%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 09:52:56 AM UTC 2026
% Result : Unsatisfiable 0.15s 10.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 6 ( 3 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma_1d_2,axiom,
! [VAR_0] : element_of_collection(VAR_0,top_of_basis(f)),
file('theBenchmark.p',lemma_1d_2) ).
cnf(c_22,plain,
element_of_collection(A,top_of_basis(f)),
inference(clausify,[status(thm)],[lemma_1d_2]) ).
fof(lemma_1d_4,axiom,
! [VAR_0,VAR_1] : ~ element_of_collection(intersection_of_sets(VAR_0,VAR_1),top_of_basis(f)),
file('theBenchmark.p',lemma_1d_4) ).
cnf(c_23,plain,
~ element_of_collection(intersection_of_sets(A,B),top_of_basis(f)),
inference(clausify,[status(thm)],[lemma_1d_4]) ).
cnf(c_24,plain,
$false,
inference(resolve,[status(thm)],[c_22,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.59 % Computer : n003.cluster.edu
% 0.09/10.59 % Model : x86_64 x86_64
% 0.09/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.59 % Memory : 8046.5625MB
% 0.09/10.59 % OS : Linux 6.8.0-71-generic
% 0.09/10.59 % CPULimit : 300
% 0.09/10.59 % WCLimit : 300
% 0.09/10.59 % DateTime : Sat Sep 26 20:31:52 UTC 2026
% 0.09/10.59 % CPUTime :
% 0.09/10.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.59 % Process 3705631 was started by sandbox2 on n003,
% 0.09/10.59 % Sat Sep 26 20:31:52 2026
% 0.09/10.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.60
% 0.15/10.60 % From the command line: assign(max_seconds, 300).
% 0.15/10.61
% 0.15/10.61 % SZS status Unsatisfiable for theBenchmark
% 0.15/10.61
% 0.15/10.61 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/10.61 % Length of proof is 3.
% 0.15/10.61 % Level of proof is 1.
% 0.15/10.61 % Maximum clause weight is 4.000.
% 0.15/10.61 % Given clauses 0.
% 0.15/10.61
% 0.15/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------