%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL001+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 : n016.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 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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 : 59 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
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(zero,X0) = X0,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : join(zero,X0) = 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_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_128,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_128]) ).
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_129,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_129]) ).
fof(nnf_14,plain,
? [X0] : join(zero,X0) != X0,
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
join(zero,sK0) != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
join(zero,sK0) != sK0,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
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_130,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_42,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_131,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_54,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_131]) ).
cnf(c_132,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_133,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_132]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_133]) ).
cnf(c_134,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_42]) ).
cnf(c_72,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_134]) ).
cnf(c_135,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_72,c_21]) ).
cnf(c_74,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_135]) ).
cnf(c_78,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_72,c_27]) ).
cnf(c_79,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_74,c_72]) ).
cnf(c_80,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_79,c_78]) ).
cnf(c_81,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_80,c_55]) ).
cnf(c_136,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_35]) ).
cnf(c_137,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_136]) ).
cnf(c_138,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_137]) ).
cnf(c_114,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_138]) ).
cnf(c_120,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_114,c_54]) ).
cnf(c_126,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_120,c_81]) ).
cnf(c_127,plain,
$false,
inference(resolve,[status(thm)],[c_126,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 05:29:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 67733 was started by sandbox on n016,
% 0.08/0.36 % Sat Sep 26 05:29:31 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.12/0.39 % Length of proof is 37.
% 0.12/0.39 % Level of proof is 9.
% 0.12/0.39 % Maximum clause weight is 14.000.
% 0.12/0.39 % Given clauses 25.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------