%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET019+4 : 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 : n012.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 08:35:21 AM UTC 2026
% Result : Theorem 0.03s 0.31s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 21 ( 8 ~; 3 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 10 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',equal_set) ).
fof(thI02,conjecture,
! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
file('theBenchmark.p',thI02) ).
fof(thI02_neg,negated_conjecture,
~ ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
=> equal_set(A,B) ),
inference(assume_negation,[status(cth)],[thI02]) ).
cnf(c_18,plain,
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
fof(nnf_12,plain,
? [A,B] :
( ~ equal_set(A,B)
& subset(B,A)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[thI02_neg]) ).
fof(sk_thI02_neg,plain,
( ~ equal_set(sK0,sK1)
& subset(sK1,sK0)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_12]) ).
cnf(c_42,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thI02_neg]) ).
cnf(c_43,negated_conjecture,
subset(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_thI02_neg]) ).
cnf(c_44,negated_conjecture,
~ equal_set(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thI02_neg]) ).
cnf(c_87,negated_conjecture,
( ~ subset(sK1,sK0)
| equal_set(sK0,sK1) ),
inference(resolve,[status(thm)],[c_42,c_18]) ).
cnf(c_88,negated_conjecture,
~ subset(sK1,sK0),
inference(resolve,[status(thm)],[c_44,c_87]) ).
cnf(c_86,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_43,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET019+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 06:52:05 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 4124899 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 06:52:05 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.03/0.31
% 0.03/0.31 % SZS status Theorem for theBenchmark
% 0.03/0.31
% 0.03/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.31 % Length of proof is 7.
% 0.03/0.31 % Level of proof is 2.
% 0.03/0.31 % Maximum clause weight is 9.000.
% 0.03/0.31 % Given clauses 30.
% 0.03/0.31
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------