%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT236-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 23.21s 6.94s
% Output : CNFRefutation 23.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 60 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 101 ( 7 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_H39,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_0,VAR_3)))) = meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_3,meet(VAR_0,VAR_2))))),
file('theBenchmark.p',equation_H39) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(A,C))))),
inference(clausify,[status(thm)],[equation_H39]) ).
cnf(c_13,plain,
meet(A,join(B,meet(C,join(D,meet(A,C))))) = meet(A,join(B,meet(C,join(A,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_5942,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_35,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_8,c_5942]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_5943,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_5943]) ).
cnf(c_40,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_5944,plain,
meet(meet(A,B),complement(B)) = meet(A,zero),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_43,plain,
meet(complement(A),meet(B,A)) = meet(B,zero),
inference(paramod,[status(thm)],[c_5,c_5944]) ).
cnf(c_5945,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(join(B,meet(A,C)),meet(C,join(A,B)))),
inference(paramod,[status(thm)],[c_18,c_13]) ).
cnf(c_5946,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(meet(C,join(A,B)),join(B,meet(A,C)))),
inference(paramod,[status(thm)],[c_6,c_5945]) ).
cnf(c_5947,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(B,join(meet(C,join(A,B)),meet(A,C)))),
inference(paramod,[status(thm)],[c_35,c_5946]) ).
cnf(c_5948,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(B,join(meet(A,C),meet(C,join(A,B))))),
inference(paramod,[status(thm)],[c_6,c_5947]) ).
cnf(c_61,plain,
meet(A,join(B,join(meet(A,C),meet(C,join(A,B))))) = meet(A,join(B,meet(A,C))),
inference(copy,[status(thm)],[c_5948]) ).
cnf(c_65,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_66,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_65,c_37]) ).
cnf(c_5949,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_40,c_6]) ).
cnf(c_67,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_5949]) ).
cnf(c_80,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_67,c_18]) ).
cnf(c_81,plain,
meet(complement(A),meet(B,A)) = zero,
inference(paramod,[status(thm)],[c_80,c_43]) ).
cnf(c_5950,plain,
meet(complement(b),a) = zero,
inference(paramod,[status(thm)],[c_15,c_81]) ).
cnf(c_93,plain,
meet(a,complement(b)) = zero,
inference(paramod,[status(thm)],[c_5,c_5950]) ).
cnf(c_5951,plain,
( complement(A) = join(complement(A),B)
| meet(A,join(complement(A),B)) != zero ),
inference(resolve,[status(thm)],[c_11,c_66]) ).
cnf(c_5952,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_460,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(resolve,[status(thm)],[c_5951,c_5952]) ).
cnf(c_5953,plain,
meet(A,join(complement(A),join(meet(A,B),meet(B,one)))) = meet(A,join(complement(A),meet(A,B))),
inference(paramod,[status(thm)],[c_9,c_61]) ).
cnf(c_5954,plain,
meet(A,join(complement(A),join(meet(A,B),B))) = meet(A,join(complement(A),meet(A,B))),
inference(paramod,[status(thm)],[c_36,c_5953]) ).
cnf(c_5955,plain,
meet(A,join(complement(A),join(B,meet(A,B)))) = meet(A,join(complement(A),meet(A,B))),
inference(paramod,[status(thm)],[c_6,c_5954]) ).
cnf(c_5956,plain,
meet(A,join(complement(A),B)) = meet(A,join(complement(A),meet(A,B))),
inference(paramod,[status(thm)],[c_18,c_5955]) ).
cnf(c_2321,plain,
meet(A,join(complement(A),meet(A,B))) = meet(A,join(complement(A),B)),
inference(copy,[status(thm)],[c_5956]) ).
cnf(c_5957,plain,
meet(a,join(complement(a),zero)) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_93,c_2321]) ).
cnf(c_5958,plain,
meet(a,join(zero,complement(a))) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_6,c_5957]) ).
cnf(c_5959,plain,
meet(a,complement(a)) = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_67,c_5958]) ).
cnf(c_5960,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_10,c_5959]) ).
cnf(c_5961,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_5960]) ).
cnf(c_5941,plain,
$false,
inference(resolve,[status(thm)],[c_460,c_5961]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT236-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n018.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 20:21:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2772059 was started by sandbox on n018,
% 0.09/0.35 % Fri Sep 25 20:21:06 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.35
% 0.13/0.35 % From the command line: assign(max_seconds, 300).
% 23.21/6.94
% 23.21/6.94 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 23.21/6.94
% 23.21/6.94 % SZS status Unsatisfiable for theBenchmark
% 23.21/6.94
% 23.21/6.94 % Proof 1 at 2.68 (+ 0.59) seconds.
% 23.21/6.94 % Length of proof is 31.
% 23.21/6.94 % Level of proof is 6.
% 23.21/6.94 % Maximum clause weight is 53.000.
% 23.21/6.94 % Given clauses 291.
% 23.21/6.94
% 23.21/6.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------