%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:17:23 AM UTC 2026
% Result : Theorem 0.14s 10.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 36 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 36 ( 16 ~; 10 |; 7 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(m__2291,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__2304,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('theBenchmark.p',m__2304) ).
fof(m__,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_63,negated_conjecture,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__2338,axiom,
~ aElementOf0(xx,xQ),
file('theBenchmark.p',m__2338) ).
cnf(c_66,plain,
~ aElementOf0(xx,xQ),
inference(clausify,[status(thm)],[m__2338]) ).
cnf(c_68,plain,
aElement0(xy),
inference(clausify,[status(thm)],[m__2304]) ).
cnf(c_72,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_175,plain,
( aElementOf0(D,A)
| ~ aElementOf0(D,C)
| sdtmndt0(A,B) != C
| ~ aElement0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_489,plain,
( aElementOf0(C,xQ)
| ~ aElementOf0(C,B)
| sdtmndt0(xQ,A) != B
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_175,c_72]) ).
cnf(c_490,plain,
( aElementOf0(B,xQ)
| ~ aElementOf0(B,A)
| sdtmndt0(xQ,xy) != A ),
inference(resolve,[status(thm)],[c_489,c_68]) ).
cnf(c_491,plain,
( aElementOf0(A,xQ)
| ~ aElementOf0(A,sdtmndt0(xQ,xy)) ),
inference(xxres,[status(thm)],[c_490]) ).
cnf(c_492,negated_conjecture,
aElementOf0(xx,xQ),
inference(resolve,[status(thm)],[c_491,c_63]) ).
cnf(c_488,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_66,c_492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n013.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sat Sep 26 03:12:51 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.39 % Process 1817829 was started by sandbox2 on n013,
% 0.09/10.39 % Sat Sep 26 03:12:51 2026
% 0.09/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/10.40
% 0.14/10.40 % From the command line: assign(max_seconds, 300).
% 0.14/10.46
% 0.14/10.46 % SZS status Theorem for theBenchmark
% 0.14/10.46
% 0.14/10.46 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.14/10.46 % Length of proof is 10.
% 0.14/10.46 % Level of proof is 2.
% 0.14/10.46 % Maximum clause weight is 25.000.
% 0.14/10.46 % Given clauses 91.
% 0.14/10.46
% 0.14/10.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------