%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL045+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 : n018.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 0.12s 5.55s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 15
% Syntax : Number of formulae : 154 ( 154 unt; 0 def)
% Number of atoms : 154 ( 153 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 203 ( 14 sgn 30 !; 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_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('theBenchmark.p',composition_associativity) ).
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] : join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(X0)),X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(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_23,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(clausify,[status(thm)],[composition_associativity]) ).
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_724,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_724]) ).
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_725,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_725]) ).
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_726,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_727,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_726]) ).
cnf(c_728,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_727]) ).
cnf(c_729,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_728]) ).
cnf(c_730,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_729]) ).
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_730]) ).
fof(nnf_17,plain,
? [X0] : composition(composition(X0,converse(X0)),X0) != join(X0,composition(composition(X0,converse(X0)),X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
composition(composition(sK0,converse(sK0)),sK0) != join(sK0,composition(composition(sK0,converse(sK0)),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
composition(composition(sK0,converse(sK0)),sK0) != join(sK0,composition(composition(sK0,converse(sK0)),sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_731,negated_conjecture,
composition(sK0,composition(converse(sK0),sK0)) != join(sK0,composition(composition(sK0,converse(sK0)),sK0)),
inference(paramod,[status(thm)],[c_23,c_40]) ).
cnf(c_732,negated_conjecture,
composition(sK0,composition(converse(sK0),sK0)) != join(sK0,composition(sK0,composition(converse(sK0),sK0))),
inference(paramod,[status(thm)],[c_23,c_731]) ).
cnf(c_41,negated_conjecture,
join(sK0,composition(sK0,composition(converse(sK0),sK0))) != composition(sK0,composition(converse(sK0),sK0)),
inference(copy,[status(thm)],[c_732]) ).
cnf(c_45,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_733,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_46,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_733]) ).
cnf(c_734,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_52,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_734]) ).
cnf(c_735,plain,
join(complement(A),composition(converse(composition(B,C)),complement(composition(B,composition(C,A))))) = complement(A),
inference(paramod,[status(thm)],[c_23,c_30]) ).
cnf(c_736,plain,
join(complement(A),composition(composition(converse(C),converse(B)),complement(composition(B,composition(C,A))))) = complement(A),
inference(paramod,[status(thm)],[c_28,c_735]) ).
cnf(c_56,plain,
join(complement(A),composition(converse(B),composition(converse(C),complement(composition(C,composition(B,A)))))) = complement(A),
inference(paramod,[status(thm)],[c_23,c_736]) ).
cnf(c_737,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_64,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_737]) ).
cnf(c_738,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_739,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_738]) ).
cnf(c_65,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_739]) ).
cnf(c_740,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_67,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_740]) ).
cnf(c_741,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_33,c_30]) ).
cnf(c_70,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_33,c_741]) ).
cnf(c_72,plain,
join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_742,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_52]) ).
cnf(c_139,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_742]) ).
cnf(c_743,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_139,c_24]) ).
cnf(c_148,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_743]) ).
cnf(c_152,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_139,c_30]) ).
cnf(c_170,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_148,c_139]) ).
cnf(c_175,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_170,c_152]) ).
cnf(c_176,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_175,c_65]) ).
cnf(c_744,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_45]) ).
cnf(c_745,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_744]) ).
cnf(c_746,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_745]) ).
cnf(c_218,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_746]) ).
cnf(c_226,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_218,c_64]) ).
cnf(c_239,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_226,c_176]) ).
cnf(c_252,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_239,c_70]) ).
cnf(c_747,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_226,c_21]) ).
cnf(c_254,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_226,c_747]) ).
cnf(c_748,plain,
join(A,complement(complement(A))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_226,c_175]) ).
cnf(c_749,plain,
join(A,A) = complement(complement(A)),
inference(paramod,[status(thm)],[c_226,c_748]) ).
cnf(c_265,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_226,c_749]) ).
cnf(c_750,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_265,c_19]) ).
cnf(c_277,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_750]) ).
cnf(c_751,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_265,c_46]) ).
cnf(c_752,plain,
complement(complement(A)) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_254,c_751]) ).
cnf(c_753,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_226,c_752]) ).
cnf(c_299,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_753]) ).
cnf(c_754,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_265,c_46]) ).
cnf(c_755,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_18,c_754]) ).
cnf(c_756,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_299,c_755]) ).
cnf(c_300,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_18,c_756]) ).
cnf(c_344,plain,
join(one,converse(complement(one))) = converse(top),
inference(paramod,[status(thm)],[c_148,c_67]) ).
cnf(c_757,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_31,c_277]) ).
cnf(c_380,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_757]) ).
cnf(c_758,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_67,c_277]) ).
cnf(c_381,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_67,c_758]) ).
cnf(c_759,plain,
join(one,converse(top)) = join(one,converse(complement(one))),
inference(paramod,[status(thm)],[c_344,c_277]) ).
cnf(c_382,plain,
join(one,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_344,c_759]) ).
cnf(c_760,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_380,c_18]) ).
cnf(c_384,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_760]) ).
cnf(c_761,plain,
composition(converse(top),A) = join(composition(one,A),composition(converse(top),A)),
inference(paramod,[status(thm)],[c_382,c_25]) ).
cnf(c_762,plain,
composition(converse(top),A) = join(A,composition(converse(top),A)),
inference(paramod,[status(thm)],[c_170,c_761]) ).
cnf(c_412,plain,
join(A,composition(converse(top),A)) = composition(converse(top),A),
inference(copy,[status(thm)],[c_762]) ).
cnf(c_416,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_381]) ).
cnf(c_421,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_416,c_384]) ).
cnf(c_763,plain,
join(A,composition(top,A)) = composition(converse(top),A),
inference(paramod,[status(thm)],[c_421,c_412]) ).
cnf(c_426,plain,
join(A,composition(top,A)) = composition(top,A),
inference(paramod,[status(thm)],[c_421,c_763]) ).
cnf(c_440,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_421,c_252]) ).
cnf(c_764,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_440,c_25]) ).
cnf(c_765,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_384,c_764]) ).
cnf(c_766,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_440,c_765]) ).
cnf(c_767,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_239,c_766]) ).
cnf(c_486,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_767]) ).
cnf(c_768,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_486,c_170]) ).
cnf(c_498,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_768]) ).
cnf(c_769,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_498,c_31]) ).
cnf(c_770,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_18,c_769]) ).
cnf(c_514,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_239,c_770]) ).
cnf(c_771,plain,
composition(top,A) = composition(top,composition(top,A)),
inference(paramod,[status(thm)],[c_514,c_23]) ).
cnf(c_518,plain,
composition(top,composition(top,A)) = composition(top,A),
inference(copy,[status(thm)],[c_771]) ).
cnf(c_593,plain,
join(A,complement(composition(top,complement(A)))) = A,
inference(paramod,[status(thm)],[c_426,c_300]) ).
cnf(c_772,plain,
join(complement(composition(top,A)),composition(converse(top),complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_518,c_30]) ).
cnf(c_773,plain,
join(complement(composition(top,A)),composition(top,complement(composition(top,A)))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_421,c_772]) ).
cnf(c_612,plain,
composition(top,complement(composition(top,A))) = complement(composition(top,A)),
inference(paramod,[status(thm)],[c_426,c_773]) ).
cnf(c_774,plain,
join(complement(A),composition(converse(top),composition(converse(top),complement(composition(top,A))))) = complement(A),
inference(paramod,[status(thm)],[c_518,c_56]) ).
cnf(c_775,plain,
join(complement(A),composition(top,composition(converse(top),complement(composition(top,A))))) = complement(A),
inference(paramod,[status(thm)],[c_421,c_774]) ).
cnf(c_776,plain,
join(complement(A),composition(top,composition(top,complement(composition(top,A))))) = complement(A),
inference(paramod,[status(thm)],[c_421,c_775]) ).
cnf(c_777,plain,
join(complement(A),composition(top,complement(composition(top,A)))) = complement(A),
inference(paramod,[status(thm)],[c_612,c_776]) ).
cnf(c_617,plain,
join(complement(A),complement(composition(top,A))) = complement(A),
inference(paramod,[status(thm)],[c_612,c_777]) ).
cnf(c_778,plain,
join(complement(complement(A)),composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_593,c_72]) ).
cnf(c_779,plain,
join(A,composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_778]) ).
cnf(c_780,plain,
join(A,composition(complement(join(zero,complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_33,c_779]) ).
cnf(c_781,plain,
join(A,composition(complement(join(zero,complement(composition(A,converse(A))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_780]) ).
cnf(c_782,plain,
join(A,composition(complement(complement(composition(A,converse(A)))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_239,c_781]) ).
cnf(c_783,plain,
join(A,composition(composition(A,converse(A)),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_782]) ).
cnf(c_784,plain,
join(A,composition(composition(A,converse(A)),complement(join(complement(A),complement(composition(converse(top),A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_783]) ).
cnf(c_785,plain,
join(A,composition(composition(A,converse(A)),complement(join(complement(A),complement(composition(top,A)))))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_421,c_784]) ).
cnf(c_786,plain,
join(A,composition(composition(A,converse(A)),complement(complement(A)))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_617,c_785]) ).
cnf(c_787,plain,
join(A,composition(composition(A,converse(A)),A)) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_786]) ).
cnf(c_788,plain,
join(A,composition(A,composition(converse(A),A))) = composition(complement(join(complement(top),complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_23,c_787]) ).
cnf(c_789,plain,
join(A,composition(A,composition(converse(A),A))) = composition(complement(join(zero,complement(composition(A,converse(complement(complement(A))))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_33,c_788]) ).
cnf(c_790,plain,
join(A,composition(A,composition(converse(A),A))) = composition(complement(join(zero,complement(composition(A,converse(A))))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_789]) ).
cnf(c_791,plain,
join(A,composition(A,composition(converse(A),A))) = composition(complement(complement(composition(A,converse(A)))),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_239,c_790]) ).
cnf(c_792,plain,
join(A,composition(A,composition(converse(A),A))) = composition(composition(A,converse(A)),complement(join(complement(complement(complement(A))),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_791]) ).
cnf(c_793,plain,
join(A,composition(A,composition(converse(A),A))) = composition(composition(A,converse(A)),complement(join(complement(A),complement(composition(converse(top),A))))),
inference(paramod,[status(thm)],[c_226,c_792]) ).
cnf(c_794,plain,
join(A,composition(A,composition(converse(A),A))) = composition(composition(A,converse(A)),complement(join(complement(A),complement(composition(top,A))))),
inference(paramod,[status(thm)],[c_421,c_793]) ).
cnf(c_795,plain,
join(A,composition(A,composition(converse(A),A))) = composition(composition(A,converse(A)),complement(complement(A))),
inference(paramod,[status(thm)],[c_617,c_794]) ).
cnf(c_796,plain,
join(A,composition(A,composition(converse(A),A))) = composition(composition(A,converse(A)),A),
inference(paramod,[status(thm)],[c_226,c_795]) ).
cnf(c_722,plain,
join(A,composition(A,composition(converse(A),A))) = composition(A,composition(converse(A),A)),
inference(paramod,[status(thm)],[c_23,c_796]) ).
cnf(c_723,plain,
$false,
inference(resolve,[status(thm)],[c_722,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL045+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n018.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 05:43:56 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.36 % Process 3850074 was started by sandbox2 on n018,
% 0.09/5.36 % Sat Sep 26 05:43:56 2026
% 0.09/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.12/5.55
% 0.12/5.55 % SZS status Theorem for theBenchmark
% 0.12/5.55
% 0.12/5.55 % Proof 1 at 0.13 (+ 0.04) seconds.
% 0.12/5.55 % Length of proof is 78.
% 0.12/5.55 % Level of proof is 20.
% 0.12/5.55 % Maximum clause weight is 48.000.
% 0.12/5.55 % Given clauses 93.
% 0.12/5.55
% 0.12/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------