%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT254-1 : 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 : n012.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 07:49:54 AM UTC 2026
% Result : Unsatisfiable 11.93s 2.04s
% Output : CNFRefutation 11.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 80 ( 77 unt; 0 def)
% Number of atoms : 85 ( 84 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 : 144 ( 18 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_meet,axiom,
! [VAR_0] : meet(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_meet) ).
cnf(c_1,plain,
meet(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_meet]) ).
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_H79,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(meet(VAR_0,join(VAR_1,meet(VAR_0,VAR_2))),meet(VAR_2,VAR_3))),
file('theBenchmark.p',equation_H79) ).
cnf(c_12,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(meet(A,join(B,meet(A,C))),meet(C,D))),
inference(clausify,[status(thm)],[equation_H79]) ).
cnf(c_13,plain,
meet(A,join(meet(A,join(B,meet(A,C))),meet(C,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_6613,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_21,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_6613]) ).
cnf(c_6614,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_24,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_6614]) ).
cnf(c_6615,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_6615]) ).
cnf(c_36,plain,
meet(A,one) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_6616,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_6616]) ).
cnf(c_39,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_6617,plain,
meet(zero,A) = meet(B,meet(complement(B),A)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_40,plain,
meet(A,meet(complement(A),B)) = meet(zero,B),
inference(copy,[status(thm)],[c_6617]) ).
cnf(c_6618,plain,
meet(A,join(meet(A,join(B,zero)),meet(complement(A),C))) = meet(A,join(B,meet(complement(A),join(A,C)))),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_61,plain,
meet(A,join(meet(A,B),meet(complement(A),C))) = meet(A,join(B,meet(complement(A),join(A,C)))),
inference(paramod,[status(thm)],[c_39,c_6618]) ).
cnf(c_6619,plain,
join(b,a) = b,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_76,plain,
join(a,b) = b,
inference(paramod,[status(thm)],[c_6,c_6619]) ).
cnf(c_79,plain,
join(one,A) = one,
inference(paramod,[status(thm)],[c_36,c_18]) ).
cnf(c_80,plain,
join(A,join(complement(A),B)) = one,
inference(paramod,[status(thm)],[c_79,c_37]) ).
cnf(c_6620,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_39,c_6]) ).
cnf(c_81,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_6620]) ).
cnf(c_94,plain,
meet(zero,A) = zero,
inference(paramod,[status(thm)],[c_39,c_19]) ).
cnf(c_96,plain,
meet(A,meet(complement(A),B)) = zero,
inference(paramod,[status(thm)],[c_94,c_40]) ).
cnf(c_99,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_81,c_18]) ).
cnf(c_6621,plain,
( complement(A) = join(complement(A),B)
| meet(A,join(complement(A),B)) != zero ),
inference(resolve,[status(thm)],[c_11,c_80]) ).
cnf(c_6622,plain,
complement(a) != join(complement(a),complement(b)),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_111,plain,
meet(a,join(complement(a),complement(b))) != zero,
inference(resolve,[status(thm)],[c_6621,c_6622]) ).
cnf(c_115,plain,
meet(A,meet(B,complement(A))) = zero,
inference(paramod,[status(thm)],[c_5,c_96]) ).
cnf(c_6623,plain,
meet(A,join(meet(A,join(B,zero)),meet(meet(C,complement(A)),D))) = meet(A,join(B,meet(meet(C,complement(A)),join(A,D)))),
inference(paramod,[status(thm)],[c_115,c_13]) ).
cnf(c_6624,plain,
meet(A,join(meet(A,B),meet(meet(C,complement(A)),D))) = meet(A,join(B,meet(meet(C,complement(A)),join(A,D)))),
inference(paramod,[status(thm)],[c_39,c_6623]) ).
cnf(c_6625,plain,
meet(A,join(meet(A,B),meet(C,meet(complement(A),D)))) = meet(A,join(B,meet(meet(C,complement(A)),join(A,D)))),
inference(paramod,[status(thm)],[c_7,c_6624]) ).
cnf(c_132,plain,
meet(A,join(meet(A,B),meet(C,meet(complement(A),D)))) = meet(A,join(B,meet(C,meet(complement(A),join(A,D))))),
inference(paramod,[status(thm)],[c_7,c_6625]) ).
cnf(c_6626,plain,
meet(A,zero) = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_10,c_24]) ).
cnf(c_6627,plain,
zero = meet(A,complement(join(A,B))),
inference(paramod,[status(thm)],[c_99,c_6626]) ).
cnf(c_147,plain,
meet(A,complement(join(A,B))) = zero,
inference(copy,[status(thm)],[c_6627]) ).
cnf(c_170,plain,
meet(a,complement(b)) = zero,
inference(paramod,[status(thm)],[c_76,c_147]) ).
cnf(c_6628,plain,
meet(a,join(zero,meet(complement(a),A))) = meet(a,join(complement(b),meet(complement(a),join(a,A)))),
inference(paramod,[status(thm)],[c_170,c_61]) ).
cnf(c_6629,plain,
meet(a,meet(complement(a),A)) = meet(a,join(complement(b),meet(complement(a),join(a,A)))),
inference(paramod,[status(thm)],[c_81,c_6628]) ).
cnf(c_6630,plain,
zero = meet(a,join(complement(b),meet(complement(a),join(a,A)))),
inference(paramod,[status(thm)],[c_96,c_6629]) ).
cnf(c_2299,plain,
meet(a,join(complement(b),meet(complement(a),join(a,A)))) = zero,
inference(copy,[status(thm)],[c_6630]) ).
cnf(c_6631,plain,
meet(A,join(meet(A,B),meet(complement(A),C))) = meet(A,join(B,meet(meet(complement(A),C),meet(complement(A),join(A,C))))),
inference(paramod,[status(thm)],[c_1,c_132]) ).
cnf(c_6632,plain,
meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(meet(complement(A),C),meet(complement(A),join(A,C))))),
inference(paramod,[status(thm)],[c_61,c_6631]) ).
cnf(c_6633,plain,
meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(complement(A),meet(meet(complement(A),C),join(A,C))))),
inference(paramod,[status(thm)],[c_27,c_6632]) ).
cnf(c_6634,plain,
meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(complement(A),meet(complement(A),meet(C,join(A,C)))))),
inference(paramod,[status(thm)],[c_7,c_6633]) ).
cnf(c_6635,plain,
meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(complement(A),meet(complement(A),C)))),
inference(paramod,[status(thm)],[c_19,c_6634]) ).
cnf(c_6283,plain,
meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(complement(A),C))),
inference(paramod,[status(thm)],[c_21,c_6635]) ).
cnf(c_6598,plain,
meet(a,join(complement(b),meet(complement(a),A))) = zero,
inference(paramod,[status(thm)],[c_6283,c_2299]) ).
cnf(c_6636,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(paramod,[status(thm)],[c_1,c_6598]) ).
cnf(c_6611,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(paramod,[status(thm)],[c_6,c_6636]) ).
cnf(c_6612,plain,
$false,
inference(resolve,[status(thm)],[c_6611,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT254-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 20:20:05 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.29 % Process 2905892 was started by sandbox2 on n012,
% 0.03/0.29 % Fri Sep 25 20:20:05 2026
% 0.03/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 11.93/2.04
% 11.93/2.04 % SZS status Unsatisfiable for theBenchmark
% 11.93/2.04
% 11.93/2.04 % Proof 1 at 1.36 (+ 0.26) seconds.
% 11.93/2.04 % Length of proof is 43.
% 11.93/2.04 % Level of proof is 9.
% 11.93/2.04 % Maximum clause weight is 25.000.
% 11.93/2.04 % Given clauses 283.
% 11.93/2.04
% 11.93/2.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------