%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM532+1 : 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 : n002.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 79 ( 33 ~; 33 |; 10 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(m__,conjecture,
aSubsetOf0(xA,xA),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aSubsetOf0(xA,xA),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_9,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(fof_nnf,[status(thm)],[mDefSub]) ).
fof(sk_mDefSub_sk,plain,
! [W0] :
( ! [W1] :
( ( ( ~ aElementOf0(sK0(W0,W1),W0)
& aElementOf0(sK0(W0,W1),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [X0] :
( aElementOf0(X0,W0)
| ~ aElementOf0(X0,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W2,sK0(W0,W1))],[nnf_9]) ).
fof(sk_mDefSub,plain,
( ! [VAR_0,VAR_1] :
( ~ aElementOf0(sK0(VAR_0,VAR_1),VAR_0)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElementOf0(sK0(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElementOf0(VAR_2,VAR_0)
| ~ aElementOf0(VAR_2,VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aSet0(VAR_1)
| ~ aSubsetOf0(VAR_1,VAR_0)
| ~ aSet0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefSub_sk]) ).
cnf(c_18,plain,
( aElementOf0(sK0(A,B),B)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
cnf(c_19,plain,
( ~ aElementOf0(sK0(A,B),A)
| ~ aSet0(B)
| aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefSub]) ).
fof(m__467,axiom,
aSet0(xA),
file('theBenchmark.p',m__467) ).
cnf(c_21,plain,
aSet0(xA),
inference(clausify,[status(thm)],[m__467]) ).
cnf(c_22,negated_conjecture,
~ aSubsetOf0(xA,xA),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_23,plain,
( aElementOf0(sK0(A,A),A)
| aSubsetOf0(A,A)
| ~ aSet0(A) ),
inference(factor,[status(thm)],[c_18]) ).
cnf(c_32,plain,
( ~ aElementOf0(sK0(xA,A),xA)
| ~ aSet0(A)
| aSubsetOf0(A,xA) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_33,negated_conjecture,
( ~ aElementOf0(sK0(xA,xA),xA)
| ~ aSet0(xA) ),
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_30,negated_conjecture,
~ aElementOf0(sK0(xA,xA),xA),
inference(resolve,[status(thm)],[c_33,c_21]) ).
cnf(c_34,plain,
( aElementOf0(sK0(xA,xA),xA)
| aSubsetOf0(xA,xA) ),
inference(resolve,[status(thm)],[c_23,c_21]) ).
cnf(c_35,negated_conjecture,
aElementOf0(sK0(xA,xA),xA),
inference(resolve,[status(thm)],[c_22,c_34]) ).
cnf(c_31,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_30,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM532+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 03:10:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 703673 was started by sandbox on n002,
% 0.10/0.36 % Sat Sep 26 03:10:36 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 9.
% 0.10/0.38 % Level of proof is 3.
% 0.10/0.38 % Maximum clause weight is 12.000.
% 0.10/0.38 % Given clauses 12.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------