%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL004+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 : n003.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 08:24:43 AM UTC 2026
% Result : Theorem 0.87s 0.52s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 117 unt; 0 def)
% Number of atoms : 117 ( 116 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 155 ( 7 sgn 21 !; 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(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] : converse(complement(X0)) = complement(converse(X0)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : converse(complement(X0)) = complement(converse(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_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_445,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_445]) ).
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_446,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_446]) ).
fof(nnf_14,plain,
? [X0] : converse(complement(X0)) != complement(converse(X0)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
converse(complement(sK0)) != complement(converse(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
converse(complement(sK0)) != complement(converse(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_34,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_35,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_447,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_38,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_447]) ).
cnf(c_448,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_45,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_448]) ).
cnf(c_449,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_450,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_449]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_450]) ).
cnf(c_451,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_28,c_24]) ).
cnf(c_48,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_451]) ).
cnf(c_452,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_38]) ).
cnf(c_64,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_452]) ).
cnf(c_453,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_64,c_21]) ).
cnf(c_66,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_453]) ).
cnf(c_70,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_64,c_27]) ).
cnf(c_71,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_66,c_64]) ).
cnf(c_72,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_71,c_70]) ).
cnf(c_73,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_72,c_46]) ).
cnf(c_454,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_35]) ).
cnf(c_455,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_454]) ).
cnf(c_456,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_455]) ).
cnf(c_76,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_456]) ).
cnf(c_77,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_76,c_45]) ).
cnf(c_78,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_77,c_76]) ).
cnf(c_79,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_77,c_73]) ).
cnf(c_80,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_79,c_78]) ).
cnf(c_457,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_77,c_18]) ).
cnf(c_95,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_77,c_457]) ).
cnf(c_458,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_77,c_34]) ).
cnf(c_97,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_77,c_458]) ).
cnf(c_459,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_80,c_28]) ).
cnf(c_460,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_16,c_459]) ).
cnf(c_102,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_460]) ).
cnf(c_461,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_80,c_77]) ).
cnf(c_462,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_77,c_461]) ).
cnf(c_103,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_462]) ).
cnf(c_463,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_102,c_15]) ).
cnf(c_117,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_463]) ).
cnf(c_464,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_102,c_24]) ).
cnf(c_119,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_464]) ).
cnf(c_465,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_103,c_16]) ).
cnf(c_121,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_465]) ).
cnf(c_143,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_23,c_119]) ).
cnf(c_146,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_143,c_117]) ).
cnf(c_148,plain,
join(converse(A),converse(complement(A))) = top,
inference(paramod,[status(thm)],[c_146,c_48]) ).
cnf(c_169,plain,
join(A,converse(complement(converse(A)))) = top,
inference(paramod,[status(thm)],[c_23,c_148]) ).
cnf(c_466,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_95,c_121]) ).
cnf(c_467,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_466]) ).
cnf(c_223,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_95,c_467]) ).
cnf(c_468,plain,
join(complement(complement(A)),complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_97,c_95]) ).
cnf(c_469,plain,
join(A,complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_77,c_468]) ).
cnf(c_470,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_77,c_469]) ).
cnf(c_471,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_15,c_470]) ).
cnf(c_472,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_16,c_471]) ).
cnf(c_473,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_223,c_472]) ).
cnf(c_242,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_77,c_473]) ).
cnf(c_474,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_97,c_97]) ).
cnf(c_475,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_77,c_474]) ).
cnf(c_476,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_77,c_475]) ).
cnf(c_477,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_15,c_476]) ).
cnf(c_478,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_16,c_477]) ).
cnf(c_479,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_242,c_478]) ).
cnf(c_480,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_121,c_479]) ).
cnf(c_244,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_77,c_480]) ).
cnf(c_481,plain,
join(converse(complement(A)),complement(top)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_148,c_244]) ).
cnf(c_482,plain,
join(converse(complement(A)),zero) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_30,c_481]) ).
cnf(c_483,plain,
join(zero,converse(complement(A))) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_15,c_482]) ).
cnf(c_484,plain,
converse(complement(A)) = join(converse(complement(A)),complement(converse(A))),
inference(paramod,[status(thm)],[c_79,c_483]) ).
cnf(c_485,plain,
converse(complement(A)) = join(complement(converse(A)),converse(complement(A))),
inference(paramod,[status(thm)],[c_15,c_484]) ).
cnf(c_373,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(A)),
inference(copy,[status(thm)],[c_485]) ).
cnf(c_486,plain,
join(converse(complement(converse(A))),complement(top)) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_169,c_244]) ).
cnf(c_487,plain,
join(converse(complement(converse(A))),zero) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_30,c_486]) ).
cnf(c_488,plain,
join(zero,converse(complement(converse(A)))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_15,c_487]) ).
cnf(c_489,plain,
converse(complement(converse(A))) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_79,c_488]) ).
cnf(c_490,plain,
converse(complement(converse(A))) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_489]) ).
cnf(c_377,plain,
join(complement(A),converse(complement(converse(A)))) = converse(complement(converse(A))),
inference(copy,[status(thm)],[c_490]) ).
cnf(c_491,plain,
converse(converse(complement(A))) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_373,c_24]) ).
cnf(c_492,plain,
complement(A) = join(converse(complement(converse(A))),converse(converse(complement(A)))),
inference(paramod,[status(thm)],[c_23,c_491]) ).
cnf(c_493,plain,
complement(A) = join(converse(complement(converse(A))),complement(A)),
inference(paramod,[status(thm)],[c_23,c_492]) ).
cnf(c_494,plain,
complement(A) = join(complement(A),converse(complement(converse(A)))),
inference(paramod,[status(thm)],[c_15,c_493]) ).
cnf(c_495,plain,
complement(A) = converse(complement(converse(A))),
inference(paramod,[status(thm)],[c_377,c_494]) ).
cnf(c_423,plain,
converse(complement(converse(A))) = complement(A),
inference(copy,[status(thm)],[c_495]) ).
cnf(c_443,plain,
converse(complement(A)) = complement(converse(A)),
inference(paramod,[status(thm)],[c_423,c_23]) ).
cnf(c_444,plain,
$false,
inference(resolve,[status(thm)],[c_443,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 05:27:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2107134 was started by sandbox2 on n003,
% 0.10/0.37 % Sat Sep 26 05:27:10 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.87/0.52
% 0.87/0.52 % SZS status Theorem for theBenchmark
% 0.87/0.52
% 0.87/0.52 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.87/0.52 % Length of proof is 63.
% 0.87/0.52 % Level of proof is 19.
% 0.87/0.52 % Maximum clause weight is 30.000.
% 0.87/0.52 % Given clauses 108.
% 0.87/0.52
% 0.87/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------