%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET604+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:36:35 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 1 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_subset,axiom,
! [B] : subset(empty_set,B),
file('theBenchmark.p',empty_set_subset) ).
fof(difference_empty_set,axiom,
! [B,C] :
( difference(B,C) = empty_set
<=> subset(B,C) ),
file('theBenchmark.p',difference_empty_set) ).
fof(prove_no_difference_with_empty_set,conjecture,
! [B] : difference(empty_set,B) = empty_set,
file('theBenchmark.p',prove_no_difference_with_empty_set) ).
fof(prove_no_difference_with_empty_set_neg,negated_conjecture,
~ ! [B] : difference(empty_set,B) = empty_set,
inference(assume_negation,[status(cth)],[prove_no_difference_with_empty_set]) ).
fof(nnf_9,plain,
? [B] : difference(empty_set,B) != empty_set,
inference(fof_nnf,[status(thm)],[prove_no_difference_with_empty_set_neg]) ).
fof(sk_prove_no_difference_with_empty_set_neg,plain,
difference(empty_set,sK0) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_9]) ).
cnf(c_13,negated_conjecture,
difference(empty_set,sK0) != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_no_difference_with_empty_set_neg]) ).
cnf(c_25,plain,
( ~ subset(A,B)
| difference(A,B) = empty_set ),
inference(clausify,[status(thm)],[difference_empty_set]) ).
cnf(c_27,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[empty_set_subset]) ).
cnf(c_35,negated_conjecture,
~ subset(empty_set,sK0),
inference(resolve,[status(thm)],[c_25,c_13]) ).
cnf(c_34,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_27,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET604+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n020.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 : Sat Sep 26 07:59:50 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 1027230 was started by sandbox2 on n020,
% 0.08/0.37 % Sat Sep 26 07:59:50 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 7.
% 0.14/0.39 % Level of proof is 2.
% 0.14/0.39 % Maximum clause weight is 8.000.
% 0.14/0.39 % Given clauses 14.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------