%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM594+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 : n017.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 08:17:30 AM UTC 2026
% Result : Theorem 39.63s 5.68s
% Output : CNFRefutation 39.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 31 ( 12 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 22 ( 4 ~; 3 |; 12 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 7 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 3 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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__4781,axiom,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ? [W0] :
( sdtlpdtrp0(xd,W0) = xx
& aElementOf0(W0,szDzozmdt0(xd)) ) ),
file('theBenchmark.p',m__4781) ).
fof(m__,conjecture,
? [W0] :
( sdtlpdtrp0(xd,W0) = xx
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(xd,W0) = xx
& aElementOf0(W0,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_907,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(clausify,[status(thm)],[m__4730]) ).
fof(nnf_88,plain,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ? [W0] :
( sdtlpdtrp0(xd,W0) = xx
& aElementOf0(W0,szDzozmdt0(xd)) ) ),
inference(fof_nnf,[status(thm)],[m__4781]) ).
fof(sk_m__4781,plain,
( aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd)))
& sdtlpdtrp0(xd,sK0) = xx
& aElementOf0(sK0,szDzozmdt0(xd)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_88]) ).
cnf(c_916,plain,
aElementOf0(sK0,szDzozmdt0(xd)),
inference(split_conjunct,[status(thm)],[sk_m__4781]) ).
cnf(c_917,plain,
sdtlpdtrp0(xd,sK0) = xx,
inference(split_conjunct,[status(thm)],[sk_m__4781]) ).
cnf(c_919,negated_conjecture,
( sdtlpdtrp0(xd,A) != xx
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_6498,plain,
aElementOf0(sK0,szNzAzT0),
inference(paramod,[status(thm)],[c_907,c_916]) ).
cnf(c_6826,negated_conjecture,
sdtlpdtrp0(xd,sK0) != xx,
inference(resolve,[status(thm)],[c_6498,c_919]) ).
cnf(c_6825,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_917,c_6826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM594+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 03:18:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 3869136 was started by sandbox on n017,
% 0.11/0.38 % Sat Sep 26 03:18:05 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.39/0.65
% 0.39/0.65 % From the command line: assign(max_seconds, 300).
% 39.63/5.68
% 39.63/5.68 % given #500 (I,wt=37): 889 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 39.63/5.68
% 39.63/5.68 % given #1000 (I,wt=79): 1655 -aSubsetOf0(f23(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | aSet0(f23(A,B,C)) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(B,szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(E,szDzozmdt0(C)) | sdtlpdtrp0(C,E) != D | -iLess0(A,xK) | -aSubsetOf0(F,f28(A,B,C)) | sbrdtbr0(F) != A | f27(A,B,C) = sdtlpdtrp0(C,F). [copy(1654),flip(n)].
% 39.63/5.68
% 39.63/5.68 % given #1500 (I,wt=77): 2433 -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) | -aSet0(B) | -aElementOf0(f22(A,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(285,a,178,f)].
% 39.63/5.68
% 39.63/5.68 % given #2000 (I,wt=91): 3156 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | 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),f28(A,B,C)) | sbrdtbr0(E) != A | f27(A,B,C) = sdtlpdtrp0(C,E). [copy(3155),flip(o)].
% 39.63/5.68
% 39.63/5.68 % given #2500 (I,wt=96): 3731 -aSubsetOf0(f23(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),B) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f25(A,B,C,D)) = D | -iLess0(A,xK) | -aSet0(f23(A,B,C)) | -aElementOf0(f29(A,B,C,f23(A,B,C)),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(1432,b,n)].
% 39.63/5.68
% 39.63/5.68 % given #3000 (I,wt=140): 4238 -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 | aSubsetOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(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) | -aSet0(C) | aElementOf0(f29(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,C),C) | sbrdtbr0(C) != A | f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) = sdtlpdtrp0(B,C). [factor(2287,b,j)].
% 39.63/5.68
% 39.63/5.68 % given #3500 (I,wt=77): 4759 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | aElementOf0(f26(A,B,C),sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aElementOf0(f22(A,B),f28(A,B,C)). [factor(2797,g,m)].
% 39.63/5.68
% 39.63/5.68 % given #4000 (I,wt=95): 5286 -aSubsetOf0(f23(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),B) | -isCountable0(B) | -aFunction0(C) | aElementOf0(D,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f23(A,B,C)) != D | -iLess0(A,xK) | -aSet0(f23(A,B,C)) | -aElementOf0(f29(A,B,C,f23(A,B,C)),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(3709,c,j)].
% 39.63/5.68
% 39.63/5.68 % given #4500 (I,wt=157): 5786 -aSet0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | sbrdtbr0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != A | -aElementOf0(f29(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,sdtlcdtrc0(B,szDzozmdt0(B))),f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(f29(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,sdtlcdtrc0(B,szDzozmdt0(B))),sdtlcdtrc0(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(C,szDzozmdt0(B)) | f22(A,sdtlcdtrc0(B,szDzozmdt0(B))) != sdtlpdtrp0(B,C) | -iLess0(A,xK) | sbrdtbr0(sdtlcdtrc0(B,szDzozmdt0(B))) != A | f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) = sdtlpdtrp0(B,sdtlcdtrc0(B,szDzozmdt0(B))). [factor(5164,h,k),flip(l)].
% 39.63/5.68
% 39.63/5.68 % SZS status Theorem for theBenchmark
% 39.63/5.68
% 39.63/5.68 % Proof 1 at 4.77 (+ 0.20) seconds.
% 39.63/5.68 % Length of proof is 9.
% 39.63/5.68 % Level of proof is 3.
% 39.63/5.68 % Maximum clause weight is 18.000.
% 39.63/5.68 % Given clauses 4632.
% 39.63/5.68
% 39.63/5.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------