%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM621+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 : 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 122.72s 24.38s
% Output : CNFRefutation 122.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 98 ( 22 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 82 ( 24 ~; 20 |; 24 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 12 !; 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__4660,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('theBenchmark.p',m__4660) ).
fof(m__4730,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )
& aSet0(W1) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('theBenchmark.p',m__4730) ).
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__5309,axiom,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('theBenchmark.p',m__5309) ).
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__,conjecture,
( ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_606,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_928,plain,
( aElementOf0(sdtlpdtrp0(xe,A),sdtlpdtrp0(xN,A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__4660]) ).
cnf(c_932,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(clausify,[status(thm)],[m__4730]) ).
cnf(c_985,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xQ) ),
inference(clausify,[status(thm)],[m__5106]) ).
cnf(c_990,plain,
aElementOf0(xp,xQ),
inference(clausify,[status(thm)],[m__5147]) ).
cnf(c_991,plain,
( sdtlseqdt0(xp,A)
| ~ aElementOf0(A,xQ) ),
inference(clausify,[status(thm)],[m__5147]) ).
cnf(c_992,plain,
szmzizndt0(xQ) = xp,
inference(clausify,[status(thm)],[m__5147]) ).
cnf(c_1010,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(clausify,[status(thm)],[m__5309]) ).
cnf(c_1011,plain,
aElementOf0(xn,szNzAzT0),
inference(paramod,[status(thm)],[c_932,c_1010]) ).
cnf(c_1015,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(clausify,[status(thm)],[m__5309]) ).
cnf(c_1018,plain,
aElementOf0(xx,xQ),
inference(clausify,[status(thm)],[m__5348]) ).
cnf(c_1019,plain,
szmzizndt0(xQ) != xx,
inference(clausify,[status(thm)],[m__5348]) ).
cnf(c_20142,plain,
xp != xx,
inference(paramod,[status(thm)],[c_992,c_1019]) ).
cnf(c_1020,plain,
xx != xp,
inference(copy,[status(thm)],[c_20142]) ).
cnf(c_1022,plain,
aElementOf0(xx,szNzAzT0),
inference(clausify,[status(thm)],[m__5365]) ).
cnf(c_1027,plain,
( sdtlseqdt0(xx,A)
| ~ aElementOf0(A,sdtlpdtrp0(xN,xm)) ),
inference(clausify,[status(thm)],[m__5401]) ).
cnf(c_1031,negated_conjecture,
( aElementOf0(A,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(A,sdtlpdtrp0(xN,xn)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_4138,plain,
aElementOf0(xp,szNzAzT0),
inference(resolve,[status(thm)],[c_990,c_985]) ).
cnf(c_20143,plain,
aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn)),
inference(resolve,[status(thm)],[c_1011,c_928]) ).
cnf(c_4275,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(paramod,[status(thm)],[c_1015,c_20143]) ).
cnf(c_4433,plain,
sdtlseqdt0(xp,xx),
inference(resolve,[status(thm)],[c_1018,c_991]) ).
cnf(c_20144,plain,
( xp = xx
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(resolve,[status(thm)],[c_4433,c_606]) ).
cnf(c_20145,plain,
( xx = xp
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(copy,[status(thm)],[c_20144]) ).
cnf(c_20146,plain,
( xx = xp
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0) ),
inference(resolve,[status(thm)],[c_1022,c_20145]) ).
cnf(c_20147,plain,
( xx = xp
| ~ sdtlseqdt0(xx,xp) ),
inference(resolve,[status(thm)],[c_4138,c_20146]) ).
cnf(c_7674,plain,
~ sdtlseqdt0(xx,xp),
inference(resolve,[status(thm)],[c_1020,c_20147]) ).
cnf(c_18754,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(resolve,[status(thm)],[c_4275,c_1031]) ).
cnf(c_20148,plain,
sdtlseqdt0(xx,xp),
inference(resolve,[status(thm)],[c_18754,c_1027]) ).
cnf(c_20141,plain,
$false,
inference(resolve,[status(thm)],[c_7674,c_20148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM621+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.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 03:31:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 4184207 was started by sandbox on n026,
% 0.09/0.36 % Sat Sep 26 03:31:43 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.42/0.69
% 0.42/0.69 % From the command line: assign(max_seconds, 300).
% 122.72/24.38
% 122.72/24.38 % given #500 (I,wt=37): 914 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 122.72/24.38
% 122.72/24.38 % given #1000 (I,wt=68): 1616 -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) | -aElementOf0(E,f28(A,B,C)) | aElementOf0(E,B). [resolve(300,a,134,e)].
% 122.72/24.38
% 122.72/24.38 % given #1500 (I,wt=64): 2440 -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(A,B),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | defn_00(A,B,C,D) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aElementOf0(f29(A,B,C,B),f28(A,B,C)) | sbrdtbr0(B) != A | f27(A,B,C) = sdtlpdtrp0(C,B). [factor(429,b,i)].
% 122.72/24.38
% 122.72/24.38 % given #2000 (I,wt=77): 2949 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(A,B),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f23(A,B,C)) != D | -iLess0(A,xK) | aElementOf0(f27(A,B,C),xT). [factor(2016,d,k)].
% 122.72/24.38
% 122.72/24.38 % given #2500 (I,wt=114): 3455 -aSet0(f23(A,szDzozmdt0(B),B)) | -aElementOf0(f24(A,szDzozmdt0(B),B),szDzozmdt0(B)) | sbrdtbr0(f23(A,szDzozmdt0(B),B)) != A | aSubsetOf0(f23(A,szDzozmdt0(B),B),szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(szDzozmdt0(B)) | aElementOf0(f22(A,szDzozmdt0(B)),szDzozmdt0(B)) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | aElementOf0(C,sdtlcdtrc0(B,szDzozmdt0(B))) | sdtlpdtrp0(B,f24(A,szDzozmdt0(B),B)) != C | -iLess0(A,xK) | -aElementOf0(f29(A,szDzozmdt0(B),B,szDzozmdt0(B)),f28(A,szDzozmdt0(B),B)) | sbrdtbr0(szDzozmdt0(B)) != A | f27(A,szDzozmdt0(B),B) = sdtlpdtrp0(B,szDzozmdt0(B)). [factor(3218,f,m)].
% 122.72/24.38
% 122.72/24.38 % given #3000 (T,wt=14): 4319 aSet0(sdtlpdtrp0(xN,xn)). [resolve(1011,a,708,a)].
% 122.72/24.38
% 122.72/24.38 % given #3500 (A,wt=29): 3801 aSet0(sdtlcdtrc0(sdtlpdtrp0(xC,sz00),szDzozmdt0(sdtlpdtrp0(xC,sz00)))). [resolve(870,a,619,a)].
% 122.72/24.38
% 122.72/24.38 % SZS status Theorem for theBenchmark
% 122.72/24.38
% 122.72/24.38 % Proof 1 at 5.30 (+ 0.75) seconds.
% 122.72/24.38 % Length of proof is 32.
% 122.72/24.38 % Level of proof is 5.
% 122.72/24.38 % Maximum clause weight is 20.000.
% 122.72/24.38 % Given clauses 3978.
% 122.72/24.38
% 122.72/24.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------