%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL043+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 08:25:05 AM UTC 2026
% Result : Theorem 32.08s 9.60s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 14
% Syntax : Number of formulae : 164 ( 160 unt; 0 def)
% Number of atoms : 168 ( 167 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 11 ( 3 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 : 210 ( 23 sgn 31 !; 3 ?)
% 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(modular_law_2,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2),
file('theBenchmark.p',modular_law_2) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( join(composition(X0,converse(X1)),X2) = X2
=> join(composition(complement(X2),X1),complement(X0)) = complement(X0) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(composition(X0,converse(X1)),X2) = X2
=> join(composition(complement(X2),X1),complement(X0)) = complement(X0) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_20,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_21,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_22,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_24,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_27,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_28,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_29,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_8420,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_30,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_8420]) ).
cnf(c_31,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_32,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_8421,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_8421]) ).
cnf(c_38,plain,
meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(clausify,[status(thm)],[modular_law_2]) ).
cnf(c_8422,plain,
meet(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_22,c_38]) ).
cnf(c_8423,plain,
complement(join(complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)),complement(B))) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_22,c_8422]) ).
cnf(c_8424,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_18,c_8423]) ).
cnf(c_8425,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),meet(composition(meet(A,composition(B,converse(C))),C),B)),
inference(paramod,[status(thm)],[c_22,c_8424]) ).
cnf(c_8426,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),meet(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C),B)),
inference(paramod,[status(thm)],[c_22,c_8425]) ).
cnf(c_8427,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),complement(join(complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)),complement(B)))),
inference(paramod,[status(thm)],[c_22,c_8426]) ).
cnf(c_8428,plain,
complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C)))) = join(complement(join(complement(composition(A,C)),complement(B))),complement(join(complement(B),complement(composition(complement(join(complement(A),complement(composition(B,converse(C))))),C))))),
inference(paramod,[status(thm)],[c_18,c_8427]) ).
cnf(c_39,plain,
join(complement(join(complement(composition(A,B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(complement(A),complement(composition(C,converse(B))))),B)))),
inference(copy,[status(thm)],[c_8428]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( complement(X0) != join(composition(complement(X2),X1),complement(X0))
& join(composition(X0,converse(X1)),X2) = X2 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( complement(sK0) != join(composition(complement(sK2),sK1),complement(sK0))
& join(composition(sK0,converse(sK1)),sK2) = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
join(composition(sK0,converse(sK1)),sK2) = sK2,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,negated_conjecture,
join(sK2,composition(sK0,converse(sK1))) = sK2,
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_42,negated_conjecture,
complement(sK0) != join(composition(complement(sK2),sK1),complement(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_8429,negated_conjecture,
complement(sK0) != join(complement(sK0),composition(complement(sK2),sK1)),
inference(paramod,[status(thm)],[c_18,c_42]) ).
cnf(c_43,negated_conjecture,
join(complement(sK0),composition(complement(sK2),sK1)) != complement(sK0),
inference(copy,[status(thm)],[c_8429]) ).
cnf(c_8430,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_45,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_19,c_8430]) ).
cnf(c_47,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_8431,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_48,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_8431]) ).
cnf(c_8432,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_54,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_8432]) ).
cnf(c_8433,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_66,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_8433]) ).
cnf(c_8434,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_8435,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_8434]) ).
cnf(c_67,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_8435]) ).
cnf(c_8436,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_69,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_8436]) ).
cnf(c_8437,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_33,c_30]) ).
cnf(c_72,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_33,c_8437]) ).
cnf(c_8438,plain,
join(A,B) = join(complement(join(complement(B),C)),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_21,c_45]) ).
cnf(c_132,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_8438]) ).
cnf(c_8439,plain,
join(A,top) = join(B,join(A,complement(B))),
inference(paramod,[status(thm)],[c_31,c_45]) ).
cnf(c_134,plain,
join(A,join(B,complement(A))) = join(B,top),
inference(copy,[status(thm)],[c_8439]) ).
cnf(c_8440,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_54]) ).
cnf(c_145,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_8440]) ).
cnf(c_8441,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_145,c_24]) ).
cnf(c_154,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_8441]) ).
cnf(c_158,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_145,c_30]) ).
cnf(c_176,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_154,c_145]) ).
cnf(c_181,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_176,c_158]) ).
cnf(c_182,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_181,c_67]) ).
cnf(c_8442,plain,
converse(A) = join(converse(zero),converse(complement(complement(A)))),
inference(paramod,[status(thm)],[c_182,c_27]) ).
cnf(c_199,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(copy,[status(thm)],[c_8442]) ).
cnf(c_8443,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_8444,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_8443]) ).
cnf(c_8445,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_8444]) ).
cnf(c_224,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_8445]) ).
cnf(c_232,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_224,c_66]) ).
cnf(c_243,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_232,c_199]) ).
cnf(c_245,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_232,c_182]) ).
cnf(c_258,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_245,c_72]) ).
cnf(c_8446,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_232,c_21]) ).
cnf(c_260,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_232,c_8446]) ).
cnf(c_262,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_33,c_232]) ).
cnf(c_8447,plain,
join(complement(join(complement(composition(complement(A),B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(A,complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(complement(complement(A)),complement(composition(C,converse(B))))),B)))),
inference(paramod,[status(thm)],[c_232,c_39]) ).
cnf(c_269,plain,
join(complement(join(complement(composition(complement(A),B)),complement(C))),complement(join(complement(C),complement(composition(complement(join(A,complement(composition(C,converse(B))))),B))))) = complement(join(complement(C),complement(composition(complement(join(A,complement(composition(C,converse(B))))),B)))),
inference(paramod,[status(thm)],[c_232,c_8447]) ).
cnf(c_8448,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_232,c_181]) ).
cnf(c_8449,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_232,c_8448]) ).
cnf(c_271,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_232,c_8449]) ).
cnf(c_8450,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_245,c_18]) ).
cnf(c_282,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_8450]) ).
cnf(c_8451,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_271,c_19]) ).
cnf(c_283,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_8451]) ).
cnf(c_8452,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_271,c_48]) ).
cnf(c_8453,plain,
complement(complement(A)) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_260,c_8452]) ).
cnf(c_8454,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_232,c_8453]) ).
cnf(c_305,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_8454]) ).
cnf(c_8455,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_271,c_48]) ).
cnf(c_8456,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_18,c_8455]) ).
cnf(c_8457,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_305,c_8456]) ).
cnf(c_306,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_18,c_8457]) ).
cnf(c_8458,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_243]) ).
cnf(c_323,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_26,c_8458]) ).
cnf(c_8459,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_323,c_282]) ).
cnf(c_328,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_8459]) ).
cnf(c_8460,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_31,c_283]) ).
cnf(c_386,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_8460]) ).
cnf(c_8461,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_69,c_283]) ).
cnf(c_387,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_69,c_8461]) ).
cnf(c_389,plain,
join(A,join(B,complement(A))) = top,
inference(paramod,[status(thm)],[c_386,c_134]) ).
cnf(c_8462,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_386,c_18]) ).
cnf(c_390,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_8462]) ).
cnf(c_422,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_387]) ).
cnf(c_427,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_422,c_390]) ).
cnf(c_446,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_427,c_258]) ).
cnf(c_462,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_232,c_389]) ).
cnf(c_8463,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_446,c_25]) ).
cnf(c_8464,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_390,c_8463]) ).
cnf(c_8465,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_446,c_8464]) ).
cnf(c_8466,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_245,c_8465]) ).
cnf(c_492,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_8466]) ).
cnf(c_8467,plain,
join(complement(composition(sK0,converse(sK1))),sK2) = top,
inference(paramod,[status(thm)],[c_41,c_462]) ).
cnf(c_497,plain,
join(sK2,complement(composition(sK0,converse(sK1)))) = top,
inference(paramod,[status(thm)],[c_18,c_8467]) ).
cnf(c_8468,plain,
converse(zero) = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_492,c_28]) ).
cnf(c_8469,plain,
zero = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_328,c_8468]) ).
cnf(c_503,plain,
composition(converse(complement(composition(top,top))),converse(A)) = zero,
inference(copy,[status(thm)],[c_8469]) ).
cnf(c_8470,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_492,c_176]) ).
cnf(c_505,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_8470]) ).
cnf(c_8471,plain,
composition(converse(zero),converse(A)) = zero,
inference(paramod,[status(thm)],[c_505,c_503]) ).
cnf(c_508,plain,
composition(zero,converse(A)) = zero,
inference(paramod,[status(thm)],[c_328,c_8471]) ).
cnf(c_529,plain,
composition(zero,A) = zero,
inference(paramod,[status(thm)],[c_26,c_508]) ).
cnf(c_543,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_306]) ).
cnf(c_8472,plain,
join(complement(join(complement(A),B)),B) = join(B,A),
inference(paramod,[status(thm)],[c_543,c_132]) ).
cnf(c_4008,plain,
join(A,complement(join(complement(B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_18,c_8472]) ).
cnf(c_4089,plain,
join(A,complement(join(A,complement(B)))) = join(A,B),
inference(paramod,[status(thm)],[c_18,c_4008]) ).
cnf(c_4758,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_232,c_4089]) ).
cnf(c_8473,plain,
join(complement(join(complement(composition(complement(sK2),sK1)),complement(sK0))),complement(join(complement(sK0),complement(composition(complement(top),sK1))))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_497,c_269]) ).
cnf(c_8474,plain,
join(complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))),complement(join(complement(sK0),complement(composition(complement(top),sK1))))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_18,c_8473]) ).
cnf(c_8475,plain,
join(complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))),complement(join(complement(sK0),complement(composition(zero,sK1))))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_33,c_8474]) ).
cnf(c_8476,plain,
join(complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))),complement(join(complement(sK0),complement(zero)))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_529,c_8475]) ).
cnf(c_8477,plain,
join(complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))),complement(join(complement(sK0),top))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_262,c_8476]) ).
cnf(c_8478,plain,
join(complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))),complement(join(top,complement(sK0)))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_18,c_8477]) ).
cnf(c_8479,plain,
join(complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))),complement(top)) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_390,c_8478]) ).
cnf(c_8480,plain,
join(complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))),zero) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_33,c_8479]) ).
cnf(c_8481,plain,
join(zero,complement(join(complement(sK0),complement(composition(complement(sK2),sK1))))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_18,c_8480]) ).
cnf(c_8482,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = complement(join(complement(sK0),complement(composition(complement(join(sK2,complement(composition(sK0,converse(sK1))))),sK1)))),
inference(paramod,[status(thm)],[c_245,c_8481]) ).
cnf(c_8483,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = complement(join(complement(sK0),complement(composition(complement(top),sK1)))),
inference(paramod,[status(thm)],[c_497,c_8482]) ).
cnf(c_8484,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = complement(join(complement(sK0),complement(composition(zero,sK1)))),
inference(paramod,[status(thm)],[c_33,c_8483]) ).
cnf(c_8485,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = complement(join(complement(sK0),complement(zero))),
inference(paramod,[status(thm)],[c_529,c_8484]) ).
cnf(c_8486,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = complement(join(complement(sK0),top)),
inference(paramod,[status(thm)],[c_262,c_8485]) ).
cnf(c_8487,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = complement(join(top,complement(sK0))),
inference(paramod,[status(thm)],[c_18,c_8486]) ).
cnf(c_8488,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = complement(top),
inference(paramod,[status(thm)],[c_390,c_8487]) ).
cnf(c_8378,plain,
complement(join(complement(sK0),complement(composition(complement(sK2),sK1)))) = zero,
inference(paramod,[status(thm)],[c_33,c_8488]) ).
cnf(c_8489,plain,
join(complement(sK0),zero) = join(complement(sK0),complement(complement(composition(complement(sK2),sK1)))),
inference(paramod,[status(thm)],[c_8378,c_4758]) ).
cnf(c_8490,plain,
join(zero,complement(sK0)) = join(complement(sK0),complement(complement(composition(complement(sK2),sK1)))),
inference(paramod,[status(thm)],[c_18,c_8489]) ).
cnf(c_8491,plain,
complement(sK0) = join(complement(sK0),complement(complement(composition(complement(sK2),sK1)))),
inference(paramod,[status(thm)],[c_245,c_8490]) ).
cnf(c_8492,plain,
complement(sK0) = join(complement(sK0),composition(complement(sK2),sK1)),
inference(paramod,[status(thm)],[c_232,c_8491]) ).
cnf(c_8418,plain,
join(complement(sK0),composition(complement(sK2),sK1)) = complement(sK0),
inference(copy,[status(thm)],[c_8492]) ).
cnf(c_8419,plain,
$false,
inference(resolve,[status(thm)],[c_8418,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL043+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n016.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 05:45:35 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 127063 was started by sandbox2 on n016,
% 0.18/5.45 % Sat Sep 26 05:45:35 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 32.08/9.60
% 32.08/9.60 % SZS status Theorem for theBenchmark
% 32.08/9.60
% 32.08/9.60 % Proof 1 at 3.45 (+ 0.64) seconds.
% 32.08/9.60 % Length of proof is 88.
% 32.08/9.60 % Level of proof is 19.
% 32.08/9.60 % Maximum clause weight is 42.000.
% 32.08/9.60 % Given clauses 455.
% 32.08/9.60
% 32.08/9.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------