%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL018+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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:24:51 AM UTC 2026
% Result : Theorem 0.22s 5.60s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 13
% Syntax : Number of formulae : 124 ( 120 unt; 0 def)
% Number of atoms : 128 ( 127 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 116 ( 10 sgn 24 !; 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] :
( composition(X0,top) = X0
=> composition(complement(X0),top) = complement(X0) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( composition(X0,top) = X0
=> composition(complement(X0),top) = complement(X0) ),
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_286,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_286]) ).
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_287,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_287]) ).
fof(nnf_14,plain,
? [X0] :
( composition(complement(X0),top) != complement(X0)
& composition(X0,top) = X0 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( composition(complement(sK0),top) != complement(sK0)
& composition(sK0,top) = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
composition(sK0,top) = sK0,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
composition(complement(sK0),top) != complement(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_35,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_36,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_288,plain,
converse(A) = join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_18,c_24]) ).
cnf(c_38,plain,
join(converse(complement(join(complement(A),B))),converse(complement(join(complement(A),complement(B))))) = converse(A),
inference(copy,[status(thm)],[c_288]) ).
cnf(c_289,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_39,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_289]) ).
cnf(c_290,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_290]) ).
cnf(c_291,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_292,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_291]) ).
cnf(c_47,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_292]) ).
cnf(c_293,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_28,c_22]) ).
cnf(c_48,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_293]) ).
cnf(c_294,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_27]) ).
cnf(c_52,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_30,c_294]) ).
cnf(c_295,plain,
join(complement(top),composition(converse(sK0),complement(sK0))) = complement(top),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_296,plain,
join(zero,composition(converse(sK0),complement(sK0))) = complement(top),
inference(paramod,[status(thm)],[c_30,c_295]) ).
cnf(c_56,plain,
join(zero,composition(converse(sK0),complement(sK0))) = zero,
inference(paramod,[status(thm)],[c_30,c_296]) ).
cnf(c_297,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_39]) ).
cnf(c_68,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_297]) ).
cnf(c_298,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_68,c_21]) ).
cnf(c_70,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_298]) ).
cnf(c_74,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_68,c_27]) ).
cnf(c_75,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_70,c_68]) ).
cnf(c_76,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_75,c_74]) ).
cnf(c_77,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_76,c_47]) ).
cnf(c_299,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_36]) ).
cnf(c_300,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_299]) ).
cnf(c_301,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_300]) ).
cnf(c_80,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_301]) ).
cnf(c_81,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_80,c_46]) ).
cnf(c_82,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_81,c_80]) ).
cnf(c_83,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_81,c_77]) ).
cnf(c_84,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_83,c_82]) ).
cnf(c_86,plain,
composition(converse(sK0),complement(sK0)) = zero,
inference(paramod,[status(thm)],[c_83,c_56]) ).
cnf(c_87,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_83,c_52]) ).
cnf(c_302,plain,
join(converse(complement(top)),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_28,c_38]) ).
cnf(c_303,plain,
join(converse(zero),converse(complement(join(complement(A),complement(complement(complement(A))))))) = converse(A),
inference(paramod,[status(thm)],[c_30,c_302]) ).
cnf(c_304,plain,
join(converse(zero),converse(complement(join(complement(A),complement(A))))) = converse(A),
inference(paramod,[status(thm)],[c_81,c_303]) ).
cnf(c_305,plain,
join(converse(zero),converse(complement(complement(A)))) = converse(A),
inference(paramod,[status(thm)],[c_76,c_304]) ).
cnf(c_89,plain,
join(converse(zero),converse(A)) = converse(A),
inference(paramod,[status(thm)],[c_81,c_305]) ).
cnf(c_306,plain,
A = join(A,zero),
inference(paramod,[status(thm)],[c_83,c_15]) ).
cnf(c_92,plain,
join(A,zero) = A,
inference(copy,[status(thm)],[c_306]) ).
cnf(c_94,plain,
complement(zero) = top,
inference(paramod,[status(thm)],[c_83,c_28]) ).
cnf(c_307,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_81,c_35]) ).
cnf(c_102,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_81,c_307]) ).
cnf(c_308,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_84,c_28]) ).
cnf(c_309,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_16,c_308]) ).
cnf(c_107,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_309]) ).
cnf(c_310,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_107,c_15]) ).
cnf(c_122,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_310]) ).
cnf(c_311,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_107,c_24]) ).
cnf(c_124,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_311]) ).
cnf(c_312,plain,
converse(zero) = composition(converse(complement(sK0)),converse(converse(sK0))),
inference(paramod,[status(thm)],[c_86,c_25]) ).
cnf(c_313,plain,
converse(zero) = composition(converse(complement(sK0)),sK0),
inference(paramod,[status(thm)],[c_23,c_312]) ).
cnf(c_132,plain,
composition(converse(complement(sK0)),sK0) = converse(zero),
inference(copy,[status(thm)],[c_313]) ).
cnf(c_314,plain,
join(converse(zero),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_89]) ).
cnf(c_143,plain,
join(converse(zero),A) = A,
inference(paramod,[status(thm)],[c_23,c_314]) ).
cnf(c_315,plain,
zero = converse(zero),
inference(paramod,[status(thm)],[c_143,c_92]) ).
cnf(c_149,plain,
converse(zero) = zero,
inference(copy,[status(thm)],[c_315]) ).
cnf(c_151,plain,
composition(converse(complement(sK0)),sK0) = zero,
inference(paramod,[status(thm)],[c_149,c_132]) ).
cnf(c_156,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_124]) ).
cnf(c_159,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_156,c_122]) ).
cnf(c_172,plain,
join(sK0,composition(complement(sK0),top)) = composition(top,top),
inference(paramod,[status(thm)],[c_31,c_48]) ).
cnf(c_316,plain,
join(complement(sK0),composition(converse(converse(complement(sK0))),complement(zero))) = complement(sK0),
inference(paramod,[status(thm)],[c_151,c_27]) ).
cnf(c_317,plain,
join(complement(sK0),composition(complement(sK0),complement(zero))) = complement(sK0),
inference(paramod,[status(thm)],[c_23,c_316]) ).
cnf(c_179,plain,
join(complement(sK0),composition(complement(sK0),top)) = complement(sK0),
inference(paramod,[status(thm)],[c_94,c_317]) ).
cnf(c_207,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_159,c_87]) ).
cnf(c_318,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_207,c_22]) ).
cnf(c_319,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_122,c_318]) ).
cnf(c_320,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_207,c_319]) ).
cnf(c_321,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_83,c_320]) ).
cnf(c_210,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_321]) ).
cnf(c_322,plain,
zero = complement(composition(top,top)),
inference(paramod,[status(thm)],[c_210,c_75]) ).
cnf(c_227,plain,
complement(composition(top,top)) = zero,
inference(copy,[status(thm)],[c_322]) ).
cnf(c_323,plain,
join(composition(top,top),zero) = top,
inference(paramod,[status(thm)],[c_227,c_28]) ).
cnf(c_324,plain,
join(zero,composition(top,top)) = top,
inference(paramod,[status(thm)],[c_15,c_323]) ).
cnf(c_237,plain,
composition(top,top) = top,
inference(paramod,[status(thm)],[c_83,c_324]) ).
cnf(c_238,plain,
join(sK0,composition(complement(sK0),top)) = top,
inference(paramod,[status(thm)],[c_237,c_172]) ).
cnf(c_325,plain,
join(complement(top),complement(join(composition(complement(sK0),top),complement(sK0)))) = complement(composition(complement(sK0),top)),
inference(paramod,[status(thm)],[c_238,c_102]) ).
cnf(c_326,plain,
join(zero,complement(join(composition(complement(sK0),top),complement(sK0)))) = complement(composition(complement(sK0),top)),
inference(paramod,[status(thm)],[c_30,c_325]) ).
cnf(c_327,plain,
join(zero,complement(join(complement(sK0),composition(complement(sK0),top)))) = complement(composition(complement(sK0),top)),
inference(paramod,[status(thm)],[c_15,c_326]) ).
cnf(c_328,plain,
join(zero,complement(complement(sK0))) = complement(composition(complement(sK0),top)),
inference(paramod,[status(thm)],[c_179,c_327]) ).
cnf(c_329,plain,
join(zero,sK0) = complement(composition(complement(sK0),top)),
inference(paramod,[status(thm)],[c_81,c_328]) ).
cnf(c_330,plain,
sK0 = complement(composition(complement(sK0),top)),
inference(paramod,[status(thm)],[c_83,c_329]) ).
cnf(c_276,plain,
complement(composition(complement(sK0),top)) = sK0,
inference(copy,[status(thm)],[c_330]) ).
cnf(c_331,plain,
complement(sK0) = composition(complement(sK0),top),
inference(paramod,[status(thm)],[c_276,c_81]) ).
cnf(c_284,plain,
composition(complement(sK0),top) = complement(sK0),
inference(copy,[status(thm)],[c_331]) ).
cnf(c_285,plain,
$false,
inference(resolve,[status(thm)],[c_284,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.46 % Computer : n008.cluster.edu
% 0.17/5.46 % Model : x86_64 x86_64
% 0.17/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.46 % Memory : 8046.5625MB
% 0.17/5.46 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Sat Sep 26 05:30:15 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.47 % Process 2868673 was started by sandbox2 on n008,
% 0.17/5.47 % Sat Sep 26 05:30:15 2026
% 0.17/5.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.48
% 0.17/5.48 % From the command line: assign(max_seconds, 300).
% 0.22/5.60
% 0.22/5.60 % SZS status Theorem for theBenchmark
% 0.22/5.60
% 0.22/5.60 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.22/5.60 % Length of proof is 75.
% 0.22/5.60 % Level of proof is 21.
% 0.22/5.60 % Maximum clause weight is 30.000.
% 0.22/5.60 % Given clauses 81.
% 0.22/5.60
% 0.22/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
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