%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT239-1 : 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 : n017.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 07:49:52 AM UTC 2026
% Result : Unsatisfiable 30.37s 4.28s
% Output : CNFRefutation 30.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 85 ( 82 unt; 0 def)
% Number of atoms : 90 ( 89 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 : 116 ( 19 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_H49,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,join(meet(VAR_0,VAR_2),meet(VAR_2,join(VAR_1,VAR_3))))),
file('theBenchmark.p',equation_H49) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))),
inference(clausify,[status(thm)],[equation_H49]) ).
cnf(c_13,plain,
meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))) = 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_19,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_8947,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_8947]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_8948,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_8948]) ).
cnf(c_8949,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_8949]) ).
cnf(c_40,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_8950,plain,
meet(zero,A) = meet(B,meet(complement(B),A)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_41,plain,
meet(A,meet(complement(A),B)) = meet(zero,B),
inference(copy,[status(thm)],[c_8950]) ).
cnf(c_8951,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_8951]) ).
cnf(c_8952,plain,
meet(a,A) = meet(a,meet(b,A)),
inference(paramod,[status(thm)],[c_15,c_7]) ).
cnf(c_62,plain,
meet(a,meet(b,A)) = meet(a,A),
inference(copy,[status(thm)],[c_8952]) ).
cnf(c_8953,plain,
A = meet(one,A),
inference(paramod,[status(thm)],[c_36,c_5]) ).
cnf(c_71,plain,
meet(one,A) = A,
inference(copy,[status(thm)],[c_8953]) ).
cnf(c_73,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_74,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_73,c_37]) ).
cnf(c_8954,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_40,c_6]) ).
cnf(c_75,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_8954]) ).
cnf(c_8955,plain,
one = join(A,one),
inference(paramod,[status(thm)],[c_73,c_6]) ).
cnf(c_85,plain,
join(A,one) = one,
inference(copy,[status(thm)],[c_8955]) ).
cnf(c_86,plain,
join(complement(A),join(B,A)) = one,
inference(paramod,[status(thm)],[c_85,c_39]) ).
cnf(c_91,plain,
meet(zero,A) = zero,
inference(paramod,[status(thm)],[c_40,c_19]) ).
cnf(c_92,plain,
meet(A,meet(complement(A),B)) = zero,
inference(paramod,[status(thm)],[c_91,c_41]) ).
cnf(c_95,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_75,c_18]) ).
cnf(c_96,plain,
meet(complement(A),meet(B,A)) = zero,
inference(paramod,[status(thm)],[c_95,c_43]) ).
cnf(c_8956,plain,
meet(complement(b),a) = zero,
inference(paramod,[status(thm)],[c_15,c_96]) ).
cnf(c_110,plain,
meet(a,complement(b)) = zero,
inference(paramod,[status(thm)],[c_5,c_8956]) ).
cnf(c_8957,plain,
meet(a,join(A,join(zero,meet(complement(b),join(A,B))))) = meet(a,join(A,meet(complement(b),join(a,B)))),
inference(paramod,[status(thm)],[c_110,c_13]) ).
cnf(c_8958,plain,
meet(a,join(A,meet(complement(b),join(A,B)))) = meet(a,join(A,meet(complement(b),join(a,B)))),
inference(paramod,[status(thm)],[c_75,c_8957]) ).
cnf(c_114,plain,
meet(a,join(A,meet(complement(b),join(a,B)))) = meet(a,join(A,meet(complement(b),join(A,B)))),
inference(copy,[status(thm)],[c_8958]) ).
cnf(c_138,plain,
meet(a,meet(A,b)) = meet(a,A),
inference(paramod,[status(thm)],[c_5,c_62]) ).
cnf(c_8959,plain,
join(meet(b,A),meet(a,A)) = meet(b,A),
inference(paramod,[status(thm)],[c_62,c_18]) ).
cnf(c_142,plain,
join(meet(a,A),meet(b,A)) = meet(b,A),
inference(paramod,[status(thm)],[c_6,c_8959]) ).
cnf(c_184,plain,
join(meet(A,b),meet(a,A)) = meet(A,b),
inference(paramod,[status(thm)],[c_138,c_18]) ).
cnf(c_186,plain,
join(a,meet(b,join(a,A))) = meet(b,join(a,A)),
inference(paramod,[status(thm)],[c_3,c_142]) ).
cnf(c_8960,plain,
join(complement(meet(a,A)),meet(A,b)) = one,
inference(paramod,[status(thm)],[c_184,c_86]) ).
cnf(c_226,plain,
join(meet(A,b),complement(meet(a,A))) = one,
inference(paramod,[status(thm)],[c_6,c_8960]) ).
cnf(c_8961,plain,
( complement(A) = join(complement(A),B)
| meet(A,join(complement(A),B)) != zero ),
inference(resolve,[status(thm)],[c_11,c_74]) ).
cnf(c_8962,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_529,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(resolve,[status(thm)],[c_8961,c_8962]) ).
cnf(c_8963,plain,
join(meet(join(a,A),b),complement(a)) = one,
inference(paramod,[status(thm)],[c_3,c_226]) ).
cnf(c_8964,plain,
join(meet(b,join(a,A)),complement(a)) = one,
inference(paramod,[status(thm)],[c_5,c_8963]) ).
cnf(c_543,plain,
join(complement(a),meet(b,join(a,A))) = one,
inference(paramod,[status(thm)],[c_6,c_8964]) ).
cnf(c_8965,plain,
meet(a,join(complement(a),meet(complement(b),join(a,meet(b,join(a,A)))))) = meet(a,join(complement(a),meet(complement(b),one))),
inference(paramod,[status(thm)],[c_543,c_114]) ).
cnf(c_8966,plain,
meet(a,join(complement(a),meet(complement(b),meet(b,join(a,A))))) = meet(a,join(complement(a),meet(complement(b),one))),
inference(paramod,[status(thm)],[c_186,c_8965]) ).
cnf(c_8967,plain,
meet(a,join(complement(a),meet(b,meet(complement(b),join(a,A))))) = meet(a,join(complement(a),meet(complement(b),one))),
inference(paramod,[status(thm)],[c_27,c_8966]) ).
cnf(c_8968,plain,
meet(a,join(complement(a),zero)) = meet(a,join(complement(a),meet(complement(b),one))),
inference(paramod,[status(thm)],[c_92,c_8967]) ).
cnf(c_8969,plain,
meet(a,join(zero,complement(a))) = meet(a,join(complement(a),meet(complement(b),one))),
inference(paramod,[status(thm)],[c_6,c_8968]) ).
cnf(c_8970,plain,
meet(a,complement(a)) = meet(a,join(complement(a),meet(complement(b),one))),
inference(paramod,[status(thm)],[c_75,c_8969]) ).
cnf(c_8971,plain,
zero = meet(a,join(complement(a),meet(complement(b),one))),
inference(paramod,[status(thm)],[c_10,c_8970]) ).
cnf(c_8972,plain,
zero = meet(a,join(complement(a),meet(one,complement(b)))),
inference(paramod,[status(thm)],[c_5,c_8971]) ).
cnf(c_8973,plain,
zero = meet(a,join(complement(a),complement(b))),
inference(paramod,[status(thm)],[c_71,c_8972]) ).
cnf(c_8974,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(copy,[status(thm)],[c_8973]) ).
cnf(c_8946,plain,
$false,
inference(resolve,[status(thm)],[c_529,c_8974]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT239-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 20:14:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3080992 was started by sandbox on n017,
% 0.09/0.37 % Fri Sep 25 20:14:33 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 30.37/4.28
% 30.37/4.28 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 30.37/4.28
% 30.37/4.28 % SZS status Unsatisfiable for theBenchmark
% 30.37/4.28
% 30.37/4.28 % Proof 1 at 3.19 (+ 0.63) seconds.
% 30.37/4.28 % Length of proof is 45.
% 30.37/4.28 % Level of proof is 7.
% 30.37/4.28 % Maximum clause weight is 55.000.
% 30.37/4.28 % Given clauses 288.
% 30.37/4.28
% 30.37/4.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------