%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL044+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 : n005.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 08:25:06 AM UTC 2026
% Result : Theorem 19.33s 2.84s
% Output : CNFRefutation 19.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of formulae : 156 ( 152 unt; 0 def)
% Number of atoms : 160 ( 159 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 202 ( 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(dedekind_law,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('theBenchmark.p',dedekind_law) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( join(composition(complement(X0),X1),complement(X2)) = complement(X2)
=> join(composition(X2,converse(X1)),X0) = X0 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(composition(complement(X0),X1),complement(X2)) = complement(X2)
=> join(composition(X2,converse(X1)),X0) = 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_4980,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_4980]) ).
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_4981,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_4981]) ).
cnf(c_34,plain,
composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(clausify,[status(thm)],[dedekind_law]) ).
cnf(c_4982,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_34]) ).
cnf(c_4983,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_4982]) ).
cnf(c_4984,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_4983]) ).
cnf(c_4985,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_4984]) ).
cnf(c_4986,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B)))))),
inference(paramod,[status(thm)],[c_22,c_4985]) ).
cnf(c_35,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C))))),
inference(copy,[status(thm)],[c_4986]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( join(composition(X2,converse(X1)),X0) != X0
& complement(X2) = join(composition(complement(X0),X1),complement(X2)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( join(composition(sK0,converse(sK2)),sK1) != sK1
& complement(sK0) = join(composition(complement(sK1),sK2),complement(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK0)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
complement(sK0) = join(composition(complement(sK1),sK2),complement(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_4987,negated_conjecture,
complement(sK0) = join(complement(sK0),composition(complement(sK1),sK2)),
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_41,negated_conjecture,
join(complement(sK0),composition(complement(sK1),sK2)) = complement(sK0),
inference(copy,[status(thm)],[c_4987]) ).
cnf(c_42,negated_conjecture,
join(composition(sK0,converse(sK2)),sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_43,negated_conjecture,
join(sK1,composition(sK0,converse(sK2))) != sK1,
inference(paramod,[status(thm)],[c_18,c_42]) ).
cnf(c_4988,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_4988]) ).
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_4989,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_4989]) ).
cnf(c_4990,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_4990]) ).
cnf(c_4991,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_4991]) ).
cnf(c_4992,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_4993,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_4992]) ).
cnf(c_67,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_4993]) ).
cnf(c_4994,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_4994]) ).
cnf(c_4995,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_4995]) ).
cnf(c_4996,plain,
join(complement(join(complement(composition(A,converse(B))),complement(C))),composition(complement(join(complement(A),complement(composition(C,B)))),complement(join(complement(converse(B)),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(converse(B)))))),complement(join(complement(converse(B)),complement(composition(converse(A),C))))),
inference(paramod,[status(thm)],[c_26,c_35]) ).
cnf(c_86,plain,
join(complement(join(complement(composition(A,converse(B))),complement(C))),composition(complement(join(complement(A),complement(composition(C,B)))),complement(join(complement(converse(B)),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,B)))),complement(join(complement(converse(B)),complement(composition(converse(A),C))))),
inference(paramod,[status(thm)],[c_26,c_4996]) ).
cnf(c_4997,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_133,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_4997]) ).
cnf(c_4998,plain,
join(A,top) = join(B,join(A,complement(B))),
inference(paramod,[status(thm)],[c_31,c_45]) ).
cnf(c_135,plain,
join(A,join(B,complement(A))) = join(B,top),
inference(copy,[status(thm)],[c_4998]) ).
cnf(c_4999,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_54]) ).
cnf(c_146,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_4999]) ).
cnf(c_5000,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_146,c_24]) ).
cnf(c_155,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_5000]) ).
cnf(c_159,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_146,c_30]) ).
cnf(c_177,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_155,c_146]) ).
cnf(c_182,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_177,c_159]) ).
cnf(c_183,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_182,c_67]) ).
cnf(c_5001,plain,
converse(A) = join(converse(zero),converse(complement(complement(A)))),
inference(paramod,[status(thm)],[c_183,c_27]) ).
cnf(c_200,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(copy,[status(thm)],[c_5001]) ).
cnf(c_5002,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_5003,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_5002]) ).
cnf(c_5004,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_5003]) ).
cnf(c_225,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_5004]) ).
cnf(c_233,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_225,c_66]) ).
cnf(c_244,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_233,c_200]) ).
cnf(c_246,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_233,c_183]) ).
cnf(c_260,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_246,c_72]) ).
cnf(c_5005,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_233,c_21]) ).
cnf(c_262,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_233,c_5005]) ).
cnf(c_5006,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_233,c_182]) ).
cnf(c_5007,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_233,c_5006]) ).
cnf(c_273,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_233,c_5007]) ).
cnf(c_5008,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_246,c_18]) ).
cnf(c_284,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_5008]) ).
cnf(c_5009,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_273,c_19]) ).
cnf(c_285,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_5009]) ).
cnf(c_5010,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_273,c_48]) ).
cnf(c_5011,plain,
complement(complement(A)) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_262,c_5010]) ).
cnf(c_5012,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_233,c_5011]) ).
cnf(c_309,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_5012]) ).
cnf(c_5013,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_273,c_48]) ).
cnf(c_5014,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_18,c_5013]) ).
cnf(c_5015,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_309,c_5014]) ).
cnf(c_310,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_18,c_5015]) ).
cnf(c_5016,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_244]) ).
cnf(c_327,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_26,c_5016]) ).
cnf(c_5017,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_327,c_284]) ).
cnf(c_332,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_5017]) ).
cnf(c_5018,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_31,c_285]) ).
cnf(c_392,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_5018]) ).
cnf(c_5019,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_69,c_285]) ).
cnf(c_393,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_69,c_5019]) ).
cnf(c_395,plain,
join(A,join(B,complement(A))) = top,
inference(paramod,[status(thm)],[c_392,c_135]) ).
cnf(c_5020,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_392,c_18]) ).
cnf(c_396,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_5020]) ).
cnf(c_428,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_393]) ).
cnf(c_433,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_428,c_396]) ).
cnf(c_452,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_433,c_260]) ).
cnf(c_468,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_233,c_395]) ).
cnf(c_5021,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_452,c_25]) ).
cnf(c_5022,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_396,c_5021]) ).
cnf(c_5023,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_452,c_5022]) ).
cnf(c_5024,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_246,c_5023]) ).
cnf(c_498,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_5024]) ).
cnf(c_5025,plain,
join(complement(composition(complement(sK1),sK2)),complement(sK0)) = top,
inference(paramod,[status(thm)],[c_41,c_468]) ).
cnf(c_503,plain,
join(complement(sK0),complement(composition(complement(sK1),sK2))) = top,
inference(paramod,[status(thm)],[c_18,c_5025]) ).
cnf(c_5026,plain,
converse(zero) = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_498,c_28]) ).
cnf(c_5027,plain,
zero = composition(converse(complement(composition(top,top))),converse(A)),
inference(paramod,[status(thm)],[c_332,c_5026]) ).
cnf(c_509,plain,
composition(converse(complement(composition(top,top))),converse(A)) = zero,
inference(copy,[status(thm)],[c_5027]) ).
cnf(c_5028,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_498,c_177]) ).
cnf(c_511,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_5028]) ).
cnf(c_5029,plain,
composition(converse(zero),converse(A)) = zero,
inference(paramod,[status(thm)],[c_511,c_509]) ).
cnf(c_514,plain,
composition(zero,converse(A)) = zero,
inference(paramod,[status(thm)],[c_332,c_5029]) ).
cnf(c_535,plain,
composition(zero,A) = zero,
inference(paramod,[status(thm)],[c_26,c_514]) ).
cnf(c_549,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_310]) ).
cnf(c_5030,plain,
join(complement(join(complement(composition(sK0,converse(sK2))),complement(complement(sK1)))),composition(complement(top),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1))))))) = composition(complement(join(complement(sK0),complement(composition(complement(sK1),sK2)))),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_503,c_86]) ).
cnf(c_5031,plain,
join(complement(join(complement(composition(sK0,converse(sK2))),sK1)),composition(complement(top),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1))))))) = composition(complement(join(complement(sK0),complement(composition(complement(sK1),sK2)))),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_233,c_5030]) ).
cnf(c_5032,plain,
join(complement(join(sK1,complement(composition(sK0,converse(sK2))))),composition(complement(top),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1))))))) = composition(complement(join(complement(sK0),complement(composition(complement(sK1),sK2)))),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_18,c_5031]) ).
cnf(c_5033,plain,
join(complement(join(sK1,complement(composition(sK0,converse(sK2))))),composition(zero,complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1))))))) = composition(complement(join(complement(sK0),complement(composition(complement(sK1),sK2)))),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_33,c_5032]) ).
cnf(c_5034,plain,
join(complement(join(sK1,complement(composition(sK0,converse(sK2))))),zero) = composition(complement(join(complement(sK0),complement(composition(complement(sK1),sK2)))),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_535,c_5033]) ).
cnf(c_5035,plain,
join(zero,complement(join(sK1,complement(composition(sK0,converse(sK2)))))) = composition(complement(join(complement(sK0),complement(composition(complement(sK1),sK2)))),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_18,c_5034]) ).
cnf(c_5036,plain,
complement(join(sK1,complement(composition(sK0,converse(sK2))))) = composition(complement(join(complement(sK0),complement(composition(complement(sK1),sK2)))),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_246,c_5035]) ).
cnf(c_5037,plain,
complement(join(sK1,complement(composition(sK0,converse(sK2))))) = composition(complement(top),complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_503,c_5036]) ).
cnf(c_5038,plain,
complement(join(sK1,complement(composition(sK0,converse(sK2))))) = composition(zero,complement(join(complement(converse(sK2)),complement(composition(converse(sK0),complement(sK1)))))),
inference(paramod,[status(thm)],[c_33,c_5037]) ).
cnf(c_1334,plain,
complement(join(sK1,complement(composition(sK0,converse(sK2))))) = zero,
inference(paramod,[status(thm)],[c_535,c_5038]) ).
cnf(c_5039,plain,
join(join(sK1,complement(composition(sK0,converse(sK2)))),zero) = top,
inference(paramod,[status(thm)],[c_1334,c_31]) ).
cnf(c_5040,plain,
join(zero,join(sK1,complement(composition(sK0,converse(sK2))))) = top,
inference(paramod,[status(thm)],[c_18,c_5039]) ).
cnf(c_1534,plain,
join(sK1,complement(composition(sK0,converse(sK2)))) = top,
inference(paramod,[status(thm)],[c_246,c_5040]) ).
cnf(c_5041,plain,
join(complement(join(complement(A),B)),B) = join(B,A),
inference(paramod,[status(thm)],[c_549,c_133]) ).
cnf(c_4134,plain,
join(A,complement(join(complement(B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_18,c_5041]) ).
cnf(c_4220,plain,
join(A,complement(join(A,complement(B)))) = join(A,B),
inference(paramod,[status(thm)],[c_18,c_4134]) ).
cnf(c_5042,plain,
join(sK1,complement(top)) = join(sK1,composition(sK0,converse(sK2))),
inference(paramod,[status(thm)],[c_1534,c_4220]) ).
cnf(c_5043,plain,
join(sK1,zero) = join(sK1,composition(sK0,converse(sK2))),
inference(paramod,[status(thm)],[c_33,c_5042]) ).
cnf(c_5044,plain,
join(zero,sK1) = join(sK1,composition(sK0,converse(sK2))),
inference(paramod,[status(thm)],[c_18,c_5043]) ).
cnf(c_5045,plain,
sK1 = join(sK1,composition(sK0,converse(sK2))),
inference(paramod,[status(thm)],[c_246,c_5044]) ).
cnf(c_4978,plain,
join(sK1,composition(sK0,converse(sK2))) = sK1,
inference(copy,[status(thm)],[c_5045]) ).
cnf(c_4979,plain,
$false,
inference(resolve,[status(thm)],[c_4978,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 05:41:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1333788 was started by sandbox2 on n005,
% 0.08/0.36 % Sat Sep 26 05:41:03 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 19.33/2.84
% 19.33/2.84 % SZS status Theorem for theBenchmark
% 19.33/2.84
% 19.33/2.84 % Proof 1 at 2.08 (+ 0.37) seconds.
% 19.33/2.84 % Length of proof is 87.
% 19.33/2.84 % Level of proof is 20.
% 19.33/2.84 % Maximum clause weight is 49.000.
% 19.33/2.84 % Given clauses 296.
% 19.33/2.84
% 19.33/2.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------