%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL042+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 : n004.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 08:25:04 AM UTC 2026
% Result : Theorem 0.15s 5.95s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 13
% Syntax : Number of formulae : 201 ( 197 unt; 0 def)
% Number of atoms : 205 ( 204 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 297 ( 13 sgn 28 !; 1 ?)
% 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] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
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_2052,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_2052]) ).
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_2053,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_2053]) ).
fof(nnf_14,plain,
? [X0] :
( join(composition(converse(X0),X0),one) != one
& ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( join(composition(converse(sK0),sK0),one) != one
& ! [X1] : meet(composition(sK0,X1),composition(sK0,complement(X1))) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
meet(composition(sK0,A),composition(sK0,complement(A))) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))) = zero,
inference(paramod,[status(thm)],[c_19,c_31]) ).
cnf(c_33,negated_conjecture,
join(composition(converse(sK0),sK0),one) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_34,negated_conjecture,
join(one,composition(converse(sK0),sK0)) != one,
inference(paramod,[status(thm)],[c_15,c_33]) ).
cnf(c_2054,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_36,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_2054]) ).
cnf(c_37,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_38,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_2055,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_39,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_2055]) ).
cnf(c_2056,plain,
join(complement(join(complement(join(complement(A),B)),join(complement(A),complement(B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_18,c_18]) ).
cnf(c_2057,plain,
join(complement(join(join(complement(A),complement(B)),complement(join(complement(A),B)))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_15,c_2056]) ).
cnf(c_2058,plain,
join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(A)) = join(complement(A),B),
inference(paramod,[status(thm)],[c_16,c_2057]) ).
cnf(c_41,plain,
join(complement(A),complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))) = join(complement(A),B),
inference(paramod,[status(thm)],[c_15,c_2058]) ).
cnf(c_2059,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_45,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_2059]) ).
cnf(c_2060,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_22,c_25]) ).
cnf(c_2061,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_24,c_2060]) ).
cnf(c_2062,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_2061]) ).
cnf(c_2063,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_2062]) ).
cnf(c_2064,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_24,c_2063]) ).
cnf(c_46,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_2064]) ).
cnf(c_2065,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_47,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_2065]) ).
cnf(c_2066,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_57,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_2066]) ).
cnf(c_2067,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_22]) ).
cnf(c_59,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_2067]) ).
cnf(c_2068,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_60,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_2068]) ).
cnf(c_2069,plain,
join(complement(join(zero,A)),complement(join(complement(top),complement(A)))) = top,
inference(paramod,[status(thm)],[c_30,c_18]) ).
cnf(c_61,plain,
join(complement(join(zero,A)),complement(join(zero,complement(A)))) = top,
inference(paramod,[status(thm)],[c_30,c_2069]) ).
cnf(c_2070,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_27]) ).
cnf(c_63,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_30,c_2070]) ).
cnf(c_2071,plain,
join(complement(join(zero,A)),complement(join(complement(join(complement(composition(sK0,B)),complement(composition(sK0,complement(B))))),complement(A)))) = join(complement(composition(sK0,B)),complement(composition(sK0,complement(B)))),
inference(paramod,[status(thm)],[c_32,c_18]) ).
cnf(c_2072,plain,
join(complement(join(zero,A)),complement(join(zero,complement(A)))) = join(complement(composition(sK0,B)),complement(composition(sK0,complement(B)))),
inference(paramod,[status(thm)],[c_32,c_2071]) ).
cnf(c_2073,plain,
top = join(complement(composition(sK0,B)),complement(composition(sK0,complement(B)))),
inference(paramod,[status(thm)],[c_61,c_2072]) ).
cnf(c_65,plain,
join(complement(composition(sK0,A)),complement(composition(sK0,complement(A)))) = top,
inference(copy,[status(thm)],[c_2073]) ).
cnf(c_2074,plain,
join(complement(join(complement(composition(sK0,A)),composition(sK0,complement(A)))),zero) = composition(sK0,A),
inference(paramod,[status(thm)],[c_32,c_18]) ).
cnf(c_67,plain,
join(zero,complement(join(complement(composition(sK0,A)),composition(sK0,complement(A))))) = composition(sK0,A),
inference(paramod,[status(thm)],[c_15,c_2074]) ).
cnf(c_2075,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_2076,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2075]) ).
cnf(c_2077,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_2076]) ).
cnf(c_93,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2077]) ).
cnf(c_2078,plain,
join(complement(join(complement(join(complement(A),complement(B))),join(complement(B),A))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_38,c_38]) ).
cnf(c_2079,plain,
join(complement(join(join(complement(B),A),complement(join(complement(A),complement(B))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_15,c_2078]) ).
cnf(c_2080,plain,
join(complement(join(complement(B),join(A,complement(join(complement(A),complement(B)))))),complement(B)) = join(complement(A),complement(B)),
inference(paramod,[status(thm)],[c_16,c_2079]) ).
cnf(c_98,plain,
join(complement(A),complement(join(complement(A),join(B,complement(join(complement(B),complement(A))))))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_15,c_2080]) ).
cnf(c_99,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_93,c_57]) ).
cnf(c_100,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_93]) ).
cnf(c_2081,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_45]) ).
cnf(c_108,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_2081]) ).
cnf(c_2082,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_108,c_21]) ).
cnf(c_110,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2082]) ).
cnf(c_114,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_108,c_27]) ).
cnf(c_115,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_110,c_108]) ).
cnf(c_116,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_115,c_114]) ).
cnf(c_120,plain,
join(complement(join(A,B)),complement(join(complement(join(complement(A),C)),complement(join(complement(join(complement(A),complement(C))),B))))) = join(complement(A),C),
inference(paramod,[status(thm)],[c_39,c_18]) ).
cnf(c_2083,plain,
join(complement(join(complement(A),B)),B) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_37,c_39]) ).
cnf(c_2084,plain,
join(B,complement(join(complement(A),B))) = join(A,complement(join(complement(B),complement(complement(A))))),
inference(paramod,[status(thm)],[c_15,c_2083]) ).
cnf(c_136,plain,
join(A,complement(join(complement(B),A))) = join(B,complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_99,c_2084]) ).
cnf(c_2085,plain,
join(A,join(complement(B),C)) = join(complement(B),join(A,complement(join(complement(B),join(complement(C),complement(join(complement(B),C))))))),
inference(paramod,[status(thm)],[c_41,c_36]) ).
cnf(c_150,plain,
join(complement(A),join(B,complement(join(complement(A),join(complement(C),complement(join(complement(A),C))))))) = join(B,join(complement(A),C)),
inference(copy,[status(thm)],[c_2085]) ).
cnf(c_2086,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),complement(complement(A))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_41,c_37]) ).
cnf(c_2087,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(complement(A),join(complement(B),complement(join(complement(A),B))))),A))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_99,c_2086]) ).
cnf(c_152,plain,
join(complement(join(complement(A),B)),complement(join(A,complement(join(complement(A),join(complement(B),complement(join(complement(A),B)))))))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_15,c_2087]) ).
cnf(c_2088,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_116,c_18]) ).
cnf(c_2089,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_15,c_2088]) ).
cnf(c_2090,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_28,c_2089]) ).
cnf(c_2091,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_30,c_2090]) ).
cnf(c_176,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_99,c_2091]) ).
cnf(c_2092,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_116,c_39]) ).
cnf(c_2093,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_18,c_2092]) ).
cnf(c_179,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_2093]) ).
cnf(c_188,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_176,c_100]) ).
cnf(c_189,plain,
complement(join(complement(composition(sK0,A)),composition(sK0,complement(A)))) = composition(sK0,A),
inference(paramod,[status(thm)],[c_176,c_67]) ).
cnf(c_190,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_176,c_63]) ).
cnf(c_192,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(B),complement(A)),
inference(paramod,[status(thm)],[c_179,c_98]) ).
cnf(c_2094,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_188,c_18]) ).
cnf(c_2095,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_188,c_2094]) ).
cnf(c_2096,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_18,c_2095]) ).
cnf(c_219,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2096]) ).
cnf(c_2097,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_23,c_46]) ).
cnf(c_2098,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_23,c_2097]) ).
cnf(c_231,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_2098]) ).
cnf(c_2099,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_219,c_16]) ).
cnf(c_250,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_2099]) ).
cnf(c_2100,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_219,c_39]) ).
cnf(c_2101,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_15,c_2100]) ).
cnf(c_2102,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_179,c_2101]) ).
cnf(c_253,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_15,c_2102]) ).
cnf(c_2103,plain,
join(complement(join(complement(A),B)),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_253,c_152]) ).
cnf(c_2104,plain,
join(complement(A),complement(join(complement(A),B))) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_15,c_2103]) ).
cnf(c_2105,plain,
join(complement(B),complement(A)) = join(complement(A),join(complement(B),complement(join(complement(A),B)))),
inference(paramod,[status(thm)],[c_192,c_2104]) ).
cnf(c_255,plain,
join(complement(A),join(complement(B),complement(join(complement(A),B)))) = join(complement(B),complement(A)),
inference(copy,[status(thm)],[c_2105]) ).
cnf(c_258,plain,
join(complement(A),join(B,complement(join(complement(C),complement(A))))) = join(B,join(complement(A),C)),
inference(paramod,[status(thm)],[c_255,c_150]) ).
cnf(c_2106,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_18]) ).
cnf(c_271,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_2106]) ).
cnf(c_336,plain,
join(one,converse(complement(one))) = converse(top),
inference(paramod,[status(thm)],[c_110,c_60]) ).
cnf(c_2107,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_28,c_250]) ).
cnf(c_376,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_2107]) ).
cnf(c_2108,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_60,c_250]) ).
cnf(c_377,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_60,c_2108]) ).
cnf(c_2109,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_376,c_15]) ).
cnf(c_380,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_2109]) ).
cnf(c_400,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_115,c_59]) ).
cnf(c_411,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_377]) ).
cnf(c_416,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_411,c_380]) ).
cnf(c_425,plain,
join(one,converse(complement(one))) = top,
inference(paramod,[status(thm)],[c_416,c_336]) ).
cnf(c_2110,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_400,c_24]) ).
cnf(c_2111,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_25,c_2110]) ).
cnf(c_2112,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_416,c_2111]) ).
cnf(c_2113,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_25,c_2112]) ).
cnf(c_574,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_2113]) ).
cnf(c_2114,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(complement(A)),C)))) = complement(A),
inference(paramod,[status(thm)],[c_253,c_47]) ).
cnf(c_2115,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(A,C)))) = complement(A),
inference(paramod,[status(thm)],[c_99,c_2114]) ).
cnf(c_765,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_47,c_2115]) ).
cnf(c_770,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_765]) ).
cnf(c_2116,plain,
join(complement(join(composition(sK0,A),B)),complement(join(complement(join(complement(composition(sK0,A)),composition(sK0,complement(A)))),complement(join(complement(top),B))))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_65,c_120]) ).
cnf(c_2117,plain,
join(complement(join(composition(sK0,A),B)),complement(join(composition(sK0,A),complement(join(complement(top),B))))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_189,c_2116]) ).
cnf(c_2118,plain,
join(complement(join(composition(sK0,A),B)),complement(join(composition(sK0,A),complement(join(zero,B))))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_30,c_2117]) ).
cnf(c_2119,plain,
join(complement(join(composition(sK0,A),B)),complement(join(composition(sK0,A),complement(B)))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_176,c_2118]) ).
cnf(c_2120,plain,
complement(composition(sK0,A)) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_271,c_2119]) ).
cnf(c_838,plain,
join(complement(composition(sK0,A)),composition(sK0,complement(A))) = complement(composition(sK0,A)),
inference(copy,[status(thm)],[c_2120]) ).
cnf(c_2121,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(C),complement(A))))) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_136,c_47]) ).
cnf(c_2122,plain,
join(composition(converse(B),complement(composition(B,A))),join(complement(A),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_258,c_2121]) ).
cnf(c_2123,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_36,c_2122]) ).
cnf(c_2124,plain,
join(complement(A),C) = join(C,complement(join(complement(complement(A)),C))),
inference(paramod,[status(thm)],[c_47,c_2123]) ).
cnf(c_2125,plain,
join(complement(A),C) = join(C,complement(join(A,C))),
inference(paramod,[status(thm)],[c_99,c_2124]) ).
cnf(c_1021,plain,
join(A,complement(join(B,A))) = join(complement(B),A),
inference(copy,[status(thm)],[c_2125]) ).
cnf(c_1042,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_15,c_1021]) ).
cnf(c_2126,plain,
join(converse(complement(one)),complement(top)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_425,c_1021]) ).
cnf(c_2127,plain,
join(converse(complement(one)),zero) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_30,c_2126]) ).
cnf(c_2128,plain,
join(zero,converse(complement(one))) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_2127]) ).
cnf(c_2129,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_176,c_2128]) ).
cnf(c_1053,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(copy,[status(thm)],[c_2129]) ).
cnf(c_2130,plain,
converse(converse(complement(one))) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_1053,c_24]) ).
cnf(c_2131,plain,
complement(one) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_23,c_2130]) ).
cnf(c_2132,plain,
complement(one) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_23,c_2131]) ).
cnf(c_2133,plain,
complement(one) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_15,c_2132]) ).
cnf(c_2134,plain,
complement(one) = converse(complement(one)),
inference(paramod,[status(thm)],[c_1053,c_2133]) ).
cnf(c_1069,plain,
converse(complement(one)) = complement(one),
inference(copy,[status(thm)],[c_2134]) ).
cnf(c_1071,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_1069,c_574]) ).
cnf(c_2135,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_1071]) ).
cnf(c_2136,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_23,c_2135]) ).
cnf(c_1276,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_23,c_2136]) ).
cnf(c_2137,plain,
join(A,complement(composition(A,top))) = join(complement(composition(A,complement(one))),A),
inference(paramod,[status(thm)],[c_1276,c_1042]) ).
cnf(c_2138,plain,
join(A,complement(composition(A,top))) = join(A,complement(composition(A,complement(one)))),
inference(paramod,[status(thm)],[c_15,c_2137]) ).
cnf(c_1302,plain,
join(A,complement(composition(A,complement(one)))) = join(A,complement(composition(A,top))),
inference(copy,[status(thm)],[c_2138]) ).
cnf(c_2139,plain,
join(complement(sK0),composition(sK0,complement(one))) = complement(composition(sK0,one)),
inference(paramod,[status(thm)],[c_21,c_838]) ).
cnf(c_1428,plain,
join(complement(sK0),composition(sK0,complement(one))) = complement(sK0),
inference(paramod,[status(thm)],[c_21,c_2139]) ).
cnf(c_2140,plain,
join(complement(composition(sK0,complement(one))),complement(complement(sK0))) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_1428,c_770]) ).
cnf(c_2141,plain,
join(complement(composition(sK0,complement(one))),sK0) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_99,c_2140]) ).
cnf(c_2142,plain,
join(sK0,complement(composition(sK0,complement(one)))) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_15,c_2141]) ).
cnf(c_2143,plain,
join(sK0,complement(composition(sK0,top))) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_1302,c_2142]) ).
cnf(c_1438,plain,
complement(composition(sK0,complement(one))) = join(sK0,complement(composition(sK0,top))),
inference(copy,[status(thm)],[c_2143]) ).
cnf(c_2144,plain,
join(complement(complement(one)),composition(converse(sK0),join(sK0,complement(composition(sK0,top))))) = complement(complement(one)),
inference(paramod,[status(thm)],[c_1438,c_27]) ).
cnf(c_2145,plain,
join(one,composition(converse(sK0),join(sK0,complement(composition(sK0,top))))) = complement(complement(one)),
inference(paramod,[status(thm)],[c_99,c_2144]) ).
cnf(c_1443,plain,
join(one,composition(converse(sK0),join(sK0,complement(composition(sK0,top))))) = one,
inference(paramod,[status(thm)],[c_99,c_2145]) ).
cnf(c_2146,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_231]) ).
cnf(c_1694,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_2146]) ).
cnf(c_2147,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_23,c_1694]) ).
cnf(c_2016,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_23,c_2147]) ).
cnf(c_2148,plain,
join(one,join(composition(converse(sK0),sK0),composition(converse(sK0),complement(composition(sK0,top))))) = one,
inference(paramod,[status(thm)],[c_2016,c_1443]) ).
cnf(c_2149,plain,
join(one,join(composition(converse(sK0),sK0),zero)) = one,
inference(paramod,[status(thm)],[c_190,c_2148]) ).
cnf(c_2150,plain,
join(one,join(zero,composition(converse(sK0),sK0))) = one,
inference(paramod,[status(thm)],[c_15,c_2149]) ).
cnf(c_2050,plain,
join(one,composition(converse(sK0),sK0)) = one,
inference(paramod,[status(thm)],[c_176,c_2150]) ).
cnf(c_2051,plain,
$false,
inference(resolve,[status(thm)],[c_2050,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL042+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 05:40:14 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 934277 was started by sandbox2 on n004,
% 0.11/5.38 % Sat Sep 26 05:40:14 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.95
% 0.15/5.95 % SZS status Theorem for theBenchmark
% 0.15/5.95
% 0.15/5.95 % Proof 1 at 0.43 (+ 0.10) seconds.
% 0.15/5.95 % Length of proof is 99.
% 0.15/5.95 % Level of proof is 23.
% 0.15/5.95 % Maximum clause weight is 93.000.
% 0.15/5.95 % Given clauses 182.
% 0.15/5.95
% 0.15/5.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------