%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM557+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 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 25 unt; 0 def)
% Number of atoms : 60 ( 21 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 15 |; 8 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSel,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSel) ).
fof(m__2202_02,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('theBenchmark.p',m__2202_02) ).
fof(m__2291,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__2431,axiom,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
file('theBenchmark.p',m__2431) ).
fof(m__,conjecture,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_65,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_66,plain,
sbrdtbr0(xP) = xk,
inference(clausify,[status(thm)],[m__2431]) ).
cnf(c_67,plain,
xk = sbrdtbr0(xP),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_68,plain,
aSubsetOf0(xP,xS),
inference(clausify,[status(thm)],[m__2431]) ).
fof(m__2357,axiom,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('theBenchmark.p',m__2357) ).
cnf(c_72,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(clausify,[status(thm)],[m__2357]) ).
cnf(c_76,plain,
sbrdtbr0(xQ) = xk,
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_633,plain,
sbrdtbr0(xQ) = sbrdtbr0(xP),
inference(paramod,[status(thm)],[c_67,c_76]) ).
cnf(c_634,plain,
sbrdtbr0(xQ) = sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(paramod,[status(thm)],[c_72,c_633]) ).
cnf(c_77,plain,
sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_634]) ).
cnf(c_90,plain,
aSet0(xS),
inference(clausify,[status(thm)],[m__2202_02]) ).
fof(m__2202,axiom,
aElementOf0(xk,szNzAzT0),
file('theBenchmark.p',m__2202) ).
cnf(c_91,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[m__2202]) ).
cnf(c_635,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(paramod,[status(thm)],[c_67,c_91]) ).
cnf(c_636,plain,
aElementOf0(sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)),szNzAzT0),
inference(paramod,[status(thm)],[c_72,c_635]) ).
cnf(c_92,plain,
aElementOf0(sbrdtbr0(xQ),szNzAzT0),
inference(paramod,[status(thm)],[c_77,c_636]) ).
cnf(c_99,plain,
( sbrdtbr0(D) != B
| ~ aSubsetOf0(D,A)
| aElementOf0(D,C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
cnf(c_637,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk)),
inference(paramod,[status(thm)],[c_72,c_65]) ).
cnf(c_638,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,sbrdtbr0(xP))),
inference(paramod,[status(thm)],[c_67,c_637]) ).
cnf(c_639,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)))),
inference(paramod,[status(thm)],[c_72,c_638]) ).
cnf(c_214,negated_conjecture,
~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,sbrdtbr0(xQ))),
inference(paramod,[status(thm)],[c_77,c_639]) ).
cnf(c_216,plain,
aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xS),
inference(paramod,[status(thm)],[c_72,c_68]) ).
cnf(c_640,plain,
( sbrdtbr0(C) != A
| ~ aSubsetOf0(C,xS)
| aElementOf0(C,B)
| slbdtsldtrb0(xS,A) != B
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_99,c_90]) ).
cnf(c_641,plain,
( sbrdtbr0(B) != sbrdtbr0(xQ)
| ~ aSubsetOf0(B,xS)
| aElementOf0(B,A)
| slbdtsldtrb0(xS,sbrdtbr0(xQ)) != A ),
inference(resolve,[status(thm)],[c_640,c_92]) ).
cnf(c_642,plain,
( sbrdtbr0(A) != sbrdtbr0(xQ)
| ~ aSubsetOf0(A,xS)
| aElementOf0(A,slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(xxres,[status(thm)],[c_641]) ).
cnf(c_643,plain,
( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != sbrdtbr0(xQ)
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,sbrdtbr0(xQ))) ),
inference(resolve,[status(thm)],[c_642,c_216]) ).
cnf(c_644,plain,
aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,sbrdtbr0(xQ))),
inference(resolve,[status(thm)],[c_643,c_77]) ).
cnf(c_632,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_214,c_644]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM557+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:12:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1817026 was started by sandbox2 on n013,
% 0.09/0.35 % Sat Sep 26 03:12:25 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.37
% 0.15/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.45
% 0.15/0.45 % SZS status Theorem for theBenchmark
% 0.15/0.45
% 0.15/0.45 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.15/0.45 % Length of proof is 19.
% 0.15/0.45 % Level of proof is 5.
% 0.15/0.45 % Maximum clause weight is 30.000.
% 0.15/0.45 % Given clauses 120.
% 0.15/0.45
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------