%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT017-1 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 07:49:33 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.56s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 55 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 22 ( 22 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 7 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(top,axiom,
! [VAR_0] : join(complement(VAR_0),VAR_0) = n1,
file('theBenchmark.p',top) ).
cnf(c_1,plain,
join(complement(A),A) = n1,
inference(clausify,[status(thm)],[top]) ).
fof(absorption2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2) ).
cnf(c_3,plain,
join(A,meet(A,B)) = A,
inference(clausify,[status(thm)],[absorption2]) ).
fof(commutativity_of_meet,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = meet(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c_4,plain,
meet(A,B) = meet(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet]) ).
fof(commutativity_of_join,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c_5,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(associativity_of_join,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(VAR_0,VAR_1),VAR_2) = join(VAR_0,join(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_join) ).
cnf(c_7,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_of_join]) ).
fof(complement_involution,axiom,
! [VAR_0] : complement(complement(VAR_0)) = VAR_0,
file('theBenchmark.p',complement_involution) ).
cnf(c_8,plain,
complement(complement(A)) = A,
inference(clausify,[status(thm)],[complement_involution]) ).
fof(meet_complement,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',meet_complement) ).
cnf(c_10,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[meet_complement]) ).
fof(prove_e2,axiom,
join(a,join(meet(complement(a),meet(join(a,complement(b)),join(a,b))),meet(complement(a),join(meet(complement(a),b),meet(complement(a),complement(b)))))) != n1,
file('theBenchmark.p',prove_e2) ).
cnf(c_11,plain,
join(a,join(meet(complement(a),meet(join(a,complement(b)),join(a,b))),meet(complement(a),join(meet(complement(a),b),meet(complement(a),complement(b)))))) != n1,
inference(clausify,[status(thm)],[prove_e2]) ).
cnf(c_490,plain,
join(a,join(meet(complement(a),meet(join(a,b),join(a,complement(b)))),meet(complement(a),join(meet(complement(a),b),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_491,plain,
join(a,join(meet(complement(a),complement(join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(meet(complement(a),b),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_10,c_490]) ).
cnf(c_492,plain,
join(a,join(complement(join(complement(complement(a)),complement(complement(join(complement(join(a,b)),complement(join(a,complement(b)))))))),meet(complement(a),join(meet(complement(a),b),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_10,c_491]) ).
cnf(c_493,plain,
join(a,join(complement(join(a,complement(complement(join(complement(join(a,b)),complement(join(a,complement(b)))))))),meet(complement(a),join(meet(complement(a),b),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_8,c_492]) ).
cnf(c_494,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(meet(complement(a),b),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_8,c_493]) ).
cnf(c_495,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(meet(b,complement(a)),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_4,c_494]) ).
cnf(c_496,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(complement(join(complement(b),complement(complement(a)))),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_10,c_495]) ).
cnf(c_497,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(complement(join(complement(b),a)),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_8,c_496]) ).
cnf(c_498,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(complement(join(a,complement(b))),meet(complement(a),complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_5,c_497]) ).
cnf(c_499,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(complement(join(a,complement(b))),complement(join(complement(complement(a)),complement(complement(b)))))))) != n1,
inference(paramod,[status(thm)],[c_10,c_498]) ).
cnf(c_500,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(complement(join(a,complement(b))),complement(join(a,complement(complement(b)))))))) != n1,
inference(paramod,[status(thm)],[c_8,c_499]) ).
cnf(c_501,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(complement(join(a,complement(b))),complement(join(a,b)))))) != n1,
inference(paramod,[status(thm)],[c_8,c_500]) ).
cnf(c_502,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),meet(complement(a),join(complement(join(a,b)),complement(join(a,complement(b))))))) != n1,
inference(paramod,[status(thm)],[c_5,c_501]) ).
cnf(c_503,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),complement(join(complement(complement(a)),complement(join(complement(join(a,b)),complement(join(a,complement(b))))))))) != n1,
inference(paramod,[status(thm)],[c_10,c_502]) ).
cnf(c_12,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),complement(join(a,complement(join(complement(join(a,b)),complement(join(a,complement(b))))))))) != n1,
inference(paramod,[status(thm)],[c_8,c_503]) ).
cnf(c_14,plain,
join(A,complement(A)) = n1,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_15,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_504,plain,
n1 = join(A,join(B,complement(join(A,B)))),
inference(paramod,[status(thm)],[c_14,c_7]) ).
cnf(c_21,plain,
join(A,join(B,complement(join(A,B)))) = n1,
inference(copy,[status(thm)],[c_504]) ).
cnf(c_27,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_8,c_15]) ).
cnf(c_505,plain,
n1 = join(A,join(B,join(C,complement(join(join(A,B),C))))),
inference(paramod,[status(thm)],[c_21,c_7]) ).
cnf(c_506,plain,
n1 = join(A,join(B,join(C,complement(join(A,join(B,C)))))),
inference(paramod,[status(thm)],[c_7,c_505]) ).
cnf(c_43,plain,
join(A,join(B,join(C,complement(join(A,join(B,C)))))) = n1,
inference(copy,[status(thm)],[c_506]) ).
cnf(c_56,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_8,c_27]) ).
cnf(c_59,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_5,c_56]) ).
cnf(c_507,plain,
join(complement(A),B) = join(complement(A),join(complement(join(A,C)),B)),
inference(paramod,[status(thm)],[c_56,c_7]) ).
cnf(c_60,plain,
join(complement(A),join(complement(join(A,B)),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_507]) ).
cnf(c_508,plain,
join(complement(join(complement(join(A,B)),C)),complement(join(complement(A),C))) = complement(join(complement(join(A,B)),C)),
inference(paramod,[status(thm)],[c_60,c_59]) ).
cnf(c_105,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,C)),B))) = complement(join(complement(join(A,C)),B)),
inference(paramod,[status(thm)],[c_5,c_508]) ).
cnf(c_509,plain,
join(complement(complement(A)),complement(join(complement(join(A,B)),complement(join(complement(complement(A)),C))))) = complement(join(complement(join(A,B)),complement(join(complement(complement(A)),C)))),
inference(paramod,[status(thm)],[c_27,c_105]) ).
cnf(c_510,plain,
join(A,complement(join(complement(join(A,B)),complement(join(complement(complement(A)),C))))) = complement(join(complement(join(A,B)),complement(join(complement(complement(A)),C)))),
inference(paramod,[status(thm)],[c_8,c_509]) ).
cnf(c_511,plain,
join(A,complement(join(complement(join(A,B)),complement(join(A,C))))) = complement(join(complement(join(A,B)),complement(join(complement(complement(A)),C)))),
inference(paramod,[status(thm)],[c_8,c_510]) ).
cnf(c_464,plain,
join(A,complement(join(complement(join(A,B)),complement(join(A,C))))) = complement(join(complement(join(A,B)),complement(join(A,C)))),
inference(paramod,[status(thm)],[c_8,c_511]) ).
cnf(c_512,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),complement(complement(join(complement(join(a,b)),complement(join(a,complement(b)))))))) != n1,
inference(paramod,[status(thm)],[c_464,c_12]) ).
cnf(c_513,plain,
join(a,join(complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))),join(complement(join(a,b)),complement(join(a,complement(b)))))) != n1,
inference(paramod,[status(thm)],[c_8,c_512]) ).
cnf(c_514,plain,
join(a,join(join(complement(join(a,b)),complement(join(a,complement(b)))),complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b)))))))) != n1,
inference(paramod,[status(thm)],[c_5,c_513]) ).
cnf(c_515,plain,
join(a,join(complement(join(a,b)),join(complement(join(a,complement(b))),complement(join(a,join(complement(join(a,b)),complement(join(a,complement(b))))))))) != n1,
inference(paramod,[status(thm)],[c_7,c_514]) ).
cnf(c_516,plain,
n1 != n1,
inference(paramod,[status(thm)],[c_43,c_515]) ).
cnf(c_489,plain,
$false,
inference(copy,[status(thm)],[c_516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT017-1 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n007.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Fri Sep 25 19:55:28 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 1737024 was started by sandbox2 on n007,
% 0.10/5.37 % Fri Sep 25 19:55:28 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.37
% 0.10/5.37 % From the command line: assign(max_seconds, 300).
% 0.15/5.56
% 0.15/5.56 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 0.15/5.56
% 0.15/5.56 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.56
% 0.15/5.56 % Proof 1 at 0.13 (+ 0.05) seconds.
% 0.15/5.56 % Length of proof is 20.
% 0.15/5.56 % Level of proof is 7.
% 0.15/5.56 % Maximum clause weight is 92.000.
% 0.15/5.56 % Given clauses 64.
% 0.15/5.56
% 0.15/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------