%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT027-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:49:34 AM UTC 2026
% Result : Unsatisfiable 10.47s 1.72s
% Output : CNFRefutation 10.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 60 unt; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 149 ( 27 sgn 15 !; 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(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(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_3,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_4,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(wal_1,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_1) ).
cnf(c_5,plain,
meet(meet(join(A,B),join(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_1]) ).
cnf(c_6,plain,
meet(A,meet(join(B,A),join(C,A))) = A,
inference(paramod,[status(thm)],[c_3,c_5]) ).
fof(wal_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_2) ).
cnf(c_7,plain,
join(join(meet(A,B),meet(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_2]) ).
cnf(c_8,plain,
join(A,join(meet(B,A),meet(C,A))) = A,
inference(paramod,[status(thm)],[c_4,c_7]) ).
fof(absorption,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,join(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',absorption) ).
cnf(c_9,plain,
meet(A,join(B,join(A,C))) = A,
inference(clausify,[status(thm)],[absorption]) ).
fof(prove_associativity_of_join,axiom,
join(join(a,b),c) != join(a,join(b,c)),
file('theBenchmark.p',prove_associativity_of_join) ).
cnf(c_10,plain,
join(join(a,b),c) != join(a,join(b,c)),
inference(clausify,[status(thm)],[prove_associativity_of_join]) ).
cnf(c_11,plain,
join(c,join(a,b)) != join(a,join(b,c)),
inference(paramod,[status(thm)],[c_4,c_10]) ).
cnf(c_12,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_16,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_19,plain,
meet(A,join(A,B)) = A,
inference(paramod,[status(thm)],[c_2,c_9]) ).
cnf(c_20,plain,
meet(A,join(B,join(C,A))) = A,
inference(paramod,[status(thm)],[c_4,c_9]) ).
cnf(c_23,plain,
join(join(A,B),join(B,meet(C,join(A,B)))) = join(A,B),
inference(paramod,[status(thm)],[c_12,c_8]) ).
cnf(c_43,plain,
meet(A,join(join(B,A),C)) = A,
inference(paramod,[status(thm)],[c_4,c_20]) ).
cnf(c_52,plain,
meet(meet(A,B),join(B,C)) = meet(A,B),
inference(paramod,[status(thm)],[c_16,c_43]) ).
cnf(c_62,plain,
join(join(A,B),join(B,A)) = join(A,B),
inference(paramod,[status(thm)],[c_19,c_23]) ).
cnf(c_91,plain,
join(join(A,B),join(B,meet(C,A))) = join(A,B),
inference(paramod,[status(thm)],[c_52,c_23]) ).
cnf(c_258,plain,
meet(join(A,B),join(C,join(B,A))) = join(A,B),
inference(paramod,[status(thm)],[c_62,c_20]) ).
cnf(c_449,plain,
meet(join(A,meet(B,C)),join(C,A)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_91,c_12]) ).
cnf(c_661,plain,
meet(join(meet(A,B),C),join(B,C)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_91,c_258]) ).
cnf(c_454,plain,
meet(join(A,B),join(meet(C,A),B)) = join(meet(C,A),B),
inference(paramod,[status(thm)],[c_3,c_661]) ).
cnf(c_662,plain,
meet(join(A,meet(B,C)),join(A,C)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_4,c_449]) ).
cnf(c_459,plain,
meet(join(A,B),join(A,meet(C,B))) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_3,c_662]) ).
cnf(c_663,plain,
meet(join(A,B),join(join(B,C),A)) = join(A,meet(B,join(B,C))),
inference(paramod,[status(thm)],[c_19,c_449]) ).
cnf(c_464,plain,
meet(join(A,B),join(join(B,C),A)) = join(A,B),
inference(paramod,[status(thm)],[c_19,c_663]) ).
cnf(c_664,plain,
meet(join(join(A,B),C),join(B,C)) = join(meet(B,join(A,B)),C),
inference(paramod,[status(thm)],[c_12,c_454]) ).
cnf(c_665,plain,
meet(join(B,C),join(join(A,B),C)) = join(meet(B,join(A,B)),C),
inference(paramod,[status(thm)],[c_3,c_664]) ).
cnf(c_485,plain,
meet(join(A,B),join(join(C,A),B)) = join(A,B),
inference(paramod,[status(thm)],[c_12,c_665]) ).
cnf(c_666,plain,
meet(join(A,join(B,C)),join(A,B)) = join(A,meet(B,join(B,C))),
inference(paramod,[status(thm)],[c_19,c_459]) ).
cnf(c_667,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,meet(B,join(B,C))),
inference(paramod,[status(thm)],[c_3,c_666]) ).
cnf(c_529,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_19,c_667]) ).
cnf(c_668,plain,
meet(join(join(A,meet(B,C)),C),join(C,A)) = join(join(A,meet(B,C)),C),
inference(paramod,[status(thm)],[c_91,c_464]) ).
cnf(c_669,plain,
meet(join(C,join(A,meet(B,C))),join(C,A)) = join(join(A,meet(B,C)),C),
inference(paramod,[status(thm)],[c_4,c_668]) ).
cnf(c_670,plain,
meet(join(C,A),join(C,join(A,meet(B,C)))) = join(join(A,meet(B,C)),C),
inference(paramod,[status(thm)],[c_3,c_669]) ).
cnf(c_671,plain,
join(C,A) = join(join(A,meet(B,C)),C),
inference(paramod,[status(thm)],[c_529,c_670]) ).
cnf(c_672,plain,
join(C,A) = join(C,join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_4,c_671]) ).
cnf(c_560,plain,
join(A,join(B,meet(C,A))) = join(A,B),
inference(copy,[status(thm)],[c_672]) ).
cnf(c_564,plain,
join(join(A,B),join(C,B)) = join(join(A,B),C),
inference(paramod,[status(thm)],[c_12,c_560]) ).
cnf(c_565,plain,
join(join(A,B),join(C,A)) = join(join(A,B),C),
inference(paramod,[status(thm)],[c_19,c_560]) ).
cnf(c_673,plain,
join(join(join(A,B),C),join(B,C)) = join(join(A,B),C),
inference(paramod,[status(thm)],[c_485,c_16]) ).
cnf(c_674,plain,
join(join(B,C),join(join(A,B),C)) = join(join(A,B),C),
inference(paramod,[status(thm)],[c_4,c_673]) ).
cnf(c_675,plain,
join(join(B,C),join(A,B)) = join(join(A,B),C),
inference(paramod,[status(thm)],[c_564,c_674]) ).
cnf(c_650,plain,
join(join(A,B),C) = join(join(C,A),B),
inference(paramod,[status(thm)],[c_565,c_675]) ).
cnf(c_658,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(paramod,[status(thm)],[c_650,c_4]) ).
cnf(c_676,plain,
join(join(A,B),C) = join(B,join(C,A)),
inference(paramod,[status(thm)],[c_650,c_4]) ).
cnf(c_677,plain,
join(A,join(B,C)) = join(B,join(C,A)),
inference(paramod,[status(thm)],[c_658,c_676]) ).
cnf(c_659,plain,
join(A,join(B,C)) = join(C,join(A,B)),
inference(copy,[status(thm)],[c_677]) ).
cnf(c_678,plain,
join(a,join(b,c)) != join(c,join(a,b)),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_660,plain,
$false,
inference(resolve,[status(thm)],[c_659,c_678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT027-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 19:58:39 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1750849 was started by sandbox on n008,
% 0.10/0.36 % Fri Sep 25 19:58:39 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 10.47/1.72
% 10.47/1.72 % SZS status Unsatisfiable for theBenchmark
% 10.47/1.72
% 10.47/1.72 % Proof 1 at 0.98 (+ 0.35) seconds.
% 10.47/1.72 % Length of proof is 34.
% 10.47/1.72 % Level of proof is 13.
% 10.47/1.72 % Maximum clause weight is 29.000.
% 10.47/1.72 % Given clauses 133.
% 10.47/1.72
% 10.47/1.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------