%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Theorem 6.90s 1.40s
% Output : CNFRefutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 13
% Syntax : Number of formulae : 144 ( 140 unt; 0 def)
% Number of atoms : 152 ( 151 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 5 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 183 ( 4 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0,X1] :
( ( join(X1,one) = one
& join(X0,one) = one )
=> composition(X0,X1) = meet(X0,X1) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( join(X1,one) = one
& join(X0,one) = one )
=> composition(X0,X1) = meet(X0,X1) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_15,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_16,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_17,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_18,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_15,c_17]) ).
cnf(c_19,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_21,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_22,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_23,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_24,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_26,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_1691,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_15,c_26]) ).
cnf(c_27,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_1691]) ).
cnf(c_28,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_29,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_1692,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_30,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_28,c_1692]) ).
fof(nnf_14,plain,
? [X0,X1] :
( composition(X0,X1) != meet(X0,X1)
& join(X1,one) = one
& join(X0,one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( composition(sK0,sK1) != meet(sK0,sK1)
& join(sK1,one) = one
& join(sK0,one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
join(sK0,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
join(one,sK0) = one,
inference(paramod,[status(thm)],[c_15,c_31]) ).
cnf(c_33,negated_conjecture,
join(sK1,one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_34,negated_conjecture,
join(one,sK1) = one,
inference(paramod,[status(thm)],[c_15,c_33]) ).
cnf(c_35,negated_conjecture,
composition(sK0,sK1) != meet(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_36,negated_conjecture,
composition(sK0,sK1) != complement(join(complement(sK0),complement(sK1))),
inference(paramod,[status(thm)],[c_19,c_35]) ).
cnf(c_1693,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_38,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_1693]) ).
cnf(c_39,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_40,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_1694,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_43,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1694]) ).
cnf(c_1695,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_50,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_1695]) ).
cnf(c_1696,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_1697,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_1696]) ).
cnf(c_51,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_1697]) ).
cnf(c_1698,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_22]) ).
cnf(c_52,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_1698]) ).
cnf(c_1699,plain,
composition(one,A) = join(composition(one,A),composition(sK0,A)),
inference(paramod,[status(thm)],[c_32,c_22]) ).
cnf(c_60,plain,
join(composition(one,A),composition(sK0,A)) = composition(one,A),
inference(copy,[status(thm)],[c_1699]) ).
cnf(c_1700,plain,
converse(one) = join(converse(one),converse(sK1)),
inference(paramod,[status(thm)],[c_34,c_24]) ).
cnf(c_65,plain,
join(converse(one),converse(sK1)) = converse(one),
inference(copy,[status(thm)],[c_1700]) ).
cnf(c_1701,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_43]) ).
cnf(c_79,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_1701]) ).
cnf(c_1702,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_79,c_21]) ).
cnf(c_81,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1702]) ).
cnf(c_85,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_79,c_27]) ).
cnf(c_86,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_81,c_79]) ).
cnf(c_1703,plain,
join(one,converse(sK1)) = converse(one),
inference(paramod,[status(thm)],[c_81,c_65]) ).
cnf(c_87,plain,
join(one,converse(sK1)) = one,
inference(paramod,[status(thm)],[c_81,c_1703]) ).
cnf(c_1704,plain,
join(A,composition(sK0,A)) = composition(one,A),
inference(paramod,[status(thm)],[c_86,c_60]) ).
cnf(c_90,plain,
join(A,composition(sK0,A)) = A,
inference(paramod,[status(thm)],[c_86,c_1704]) ).
cnf(c_91,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_86,c_85]) ).
cnf(c_92,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_91,c_51]) ).
cnf(c_1705,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_40]) ).
cnf(c_1706,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1705]) ).
cnf(c_1707,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_1706]) ).
cnf(c_95,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1707]) ).
cnf(c_96,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_95,c_50]) ).
cnf(c_97,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_95]) ).
cnf(c_98,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_96,c_92]) ).
cnf(c_99,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_98,c_97]) ).
cnf(c_1708,plain,
composition(one,A) = join(composition(one,A),composition(converse(sK1),A)),
inference(paramod,[status(thm)],[c_87,c_22]) ).
cnf(c_1709,plain,
A = join(composition(one,A),composition(converse(sK1),A)),
inference(paramod,[status(thm)],[c_86,c_1708]) ).
cnf(c_1710,plain,
A = join(A,composition(converse(sK1),A)),
inference(paramod,[status(thm)],[c_86,c_1709]) ).
cnf(c_115,plain,
join(A,composition(converse(sK1),A)) = A,
inference(copy,[status(thm)],[c_1710]) ).
cnf(c_1711,plain,
join(A,B) = join(B,join(A,composition(sK0,B))),
inference(paramod,[status(thm)],[c_90,c_38]) ).
cnf(c_144,plain,
join(A,join(B,composition(sK0,A))) = join(B,A),
inference(copy,[status(thm)],[c_1711]) ).
cnf(c_1712,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_18]) ).
cnf(c_148,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_96,c_1712]) ).
cnf(c_1713,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_96,c_39]) ).
cnf(c_150,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_96,c_1713]) ).
cnf(c_1714,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_99,c_28]) ).
cnf(c_1715,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_16,c_1714]) ).
cnf(c_165,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_1715]) ).
cnf(c_1716,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_99,c_96]) ).
cnf(c_1717,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_96,c_1716]) ).
cnf(c_166,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1717]) ).
cnf(c_1718,plain,
composition(top,A) = join(composition(B,A),composition(top,A)),
inference(paramod,[status(thm)],[c_165,c_22]) ).
cnf(c_169,plain,
join(composition(A,B),composition(top,B)) = composition(top,B),
inference(copy,[status(thm)],[c_1718]) ).
cnf(c_1719,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_166,c_16]) ).
cnf(c_172,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1719]) ).
cnf(c_1720,plain,
join(A,composition(top,B)) = join(composition(C,B),join(A,composition(complement(C),B))),
inference(paramod,[status(thm)],[c_52,c_38]) ).
cnf(c_189,plain,
join(composition(A,B),join(C,composition(complement(A),B))) = join(C,composition(top,B)),
inference(copy,[status(thm)],[c_1720]) ).
cnf(c_1721,plain,
converse(A) = join(converse(A),converse(composition(converse(sK1),A))),
inference(paramod,[status(thm)],[c_115,c_24]) ).
cnf(c_1722,plain,
converse(A) = join(converse(A),composition(converse(A),converse(converse(sK1)))),
inference(paramod,[status(thm)],[c_25,c_1721]) ).
cnf(c_1723,plain,
converse(A) = join(converse(A),composition(converse(A),sK1)),
inference(paramod,[status(thm)],[c_23,c_1722]) ).
cnf(c_293,plain,
join(converse(A),composition(converse(A),sK1)) = converse(A),
inference(copy,[status(thm)],[c_1723]) ).
cnf(c_449,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_86,c_169]) ).
cnf(c_1724,plain,
join(A,composition(top,B)) = join(B,join(A,composition(top,B))),
inference(paramod,[status(thm)],[c_449,c_38]) ).
cnf(c_453,plain,
join(A,join(B,composition(top,A))) = join(B,composition(top,A)),
inference(copy,[status(thm)],[c_1724]) ).
cnf(c_1725,plain,
join(A,composition(converse(converse(A)),sK1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_293]) ).
cnf(c_1726,plain,
join(A,composition(A,sK1)) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_1725]) ).
cnf(c_695,plain,
join(A,composition(A,sK1)) = A,
inference(paramod,[status(thm)],[c_23,c_1726]) ).
cnf(c_1727,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_148,c_172]) ).
cnf(c_1728,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_1727]) ).
cnf(c_739,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_148,c_1728]) ).
cnf(c_1729,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_150,c_148]) ).
cnf(c_1730,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_96,c_1729]) ).
cnf(c_1731,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_96,c_1730]) ).
cnf(c_1732,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_15,c_1731]) ).
cnf(c_1733,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_16,c_1732]) ).
cnf(c_1734,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_739,c_1733]) ).
cnf(c_834,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_96,c_1734]) ).
cnf(c_1735,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_150,c_150]) ).
cnf(c_1736,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_96,c_1735]) ).
cnf(c_1737,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_96,c_1736]) ).
cnf(c_1738,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_1737]) ).
cnf(c_1739,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_16,c_1738]) ).
cnf(c_1740,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_834,c_1739]) ).
cnf(c_1741,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_172,c_1740]) ).
cnf(c_839,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_96,c_1741]) ).
cnf(c_1742,plain,
join(composition(A,sK1),complement(A)) = join(complement(A),composition(top,sK1)),
inference(paramod,[status(thm)],[c_695,c_189]) ).
cnf(c_1743,plain,
join(complement(A),composition(A,sK1)) = join(complement(A),composition(top,sK1)),
inference(paramod,[status(thm)],[c_15,c_1742]) ).
cnf(c_1111,plain,
join(complement(A),composition(top,sK1)) = join(complement(A),composition(A,sK1)),
inference(copy,[status(thm)],[c_1743]) ).
cnf(c_1744,plain,
join(sK1,join(complement(sK0),composition(top,sK1))) = join(complement(sK0),sK1),
inference(paramod,[status(thm)],[c_1111,c_144]) ).
cnf(c_1745,plain,
join(complement(sK0),composition(top,sK1)) = join(complement(sK0),sK1),
inference(paramod,[status(thm)],[c_453,c_1744]) ).
cnf(c_1581,plain,
join(complement(sK0),composition(top,sK1)) = join(sK1,complement(sK0)),
inference(paramod,[status(thm)],[c_15,c_1745]) ).
cnf(c_1746,plain,
join(sK1,complement(sK0)) = join(complement(sK0),composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_1581,c_1111]) ).
cnf(c_1649,plain,
join(complement(sK0),composition(sK0,sK1)) = join(sK1,complement(sK0)),
inference(copy,[status(thm)],[c_1746]) ).
cnf(c_1747,plain,
join(complement(join(sK1,complement(sK0))),complement(join(composition(sK0,sK1),complement(complement(sK0))))) = complement(composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_1649,c_150]) ).
cnf(c_1748,plain,
join(complement(join(sK1,complement(sK0))),complement(join(composition(sK0,sK1),sK0))) = complement(composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_96,c_1747]) ).
cnf(c_1749,plain,
join(complement(join(sK1,complement(sK0))),complement(join(sK0,composition(sK0,sK1)))) = complement(composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_15,c_1748]) ).
cnf(c_1750,plain,
join(complement(join(sK1,complement(sK0))),complement(sK0)) = complement(composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_695,c_1749]) ).
cnf(c_1751,plain,
join(complement(sK0),complement(join(sK1,complement(sK0)))) = complement(composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_15,c_1750]) ).
cnf(c_1752,plain,
join(complement(sK0),complement(sK1)) = complement(composition(sK0,sK1)),
inference(paramod,[status(thm)],[c_839,c_1751]) ).
cnf(c_1680,plain,
complement(composition(sK0,sK1)) = join(complement(sK0),complement(sK1)),
inference(copy,[status(thm)],[c_1752]) ).
cnf(c_1753,plain,
complement(join(complement(sK0),complement(sK1))) = composition(sK0,sK1),
inference(paramod,[status(thm)],[c_1680,c_96]) ).
cnf(c_1689,plain,
composition(sK0,sK1) = complement(join(complement(sK0),complement(sK1))),
inference(copy,[status(thm)],[c_1753]) ).
cnf(c_1690,plain,
$false,
inference(resolve,[status(thm)],[c_1689,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL028+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n009.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 05:33:14 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3464233 was started by sandbox2 on n009,
% 0.16/0.42 % Sat Sep 26 05:33:14 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 6.90/1.40
% 6.90/1.40 % SZS status Theorem for theBenchmark
% 6.90/1.40
% 6.90/1.40 % Proof 1 at 0.70 (+ 0.22) seconds.
% 6.90/1.40 % Length of proof is 78.
% 6.90/1.40 % Level of proof is 18.
% 6.90/1.40 % Maximum clause weight is 30.000.
% 6.90/1.40 % Given clauses 280.
% 6.90/1.40
% 6.90/1.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------