%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT035-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 07:49:35 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(k_on_join,axiom,
! [VAR_0,VAR_1] : k(join(VAR_0,VAR_1)) = meet(k(VAR_0),k(VAR_1)),
file('theBenchmark.p',k_on_join) ).
cnf(c_15,plain,
k(join(A,B)) = meet(k(A),k(B)),
inference(clausify,[status(thm)],[k_on_join]) ).
fof(k_on_bottom,axiom,
k(n0) = n1,
file('theBenchmark.p',k_on_bottom) ).
cnf(c_17,plain,
k(n0) = n1,
inference(clausify,[status(thm)],[k_on_bottom]) ).
fof(f_on_meet,axiom,
! [VAR_0,VAR_1] : f(meet(VAR_0,VAR_1)) = join(f(VAR_0),f(VAR_1)),
file('theBenchmark.p',f_on_meet) ).
cnf(c_19,plain,
f(meet(A,B)) = join(f(A),f(B)),
inference(clausify,[status(thm)],[f_on_meet]) ).
fof(f_on_top,axiom,
f(n1) = n0,
file('theBenchmark.p',f_on_top) ).
cnf(c_20,plain,
f(n1) = n0,
inference(clausify,[status(thm)],[f_on_top]) ).
fof(comp_join_hemimorphism,axiom,
( f(k(n0)) != n0
| f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ),
file('theBenchmark.p',comp_join_hemimorphism) ).
cnf(c_21,plain,
( f(k(n0)) != n0
| f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb))) ),
inference(clausify,[status(thm)],[comp_join_hemimorphism]) ).
cnf(c_23,plain,
( f(k(n0)) != n0
| f(meet(k(aa),k(bb))) != join(f(k(aa)),f(k(bb))) ),
inference(paramod,[status(thm)],[c_15,c_21]) ).
cnf(c_24,plain,
( f(k(n0)) != n0
| join(f(k(aa)),f(k(bb))) != join(f(k(aa)),f(k(bb))) ),
inference(paramod,[status(thm)],[c_19,c_23]) ).
cnf(c_25,plain,
( f(n1) != n0
| join(f(k(aa)),f(k(bb))) != join(f(k(aa)),f(k(bb))) ),
inference(paramod,[status(thm)],[c_17,c_24]) ).
cnf(c_26,plain,
( n0 != n0
| join(f(k(aa)),f(k(bb))) != join(f(k(aa)),f(k(bb))) ),
inference(paramod,[status(thm)],[c_20,c_25]) ).
cnf(c_27,plain,
n0 != n0,
inference(copy,[status(thm)],[c_26]) ).
cnf(c_22,plain,
$false,
inference(copy,[status(thm)],[c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT035-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 20:00:41 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 2714747 was started by sandbox on n018,
% 0.10/5.39 % Fri Sep 25 20:00:41 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 6.
% 0.15/5.40 % Level of proof is 1.
% 0.15/5.40 % Maximum clause weight is 10.000.
% 0.15/5.40 % Given clauses 0.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------