%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM533+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:17:18 AM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 47 ( 13 ~; 8 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( aSubsetOf0(xB,xC)
& ! [W0] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,xC) )
& aSubsetOf0(xA,xB)
& ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,xB) ) )
=> ( aSubsetOf0(xA,xC)
| ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,xC) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( aSubsetOf0(xB,xC)
& ! [W0] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,xC) )
& aSubsetOf0(xA,xB)
& ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,xB) ) )
=> ( aSubsetOf0(xA,xC)
| ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,xC) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_14,plain,
( ~ aSubsetOf0(xA,xC)
& ? [W0] :
( ~ aElementOf0(W0,xC)
& aElementOf0(W0,xA) )
& aSubsetOf0(xB,xC)
& ! [X1] :
( aElementOf0(X1,xC)
| ~ aElementOf0(X1,xB) )
& aSubsetOf0(xA,xB)
& ! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xA) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( ~ aSubsetOf0(xA,xC)
& ~ aElementOf0(sK0,xC)
& aElementOf0(sK0,xA)
& aSubsetOf0(xB,xC)
& ! [X1] :
( aElementOf0(X1,xC)
| ~ aElementOf0(X1,xB) )
& aSubsetOf0(xA,xB)
& ! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xA) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_14]) ).
cnf(c_29,negated_conjecture,
( aElementOf0(A,xB)
| ~ aElementOf0(A,xA) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_31,negated_conjecture,
( aElementOf0(A,xC)
| ~ aElementOf0(A,xB) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_33,negated_conjecture,
aElementOf0(sK0,xA),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_34,negated_conjecture,
~ aElementOf0(sK0,xC),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_54,plain,
aElementOf0(sK0,xB),
inference(resolve,[status(thm)],[c_33,c_29]) ).
cnf(c_58,negated_conjecture,
~ aElementOf0(sK0,xB),
inference(resolve,[status(thm)],[c_31,c_34]) ).
cnf(c_57,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_54,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM533+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 03:08:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2012730 was started by sandbox on n014,
% 0.08/0.36 % Sat Sep 26 03:08:02 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 7.
% 0.08/0.37 % Level of proof is 3.
% 0.08/0.37 % Maximum clause weight is 6.000.
% 0.08/0.37 % Given clauses 20.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------