%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM578+3 : 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 08:17:27 AM UTC 2026
% Result : Theorem 33.46s 4.76s
% Output : CNFRefutation 33.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 91 ( 14 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 98 ( 27 ~; 15 |; 31 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3856,axiom,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('theBenchmark.p',m__3856) ).
fof(m__3856_02,axiom,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ) ),
file('theBenchmark.p',m__3856_02) ).
fof(m__,conjecture,
( ! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),W1)
=> ( ~ ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1)) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0))
| ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0)) ) ) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ) )
=> ( xi != xj
=> ~ ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xj))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W0),W1)
=> ( ~ ( ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W1)) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W1)) = szmzizndt0(sdtlpdtrp0(xN,W0))
| ( ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W1)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W1)),sdtlpdtrp0(xN,W0)) ) ) )
& aSubsetOf0(sdtlpdtrp0(xN,W1),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W1))
=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& ! [W2] :
( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W2,sdtlpdtrp0(xN,W0))
& aElement0(W2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ) )
=> ( xi != xj
=> ~ ( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xj))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_423,negated_conjecture,
szmzizndt0(sdtlpdtrp0(xN,xj)) = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_428,negated_conjecture,
xj != xi,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_429,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,B)) != szmzizndt0(sdtlpdtrp0(xN,A))
| ~ sdtlseqdt0(szszuzczcdt0(A),B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_443,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| xj = xi ),
inference(clausify,[status(thm)],[m__3856_02]) ).
cnf(c_444,negated_conjecture,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ),
inference(resolve,[status(thm)],[c_428,c_443]) ).
cnf(c_445,plain,
aElementOf0(xj,szNzAzT0),
inference(clausify,[status(thm)],[m__3856]) ).
cnf(c_446,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__3856]) ).
cnf(c_7571,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_429,c_423]) ).
cnf(c_7572,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolve,[status(thm)],[c_446,c_7571]) ).
cnf(c_7566,negated_conjecture,
~ sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(resolve,[status(thm)],[c_445,c_7572]) ).
cnf(c_7573,negated_conjecture,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(copy,[status(thm)],[c_423]) ).
cnf(c_7574,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolve,[status(thm)],[c_429,c_7573]) ).
cnf(c_7575,negated_conjecture,
( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_445,c_7574]) ).
cnf(c_7567,negated_conjecture,
~ sdtlseqdt0(szszuzczcdt0(xj),xi),
inference(resolve,[status(thm)],[c_446,c_7575]) ).
cnf(c_7576,negated_conjecture,
sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(resolve,[status(thm)],[c_7567,c_444]) ).
cnf(c_7570,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7566,c_7576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM578+3 : 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 : n002.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 03:21:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 720835 was started by sandbox on n002,
% 0.08/0.35 % Sat Sep 26 03:21:05 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 33.46/4.76
% 33.46/4.76 % SZS status Theorem for theBenchmark
% 33.46/4.76
% 33.46/4.76 % Proof 1 at 4.10 (+ 0.10) seconds.
% 33.46/4.76 % Length of proof is 13.
% 33.46/4.76 % Level of proof is 3.
% 33.46/4.76 % Maximum clause weight is 25.000.
% 33.46/4.76 % Given clauses 102.
% 33.46/4.76
% 33.46/4.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------