%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT011-1 : 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 : n015.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 07:49:32 AM UTC 2026
% Result : Unsatisfiable 2.28s 0.68s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 10 sgn 20 !; 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(commutativity_of_meet2,axiom,
! [VAR_0,VAR_1] : meet2(VAR_0,VAR_1) = meet2(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet2) ).
cnf(c_10,plain,
meet2(A,B) = meet2(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet2]) ).
fof(absorption1_2,axiom,
! [VAR_0,VAR_1] : meet2(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption1_2) ).
cnf(c_11,plain,
meet2(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption1_2]) ).
fof(absorption2_2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet2(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2_2) ).
cnf(c_12,plain,
join(A,meet2(A,B)) = A,
inference(clausify,[status(thm)],[absorption2_2]) ).
fof(associativity_of_meet2,axiom,
! [VAR_0,VAR_1,VAR_2] : meet2(meet2(VAR_0,VAR_1),VAR_2) = meet2(VAR_0,meet2(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_meet2) ).
cnf(c_13,plain,
meet2(meet2(A,B),C) = meet2(A,meet2(B,C)),
inference(clausify,[status(thm)],[associativity_of_meet2]) ).
fof(prove_meets_are_same,axiom,
meet(a,b) != meet2(a,b),
file('theBenchmark.p',prove_meets_are_same) ).
cnf(c_14,plain,
meet(a,b) != meet2(a,b),
inference(clausify,[status(thm)],[prove_meets_are_same]) ).
cnf(c_15,plain,
meet2(a,b) != meet(a,b),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_16,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_17,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_23,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_34,plain,
meet2(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_11]) ).
cnf(c_38,plain,
join(A,meet2(B,A)) = A,
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_792,plain,
meet2(meet2(A,B),C) = meet2(B,meet2(A,C)),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_43,plain,
meet2(A,meet2(B,C)) = meet2(B,meet2(A,C)),
inference(paramod,[status(thm)],[c_13,c_792]) ).
cnf(c_793,plain,
meet(meet2(A,B),A) = meet2(A,B),
inference(paramod,[status(thm)],[c_12,c_17]) ).
cnf(c_53,plain,
meet(A,meet2(A,B)) = meet2(A,B),
inference(paramod,[status(thm)],[c_5,c_793]) ).
cnf(c_794,plain,
meet2(meet(A,B),A) = meet(A,B),
inference(paramod,[status(thm)],[c_4,c_34]) ).
cnf(c_54,plain,
meet2(A,meet(A,B)) = meet(A,B),
inference(paramod,[status(thm)],[c_10,c_794]) ).
cnf(c_795,plain,
meet2(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_16,c_34]) ).
cnf(c_58,plain,
meet2(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_10,c_795]) ).
cnf(c_796,plain,
meet(meet2(A,B),B) = meet2(A,B),
inference(paramod,[status(thm)],[c_38,c_17]) ).
cnf(c_62,plain,
meet(A,meet2(B,A)) = meet2(B,A),
inference(paramod,[status(thm)],[c_5,c_796]) ).
cnf(c_184,plain,
join(meet(A,B),meet(A,meet2(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_53,c_23]) ).
cnf(c_722,plain,
join(meet(A,B),meet2(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_62,c_184]) ).
cnf(c_797,plain,
meet2(meet2(A,B),meet(B,A)) = meet2(A,B),
inference(paramod,[status(thm)],[c_722,c_34]) ).
cnf(c_798,plain,
meet2(meet(B,A),meet2(A,B)) = meet2(A,B),
inference(paramod,[status(thm)],[c_10,c_797]) ).
cnf(c_799,plain,
meet2(A,meet2(meet(B,A),B)) = meet2(A,B),
inference(paramod,[status(thm)],[c_43,c_798]) ).
cnf(c_800,plain,
meet2(A,meet2(B,meet(B,A))) = meet2(A,B),
inference(paramod,[status(thm)],[c_10,c_799]) ).
cnf(c_801,plain,
meet2(A,meet(B,A)) = meet2(A,B),
inference(paramod,[status(thm)],[c_54,c_800]) ).
cnf(c_802,plain,
meet(B,A) = meet2(A,B),
inference(paramod,[status(thm)],[c_58,c_801]) ).
cnf(c_759,plain,
meet2(A,B) = meet(B,A),
inference(copy,[status(thm)],[c_802]) ).
cnf(c_803,plain,
meet(b,a) != meet(a,b),
inference(paramod,[status(thm)],[c_759,c_15]) ).
cnf(c_804,plain,
meet(a,b) != meet(a,b),
inference(paramod,[status(thm)],[c_5,c_803]) ).
cnf(c_791,plain,
$false,
inference(copy,[status(thm)],[c_804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT011-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:59:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2106114 was started by sandbox on n015,
% 0.10/0.37 % Fri Sep 25 19:59:43 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 2.28/0.68
% 2.28/0.68 % SZS status Unsatisfiable for theBenchmark
% 2.28/0.68
% 2.28/0.68 % Proof 1 at 0.21 (+ 0.09) seconds.
% 2.28/0.68 % Length of proof is 25.
% 2.28/0.68 % Level of proof is 6.
% 2.28/0.68 % Maximum clause weight is 38.000.
% 2.28/0.68 % Given clauses 86.
% 2.28/0.68
% 2.28/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------