%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT243-1 : 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 : n010.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 152.19s 20.20s
% Output : CNFRefutation 156.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 74 unt; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 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 : 122 ( 13 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_join,axiom,
! [VAR_0] : join(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_join) ).
cnf(c_2,plain,
join(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_join]) ).
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_H57,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,meet(VAR_0,join(VAR_1,VAR_2)))) = meet(VAR_0,join(VAR_1,meet(join(VAR_0,VAR_1),join(VAR_2,meet(VAR_0,VAR_1))))),
file('theBenchmark.p',equation_H57) ).
cnf(c_12,plain,
meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,meet(join(A,B),join(C,meet(A,B))))),
inference(clausify,[status(thm)],[equation_H57]) ).
cnf(c_13,plain,
meet(A,join(B,meet(join(A,B),join(C,meet(A,B))))) = meet(A,join(B,meet(A,join(B,C)))),
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_23,plain,
meet(A,meet(B,join(meet(A,B),C))) = meet(A,B),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_7352,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_7352]) ).
cnf(c_7353,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_29,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_7353]) ).
cnf(c_7354,plain,
one = join(A,join(B,complement(join(A,B)))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_38,plain,
join(A,join(B,complement(join(A,B)))) = one,
inference(copy,[status(thm)],[c_7354]) ).
cnf(c_40,plain,
join(A,zero) = A,
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_7355,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_7355]) ).
cnf(c_46,plain,
meet(A,join(B,meet(join(B,A),join(C,meet(A,B))))) = meet(A,join(B,meet(A,join(B,C)))),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_58,plain,
join(A,meet(B,meet(C,A))) = A,
inference(paramod,[status(thm)],[c_7,c_18]) ).
cnf(c_7356,plain,
A = join(zero,A),
inference(paramod,[status(thm)],[c_40,c_6]) ).
cnf(c_69,plain,
join(zero,A) = A,
inference(copy,[status(thm)],[c_7356]) ).
cnf(c_82,plain,
meet(A,zero) = zero,
inference(paramod,[status(thm)],[c_69,c_18]) ).
cnf(c_83,plain,
meet(complement(A),meet(B,A)) = zero,
inference(paramod,[status(thm)],[c_82,c_43]) ).
cnf(c_7357,plain,
meet(complement(b),a) = zero,
inference(paramod,[status(thm)],[c_15,c_83]) ).
cnf(c_119,plain,
meet(a,complement(b)) = zero,
inference(paramod,[status(thm)],[c_5,c_7357]) ).
cnf(c_7358,plain,
meet(a,join(complement(b),meet(join(a,complement(b)),join(A,zero)))) = meet(a,join(complement(b),meet(a,join(complement(b),A)))),
inference(paramod,[status(thm)],[c_119,c_13]) ).
cnf(c_123,plain,
meet(a,join(complement(b),meet(join(a,complement(b)),A))) = meet(a,join(complement(b),meet(a,join(complement(b),A)))),
inference(paramod,[status(thm)],[c_40,c_7358]) ).
cnf(c_7359,plain,
join(meet(A,join(meet(B,A),C)),meet(B,A)) = meet(A,join(meet(B,A),C)),
inference(paramod,[status(thm)],[c_23,c_18]) ).
cnf(c_132,plain,
join(meet(A,B),meet(B,join(meet(A,B),C))) = meet(B,join(meet(A,B),C)),
inference(paramod,[status(thm)],[c_6,c_7359]) ).
cnf(c_7360,plain,
meet(A,B) = meet(B,meet(A,join(C,B))),
inference(paramod,[status(thm)],[c_19,c_27]) ).
cnf(c_210,plain,
meet(A,meet(B,join(C,A))) = meet(B,A),
inference(copy,[status(thm)],[c_7360]) ).
cnf(c_7361,plain,
meet(A,join(meet(B,C),meet(join(meet(B,C),A),C))) = meet(A,join(meet(B,C),meet(A,join(meet(B,C),C)))),
inference(paramod,[status(thm)],[c_58,c_46]) ).
cnf(c_7362,plain,
meet(A,join(meet(B,C),meet(C,join(meet(B,C),A)))) = meet(A,join(meet(B,C),meet(A,join(meet(B,C),C)))),
inference(paramod,[status(thm)],[c_5,c_7361]) ).
cnf(c_7363,plain,
meet(A,meet(C,join(meet(B,C),A))) = meet(A,join(meet(B,C),meet(A,join(meet(B,C),C)))),
inference(paramod,[status(thm)],[c_132,c_7362]) ).
cnf(c_7364,plain,
meet(C,A) = meet(A,join(meet(B,C),meet(A,join(meet(B,C),C)))),
inference(paramod,[status(thm)],[c_210,c_7363]) ).
cnf(c_7365,plain,
meet(C,A) = meet(A,join(meet(B,C),meet(A,join(C,meet(B,C))))),
inference(paramod,[status(thm)],[c_6,c_7364]) ).
cnf(c_7366,plain,
meet(C,A) = meet(A,join(meet(B,C),meet(A,C))),
inference(paramod,[status(thm)],[c_18,c_7365]) ).
cnf(c_623,plain,
meet(A,join(meet(B,C),meet(A,C))) = meet(C,A),
inference(copy,[status(thm)],[c_7366]) ).
cnf(c_7367,plain,
meet(a,join(complement(b),zero)) = meet(a,join(complement(b),meet(a,join(complement(b),complement(join(a,complement(b))))))),
inference(paramod,[status(thm)],[c_10,c_123]) ).
cnf(c_7368,plain,
meet(a,join(zero,complement(b))) = meet(a,join(complement(b),meet(a,join(complement(b),complement(join(a,complement(b))))))),
inference(paramod,[status(thm)],[c_6,c_7367]) ).
cnf(c_7369,plain,
meet(a,complement(b)) = meet(a,join(complement(b),meet(a,join(complement(b),complement(join(a,complement(b))))))),
inference(paramod,[status(thm)],[c_69,c_7368]) ).
cnf(c_7370,plain,
zero = meet(a,join(complement(b),meet(a,join(complement(b),complement(join(a,complement(b))))))),
inference(paramod,[status(thm)],[c_119,c_7369]) ).
cnf(c_5523,plain,
meet(a,join(complement(b),meet(a,join(complement(b),complement(join(a,complement(b))))))) = zero,
inference(copy,[status(thm)],[c_7370]) ).
cnf(c_5642,plain,
meet(A,join(B,meet(A,join(B,C)))) = meet(join(B,C),A),
inference(paramod,[status(thm)],[c_3,c_623]) ).
cnf(c_7371,plain,
meet(join(complement(b),complement(join(a,complement(b)))),a) = zero,
inference(paramod,[status(thm)],[c_5642,c_5523]) ).
cnf(c_5902,plain,
meet(a,join(complement(b),complement(join(a,complement(b))))) = zero,
inference(paramod,[status(thm)],[c_5,c_7371]) ).
cnf(c_7372,plain,
( complement(a) = join(complement(b),complement(join(a,complement(b))))
| join(a,join(complement(b),complement(join(a,complement(b))))) != one ),
inference(resolve,[status(thm)],[c_11,c_5902]) ).
cnf(c_7373,plain,
complement(a) = join(complement(b),complement(join(a,complement(b)))),
inference(resolve,[status(thm)],[c_7372,c_38]) ).
cnf(c_7343,plain,
join(complement(b),complement(join(a,complement(b)))) = complement(a),
inference(copy,[status(thm)],[c_7373]) ).
cnf(c_7374,plain,
join(complement(b),complement(a)) = join(complement(b),complement(join(a,complement(b)))),
inference(paramod,[status(thm)],[c_7343,c_29]) ).
cnf(c_7375,plain,
join(complement(a),complement(b)) = join(complement(b),complement(join(a,complement(b)))),
inference(paramod,[status(thm)],[c_6,c_7374]) ).
cnf(c_7376,plain,
join(complement(a),complement(b)) = complement(a),
inference(paramod,[status(thm)],[c_7343,c_7375]) ).
cnf(c_7351,plain,
$false,
inference(resolve,[status(thm)],[c_17,c_7376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT243-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n010.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 20:19:45 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.38 % Process 1575303 was started by sandbox on n010,
% 0.08/0.38 % Fri Sep 25 20:19:45 2026
% 0.08/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 152.19/20.20
% 152.19/20.20 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 152.19/20.20
% 152.19/20.20 % SZS status Unsatisfiable for theBenchmark
% 152.19/20.20
% 152.19/20.20 % Proof 1 at 3.12 (+ 0.57) seconds.
% 152.19/20.20 % Length of proof is 39.
% 152.19/20.20 % Level of proof is 10.
% 152.19/20.20 % Maximum clause weight is 23.000.
% 152.19/20.20 % Given clauses 285.
% 152.19/20.20
% 152.19/20.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------