%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT234-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:49:51 AM UTC 2026
% Result : Unsatisfiable 33.84s 5.42s
% Output : CNFRefutation 33.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 76 ( 73 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 109 ( 15 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(absorption1,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption1) ).
cnf(c_3,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption1]) ).
fof(absorption2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2) ).
cnf(c_4,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_5,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_6,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(associativity_of_meet,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(VAR_0,VAR_1),VAR_2) = meet(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_meet) ).
cnf(c_7,plain,
meet(meet(A,B),C) = meet(A,meet(B,C)),
inference(clausify,[status(thm)],[associativity_of_meet]) ).
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_8,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_of_join]) ).
fof(complement_join,axiom,
! [VAR_0] : join(VAR_0,complement(VAR_0)) = one,
file('theBenchmark.p',complement_join) ).
cnf(c_9,plain,
join(A,complement(A)) = one,
inference(clausify,[status(thm)],[complement_join]) ).
fof(complement_meet,axiom,
! [VAR_0] : meet(VAR_0,complement(VAR_0)) = zero,
file('theBenchmark.p',complement_meet) ).
cnf(c_10,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[complement_meet]) ).
fof(meet_join_complement,axiom,
! [VAR_0,VAR_1] :
( complement(VAR_0) = VAR_1
| join(VAR_0,VAR_1) != one
| meet(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',meet_join_complement) ).
cnf(c_11,plain,
( complement(A) = B
| join(A,B) != one
| meet(A,B) != zero ),
inference(clausify,[status(thm)],[meet_join_complement]) ).
fof(equation_H32,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : meet(VAR_0,join(VAR_1,meet(VAR_0,meet(VAR_2,VAR_3)))) = meet(VAR_0,join(VAR_1,meet(VAR_2,join(meet(VAR_0,VAR_3),meet(VAR_1,VAR_3))))),
file('theBenchmark.p',equation_H32) ).
cnf(c_12,plain,
meet(A,join(B,meet(A,meet(C,D)))) = meet(A,join(B,meet(C,join(meet(A,D),meet(B,D))))),
inference(clausify,[status(thm)],[equation_H32]) ).
cnf(c_13,plain,
meet(A,join(B,meet(C,join(meet(A,D),meet(B,D))))) = meet(A,join(B,meet(A,meet(C,D)))),
inference(copy,[status(thm)],[c_12]) ).
fof(prove_distributivity_hypothesis,axiom,
meet(b,a) = a,
file('theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(c_14,plain,
meet(b,a) = a,
inference(clausify,[status(thm)],[prove_distributivity_hypothesis]) ).
cnf(c_15,plain,
meet(a,b) = a,
inference(paramod,[status(thm)],[c_5,c_14]) ).
fof(prove_distributivity,axiom,
join(complement(b),complement(a)) != complement(a),
file('theBenchmark.p',prove_distributivity) ).
cnf(c_16,plain,
join(complement(b),complement(a)) != complement(a),
inference(clausify,[status(thm)],[prove_distributivity]) ).
cnf(c_17,plain,
join(complement(a),complement(b)) != complement(a),
inference(paramod,[status(thm)],[c_6,c_16]) ).
cnf(c_18,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_19,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_6171,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_27,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_6171]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_6172,plain,
join(one,A) = join(B,join(complement(B),A)),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_37,plain,
join(A,join(complement(A),B)) = join(one,B),
inference(copy,[status(thm)],[c_6172]) ).
cnf(c_6173,plain,
join(join(A,B),complement(B)) = join(A,one),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_39,plain,
join(complement(A),join(B,A)) = join(B,one),
inference(paramod,[status(thm)],[c_6,c_6173]) ).
cnf(c_40,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_6174,plain,
meet(A,join(B,meet(C,join(meet(A,join(B,D)),B)))) = meet(A,join(B,meet(A,meet(C,join(B,D))))),
inference(paramod,[status(thm)],[c_3,c_13]) ).
cnf(c_49,plain,
meet(A,join(B,meet(C,join(B,meet(A,join(B,D)))))) = meet(A,join(B,meet(A,meet(C,join(B,D))))),
inference(paramod,[status(thm)],[c_6,c_6174]) ).
cnf(c_6175,plain,
meet(a,A) = meet(a,meet(b,A)),
inference(paramod,[status(thm)],[c_15,c_7]) ).
cnf(c_63,plain,
meet(a,meet(b,A)) = meet(a,A),
inference(copy,[status(thm)],[c_6175]) ).
cnf(c_75,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_76,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_75,c_37]) ).
cnf(c_6176,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_40,c_6]) ).
cnf(c_77,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_6176]) ).
cnf(c_6177,plain,
one = join(A,one),
inference(paramod,[status(thm)],[c_75,c_6]) ).
cnf(c_82,plain,
join(A,one) = one,
inference(copy,[status(thm)],[c_6177]) ).
cnf(c_83,plain,
join(complement(A),join(B,A)) = one,
inference(paramod,[status(thm)],[c_82,c_39]) ).
cnf(c_93,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_77,c_18]) ).
cnf(c_131,plain,
meet(a,meet(A,b)) = meet(a,A),
inference(paramod,[status(thm)],[c_5,c_63]) ).
cnf(c_181,plain,
join(meet(A,b),meet(a,A)) = meet(A,b),
inference(paramod,[status(thm)],[c_131,c_18]) ).
cnf(c_6178,plain,
join(complement(meet(a,A)),meet(A,b)) = one,
inference(paramod,[status(thm)],[c_181,c_83]) ).
cnf(c_220,plain,
join(meet(A,b),complement(meet(a,A))) = one,
inference(paramod,[status(thm)],[c_6,c_6178]) ).
cnf(c_6179,plain,
meet(A,zero) = meet(B,meet(A,complement(B))),
inference(paramod,[status(thm)],[c_10,c_27]) ).
cnf(c_6180,plain,
zero = meet(B,meet(A,complement(B))),
inference(paramod,[status(thm)],[c_93,c_6179]) ).
cnf(c_243,plain,
meet(A,meet(B,complement(A))) = zero,
inference(copy,[status(thm)],[c_6180]) ).
cnf(c_6181,plain,
( complement(A) = join(complement(A),B)
| meet(A,join(complement(A),B)) != zero ),
inference(resolve,[status(thm)],[c_11,c_76]) ).
cnf(c_6182,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_517,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(resolve,[status(thm)],[c_6181,c_6182]) ).
cnf(c_6183,plain,
join(meet(join(A,a),b),complement(a)) = one,
inference(paramod,[status(thm)],[c_19,c_220]) ).
cnf(c_6184,plain,
join(meet(b,join(A,a)),complement(a)) = one,
inference(paramod,[status(thm)],[c_5,c_6183]) ).
cnf(c_536,plain,
join(complement(a),meet(b,join(A,a))) = one,
inference(paramod,[status(thm)],[c_6,c_6184]) ).
cnf(c_6185,plain,
meet(b,join(complement(a),meet(A,one))) = meet(b,join(complement(a),meet(b,meet(A,join(complement(a),a))))),
inference(paramod,[status(thm)],[c_536,c_49]) ).
cnf(c_6186,plain,
meet(b,join(complement(a),A)) = meet(b,join(complement(a),meet(b,meet(A,join(complement(a),a))))),
inference(paramod,[status(thm)],[c_36,c_6185]) ).
cnf(c_6187,plain,
meet(b,join(complement(a),A)) = meet(b,join(complement(a),meet(b,meet(A,join(a,complement(a)))))),
inference(paramod,[status(thm)],[c_6,c_6186]) ).
cnf(c_6188,plain,
meet(b,join(complement(a),A)) = meet(b,join(complement(a),meet(b,meet(A,one)))),
inference(paramod,[status(thm)],[c_9,c_6187]) ).
cnf(c_6189,plain,
meet(b,join(complement(a),A)) = meet(b,join(complement(a),meet(b,A))),
inference(paramod,[status(thm)],[c_36,c_6188]) ).
cnf(c_633,plain,
meet(b,join(complement(a),meet(b,A))) = meet(b,join(complement(a),A)),
inference(copy,[status(thm)],[c_6189]) ).
cnf(c_6190,plain,
meet(b,join(complement(a),zero)) = meet(b,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_10,c_633]) ).
cnf(c_6191,plain,
meet(b,join(zero,complement(a))) = meet(b,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_6,c_6190]) ).
cnf(c_6192,plain,
meet(b,complement(a)) = meet(b,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_77,c_6191]) ).
cnf(c_6078,plain,
meet(b,join(complement(a),complement(b))) = meet(b,complement(a)),
inference(copy,[status(thm)],[c_6192]) ).
cnf(c_6193,plain,
meet(a,meet(b,complement(a))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_6078,c_63]) ).
cnf(c_6194,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_243,c_6193]) ).
cnf(c_6195,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_6194]) ).
cnf(c_6170,plain,
$false,
inference(resolve,[status(thm)],[c_517,c_6195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT234-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.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 : Fri Sep 25 20:23:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3205884 was started by sandbox2 on n016,
% 0.10/0.38 % Fri Sep 25 20:23:45 2026
% 0.10/0.38 % 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).
% 33.84/5.42
% 33.84/5.42 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 33.84/5.42
% 33.84/5.42 % SZS status Unsatisfiable for theBenchmark
% 33.84/5.42
% 33.84/5.42 % Proof 1 at 3.71 (+ 0.88) seconds.
% 33.84/5.42 % Length of proof is 39.
% 33.84/5.42 % Level of proof is 9.
% 33.84/5.42 % Maximum clause weight is 62.000.
% 33.84/5.42 % Given clauses 291.
% 33.84/5.42
% 33.84/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------