%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET063+3 : 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 : n017.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 08:35:34 AM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 24 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 4 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 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(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(prove_subset_of_empty_set_is_empty_set,conjecture,
! [B] :
( subset(B,empty_set)
=> B = empty_set ),
file('theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).
fof(prove_subset_of_empty_set_is_empty_set_neg,negated_conjecture,
~ ! [B] :
( subset(B,empty_set)
=> B = empty_set ),
inference(assume_negation,[status(cth)],[prove_subset_of_empty_set_is_empty_set]) ).
fof(nnf_7,plain,
? [B] :
( B != empty_set
& subset(B,empty_set) ),
inference(fof_nnf,[status(thm)],[prove_subset_of_empty_set_is_empty_set_neg]) ).
fof(sk_prove_subset_of_empty_set_is_empty_set_neg,plain,
( sK0 != empty_set
& subset(sK0,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_7]) ).
cnf(c_11,negated_conjecture,
sK0 != empty_set,
inference(split_conjunct,[status(thm)],[sk_prove_subset_of_empty_set_is_empty_set_neg]) ).
cnf(c_12,negated_conjecture,
subset(sK0,empty_set),
inference(split_conjunct,[status(thm)],[sk_prove_subset_of_empty_set_is_empty_set_neg]) ).
cnf(c_14,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_21,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[empty_set_subset]) ).
cnf(c_23,negated_conjecture,
( ~ subset(empty_set,sK0)
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_14,c_12]) ).
cnf(c_24,negated_conjecture,
( ~ subset(empty_set,sK0)
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_25,negated_conjecture,
~ subset(empty_set,sK0),
inference(resolve,[status(thm)],[c_11,c_24]) ).
cnf(c_22,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_21,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 06:56:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 88011 was started by sandbox on n017,
% 0.08/0.36 % Sat Sep 26 06:56:19 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 8.
% 0.08/0.38 % Level of proof is 2.
% 0.08/0.38 % Maximum clause weight is 9.000.
% 0.08/0.38 % Given clauses 5.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------