%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM623+3 : 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 : n026.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 08:17:36 AM UTC 2026
% Result : Theorem 29.58s 4.91s
% Output : CNFRefutation 29.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 59 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 51 ( 19 ~; 16 |; 11 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 11 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(m__5106,axiom,
( aSubsetOf0(xQ,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ) ),
file('theBenchmark.p',m__5106) ).
fof(m__5147,axiom,
( xp = szmzizndt0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(xp,W0) )
& aElementOf0(xp,xQ) ),
file('theBenchmark.p',m__5147) ).
fof(m__5348,axiom,
( aElementOf0(xx,xP)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xQ)
& aElement0(xx) ),
file('theBenchmark.p',m__5348) ).
fof(m__5365,axiom,
( ? [W0] :
( sdtlpdtrp0(xe,W0) = xx
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ),
file('theBenchmark.p',m__5365) ).
fof(m__5401,axiom,
! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,W0) ),
file('theBenchmark.p',m__5401) ).
fof(m__5481,axiom,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('theBenchmark.p',m__5481) ).
fof(m__,conjecture,
xp = xx,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
xp != xx,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_612,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_971,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xQ) ),
inference(clausify,[status(thm)],[m__5106]) ).
cnf(c_976,plain,
aElementOf0(xp,xQ),
inference(clausify,[status(thm)],[m__5147]) ).
cnf(c_977,plain,
( sdtlseqdt0(xp,A)
| ~ aElementOf0(A,xQ) ),
inference(clausify,[status(thm)],[m__5147]) ).
cnf(c_1000,plain,
aElementOf0(xx,xQ),
inference(clausify,[status(thm)],[m__5348]) ).
cnf(c_1003,plain,
aElementOf0(xx,szNzAzT0),
inference(clausify,[status(thm)],[m__5365]) ).
cnf(c_1008,plain,
( sdtlseqdt0(xx,A)
| ~ aElementOf0(A,sdtlpdtrp0(xN,xm)) ),
inference(clausify,[status(thm)],[m__5401]) ).
cnf(c_1014,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(clausify,[status(thm)],[m__5481]) ).
cnf(c_1015,negated_conjecture,
xx != xp,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_5689,plain,
aElementOf0(xp,szNzAzT0),
inference(resolve,[status(thm)],[c_976,c_971]) ).
cnf(c_6079,plain,
sdtlseqdt0(xp,xx),
inference(resolve,[status(thm)],[c_1000,c_977]) ).
cnf(c_6526,plain,
sdtlseqdt0(xx,xp),
inference(resolve,[status(thm)],[c_1014,c_1008]) ).
cnf(c_7691,plain,
( xp = xx
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(resolve,[status(thm)],[c_6079,c_612]) ).
cnf(c_7692,plain,
( xx = xp
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(copy,[status(thm)],[c_7691]) ).
cnf(c_7693,plain,
( xx = xp
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0) ),
inference(resolve,[status(thm)],[c_1003,c_7692]) ).
cnf(c_7694,plain,
( xx = xp
| ~ sdtlseqdt0(xx,xp) ),
inference(resolve,[status(thm)],[c_5689,c_7693]) ).
cnf(c_7695,plain,
xx = xp,
inference(resolve,[status(thm)],[c_6526,c_7694]) ).
cnf(c_7690,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1015,c_7695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM623+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 03:32:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 4185985 was started by sandbox2 on n026,
% 0.09/0.37 % Sat Sep 26 03:32:12 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.38/0.70
% 0.38/0.70 % From the command line: assign(max_seconds, 300).
% 29.58/4.91
% 29.58/4.91 % given #500 (I,wt=37): 908 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 29.58/4.91
% 29.58/4.91 % given #1000 (I,wt=80): 1595 -aSubsetOf0(f23(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aElementOf0(f26(A,B,C),sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aSet0(E) | aElementOf0(f29(A,B,C,E),E) | sbrdtbr0(E) != A | f27(A,B,C) = sdtlpdtrp0(C,E). [copy(1594),flip(n)].
% 29.58/4.91
% 29.58/4.91 % given #1500 (I,wt=67): 2427 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(f26(A,B,C),xT) | -iLess0(A,xK) | aElementOf0(f27(A,B,C),xT). [resolve(306,a,129,e)].
% 29.58/4.91
% 29.58/4.91 % given #2000 (I,wt=61): 3089 -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f36(A,B),sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) | -isCountable0(B) | -aElementOf0(B,slbdtsldtrb0(B,xk)) | aElementOf0(B,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A))),xk)). [factor(893,b,e)].
% 29.58/4.91
% 29.58/4.91 % given #2500 (I,wt=120): 3596 -aSet0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | -aElementOf0(f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | sbrdtbr0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != A | -aElementOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(sdtlcdtrc0(B,szDzozmdt0(B))) | aElementOf0(f22(A,sdtlcdtrc0(B,szDzozmdt0(B))),sdtlcdtrc0(B,szDzozmdt0(B))) | -isCountable0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aFunction0(B) | aElementOf0(f25(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)),szDzozmdt0(B)) | -iLess0(A,xK) | aElementOf0(f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),xT). [factor(2115,b,j)].
% 29.58/4.91
% 29.58/4.91 % given #3000 (I,wt=82): 4113 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f22(A,B),f23(A,B,C)) | aElementOf0(f22(A,B),B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -isCountable0(B) | -aFunction0(C) | aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(E,szDzozmdt0(C)) | sdtlpdtrp0(C,E) != D | -iLess0(A,xK) | -aElementOf0(F,f28(A,B,C)) | aElementOf0(F,B). [factor(2633,e,h)].
% 29.58/4.91
% 29.58/4.91 % given #3500 (I,wt=118): 4623 -aSet0(f23(A,szDzozmdt0(B),B)) | -aElementOf0(f24(A,szDzozmdt0(B),B),szDzozmdt0(B)) | sbrdtbr0(f23(A,szDzozmdt0(B),B)) != A | -aElementOf0(f25(A,szDzozmdt0(B),B,C),f23(A,szDzozmdt0(B),B)) | aElementOf0(f25(A,szDzozmdt0(B),B,C),szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(szDzozmdt0(B)) | -aElementOf0(f22(A,szDzozmdt0(B)),szNzAzT0) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | -aElementOf0(C,sdtlcdtrc0(B,szDzozmdt0(B))) | -iLess0(A,xK) | aElementOf0(f29(A,szDzozmdt0(B),B,f23(A,szDzozmdt0(B),B)),f23(A,szDzozmdt0(B),B)) | f27(A,szDzozmdt0(B),B) = sdtlpdtrp0(B,f23(A,szDzozmdt0(B),B)). [factor(3991,e,l)].
% 29.58/4.91
% 29.58/4.91 % SZS status Theorem for theBenchmark
% 29.58/4.91
% 29.58/4.91 % Proof 1 at 3.95 (+ 0.21) seconds.
% 29.58/4.91 % Length of proof is 21.
% 29.58/4.91 % Level of proof is 3.
% 29.58/4.91 % Maximum clause weight is 20.000.
% 29.58/4.91 % Given clauses 3806.
% 29.58/4.91
% 29.58/4.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------