%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL002+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:24:42 AM UTC 2026
% Result : Theorem 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 81 ( 3 sgn 19 !; 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_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] : join(X0,top) = top,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : join(X0,top) = top,
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_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_373,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_373]) ).
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_374,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_374]) ).
fof(nnf_14,plain,
? [X0] : join(X0,top) != top,
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
join(sK0,top) != top,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
join(sK0,top) != top,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
join(top,sK0) != top,
inference(paramod,[status(thm)],[c_15,c_31]) ).
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_375,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_43,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_375]) ).
cnf(c_376,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_376]) ).
cnf(c_377,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_36]) ).
cnf(c_378,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_377]) ).
cnf(c_379,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_378]) ).
cnf(c_86,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_379]) ).
cnf(c_92,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_86,c_55]) ).
cnf(c_93,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_92,c_86]) ).
cnf(c_380,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_43]) ).
cnf(c_101,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_380]) ).
cnf(c_381,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_101,c_21]) ).
cnf(c_103,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_381]) ).
cnf(c_107,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_101,c_27]) ).
cnf(c_108,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_103,c_101]) ).
cnf(c_109,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_108,c_107]) ).
cnf(c_382,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_109,c_18]) ).
cnf(c_383,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_15,c_382]) ).
cnf(c_384,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_28,c_383]) ).
cnf(c_385,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_30,c_384]) ).
cnf(c_168,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_92,c_385]) ).
cnf(c_180,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_168,c_93]) ).
cnf(c_386,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_180,c_18]) ).
cnf(c_387,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_180,c_386]) ).
cnf(c_388,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_18,c_387]) ).
cnf(c_210,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_388]) ).
cnf(c_389,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_210,c_16]) ).
cnf(c_241,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_389]) ).
cnf(c_390,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_28,c_241]) ).
cnf(c_367,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_28,c_390]) ).
cnf(c_391,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_367,c_15]) ).
cnf(c_371,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_391]) ).
cnf(c_372,plain,
$false,
inference(resolve,[status(thm)],[c_371,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/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 05:26:39 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 2105197 was started by sandbox on n003,
% 0.10/0.37 % Sat Sep 26 05:26:39 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.50
% 0.14/0.50 % SZS status Theorem for theBenchmark
% 0.14/0.50
% 0.14/0.50 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.14/0.50 % Length of proof is 44.
% 0.14/0.50 % Level of proof is 13.
% 0.14/0.50 % Maximum clause weight is 57.000.
% 0.14/0.50 % Given clauses 57.
% 0.14/0.50
% 0.14/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------