2)),
inference(paramod,[status(thm)],[c_11,c_1712]) ).
cnf(c_282,plain,
join(converse(A),composition(converse(A),sk2)) = converse(A),
inference(copy,[status(thm)],[c_1713]) ).
cnf(c_438,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_75,c_158]) ).
cnf(c_1714,plain,
join(A,composition(top,B)) = join(B,join(A,composition(top,B))),
inference(paramod,[status(thm)],[c_438,c_27]) ).
cnf(c_442,plain,
join(A,join(B,composition(top,A))) = join(B,composition(top,A)),
inference(copy,[status(thm)],[c_1714]) ).
cnf(c_1715,plain,
join(A,composition(converse(converse(A)),sk2)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_282]) ).
cnf(c_1716,plain,
join(A,composition(A,sk2)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_1715]) ).
cnf(c_684,plain,
join(A,composition(A,sk2)) = A,
inference(paramod,[status(thm)],[c_11,c_1716]) ).
cnf(c_1717,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_137,c_161]) ).
cnf(c_1718,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_1717]) ).
cnf(c_728,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_137,c_1718]) ).
cnf(c_1719,plain,
join(complement(complement(A)),complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_139,c_137]) ).
cnf(c_1720,plain,
join(A,complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_85,c_1719]) ).
cnf(c_1721,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_85,c_1720]) ).
cnf(c_1722,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_1,c_1721]) ).
cnf(c_1723,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_3,c_1722]) ).
cnf(c_1724,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_728,c_1723]) ).
cnf(c_823,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_85,c_1724]) ).
cnf(c_1725,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_139,c_139]) ).
cnf(c_1726,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_85,c_1725]) ).
cnf(c_1727,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_85,c_1726]) ).
cnf(c_1728,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_1,c_1727]) ).
cnf(c_1729,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_3,c_1728]) ).
cnf(c_1730,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_823,c_1729]) ).
cnf(c_1731,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_161,c_1730]) ).
cnf(c_828,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_85,c_1731]) ).
cnf(c_1732,plain,
join(composition(A,sk2),complement(A)) = join(complement(A),composition(top,sk2)),
inference(paramod,[status(thm)],[c_684,c_178]) ).
cnf(c_1733,plain,
join(complement(A),composition(A,sk2)) = join(complement(A),composition(top,sk2)),
inference(paramod,[status(thm)],[c_1,c_1732]) ).
cnf(c_1100,plain,
join(complement(A),composition(top,sk2)) = join(complement(A),composition(A,sk2)),
inference(copy,[status(thm)],[c_1733]) ).
cnf(c_1734,plain,
join(sk2,join(complement(sk1),composition(top,sk2))) = join(complement(sk1),sk2),
inference(paramod,[status(thm)],[c_1100,c_133]) ).
cnf(c_1735,plain,
join(complement(sk1),composition(top,sk2)) = join(complement(sk1),sk2),
inference(paramod,[status(thm)],[c_442,c_1734]) ).
cnf(c_1570,plain,
join(complement(sk1),composition(top,sk2)) = join(sk2,complement(sk1)),
inference(paramod,[status(thm)],[c_1,c_1735]) ).
cnf(c_1736,plain,
join(sk2,complement(sk1)) = join(complement(sk1),composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_1570,c_1100]) ).
cnf(c_1638,plain,
join(complement(sk1),composition(sk1,sk2)) = join(sk2,complement(sk1)),
inference(copy,[status(thm)],[c_1736]) ).
cnf(c_1737,plain,
join(complement(join(sk2,complement(sk1))),complement(join(composition(sk1,sk2),complement(complement(sk1))))) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_1638,c_139]) ).
cnf(c_1738,plain,
join(complement(join(sk2,complement(sk1))),complement(join(composition(sk1,sk2),sk1))) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_85,c_1737]) ).
cnf(c_1739,plain,
join(complement(join(sk2,complement(sk1))),complement(join(sk1,composition(sk1,sk2)))) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_1,c_1738]) ).
cnf(c_1740,plain,
join(complement(join(sk2,complement(sk1))),complement(sk1)) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_684,c_1739]) ).
cnf(c_1741,plain,
join(complement(sk1),complement(join(sk2,complement(sk1)))) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_1,c_1740]) ).
cnf(c_1742,plain,
join(complement(sk1),complement(sk2)) = complement(composition(sk1,sk2)),
inference(paramod,[status(thm)],[c_828,c_1741]) ).
cnf(c_1669,plain,
complement(composition(sk1,sk2)) = join(complement(sk1),complement(sk2)),
inference(copy,[status(thm)],[c_1742]) ).
cnf(c_1743,plain,
complement(join(complement(sk1),complement(sk2))) = composition(sk1,sk2),
inference(paramod,[status(thm)],[c_1669,c_85]) ).
cnf(c_1678,plain,
composition(sk1,sk2) = complement(join(complement(sk1),complement(sk2))),
inference(copy,[status(thm)],[c_1743]) ).
cnf(c_1679,plain,
$false,
inference(resolve,[status(thm)],[c_1678,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL028-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.40 % Computer : n017.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Sat Sep 26 05:28:48 UTC 2026
% 0.08/0.40 % CPUTime :
% 0.08/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.40 % Process 4135226 was started by sandbox on n017,
% 0.08/0.40 % Sat Sep 26 05:28:48 2026
% 0.08/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.41
% 0.10/0.41 % From the command line: assign(max_seconds, 300).
% 3.77/1.60
% 3.77/1.60 % SZS status Unsatisfiable for theBenchmark
% 3.77/1.60
% 3.77/1.60 % Proof 1 at 0.38 (+ 0.15) seconds.
% 3.77/1.60 % Length of proof is 67.
% 3.77/1.60 % Level of proof is 17.
% 3.77/1.60 % Maximum clause weight is 30.000.
% 3.77/1.60 % Given clauses 280.
% 3.77/1.60
% 3.77/1.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------