%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM625+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 : n015.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 08:17:37 AM UTC 2026
% Result : Theorem 2.39s 0.77s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 63 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 55 ( 23 ~; 16 |; 8 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
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__4891,axiom,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('theBenchmark.p',m__4891) ).
fof(m__5093,axiom,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('theBenchmark.p',m__5093) ).
fof(m__5164,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('theBenchmark.p',m__5164) ).
cnf(c_98,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_105,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_125,plain,
( D != B
| ~ aElementOf0(D,C)
| sdtmndt0(A,B) != C
| ~ aElement0(B)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_291,plain,
aSet0(xO),
inference(clausify,[status(thm)],[m__4891]) ).
cnf(c_299,plain,
aSubsetOf0(xQ,xO),
inference(clausify,[status(thm)],[m__5093]) ).
fof(m__5147,axiom,
xp = szmzizndt0(xQ),
file('theBenchmark.p',m__5147) ).
cnf(c_303,plain,
xp = szmzizndt0(xQ),
inference(clausify,[status(thm)],[m__5147]) ).
cnf(c_304,plain,
szmzizndt0(xQ) = xp,
inference(copy,[status(thm)],[c_303]) ).
cnf(c_305,plain,
aSet0(xP),
inference(clausify,[status(thm)],[m__5164]) ).
cnf(c_306,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(clausify,[status(thm)],[m__5164]) ).
cnf(c_307,plain,
sdtmndt0(xQ,xp) = xP,
inference(paramod,[status(thm)],[c_304,c_306]) ).
fof(m__5348,axiom,
aElementOf0(xx,xP),
file('theBenchmark.p',m__5348) ).
cnf(c_318,plain,
aElementOf0(xx,xP),
inference(clausify,[status(thm)],[m__5348]) ).
fof(m__5496,axiom,
xp = xx,
file('theBenchmark.p',m__5496) ).
cnf(c_329,plain,
xp = xx,
inference(clausify,[status(thm)],[m__5496]) ).
cnf(c_361,plain,
sdtmndt0(xQ,xx) = xP,
inference(paramod,[status(thm)],[c_329,c_307]) ).
cnf(c_4283,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolve,[status(thm)],[c_299,c_105]) ).
cnf(c_935,plain,
aSet0(xQ),
inference(resolve,[status(thm)],[c_291,c_4283]) ).
cnf(c_4284,plain,
( aElement0(xx)
| ~ aSet0(xP) ),
inference(resolve,[status(thm)],[c_318,c_98]) ).
cnf(c_1219,plain,
aElement0(xx),
inference(resolve,[status(thm)],[c_305,c_4284]) ).
cnf(c_4285,plain,
( C != A
| ~ aElementOf0(C,B)
| sdtmndt0(xQ,A) != B
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_125,c_935]) ).
cnf(c_4286,plain,
( B != xx
| ~ aElementOf0(B,A)
| sdtmndt0(xQ,xx) != A ),
inference(resolve,[status(thm)],[c_4285,c_1219]) ).
cnf(c_4287,plain,
( A != xx
| ~ aElementOf0(A,xP) ),
inference(resolve,[status(thm)],[c_4286,c_361]) ).
cnf(c_4288,plain,
xx != xx,
inference(resolve,[status(thm)],[c_4287,c_318]) ).
cnf(c_4282,plain,
$false,
inference(xxres,[status(thm)],[c_4288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM625+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 03:33:13 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 3007789 was started by sandbox on n015,
% 0.10/0.36 % Sat Sep 26 03:33:13 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 2.39/0.77
% 2.39/0.77 % SZS status Theorem for theBenchmark
% 2.39/0.77
% 2.39/0.77 % Proof 1 at 0.29 (+ 0.06) seconds.
% 2.39/0.77 % Length of proof is 22.
% 2.39/0.77 % Level of proof is 4.
% 2.39/0.77 % Maximum clause weight is 25.000.
% 2.39/0.77 % Given clauses 263.
% 2.39/0.77
% 2.39/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------