%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM610+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 08:17:33 AM UTC 2026
% Result : Theorem 30.96s 5.10s
% Output : CNFRefutation 30.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 35 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 31 ( 9 ~; 4 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5078,axiom,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSet0(xQ) ),
file('theBenchmark.p',m__5078) ).
fof(m__5164,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& aSet0(xP) ),
file('theBenchmark.p',m__5164) ).
fof(m__,conjecture,
( aSubsetOf0(xP,xO)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xO) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aSubsetOf0(xP,xO)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xO) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_957,plain,
( aElementOf0(A,xO)
| ~ aElementOf0(A,xQ) ),
inference(clausify,[status(thm)],[m__5078]) ).
cnf(c_974,plain,
( aElementOf0(A,xQ)
| ~ aElementOf0(A,xP) ),
inference(clausify,[status(thm)],[m__5164]) ).
fof(nnf_101,plain,
( ~ aSubsetOf0(xP,xO)
& ? [W0] :
( ~ aElementOf0(W0,xO)
& aElementOf0(W0,xP) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( ~ aSubsetOf0(xP,xO)
& ~ aElementOf0(sK0,xO)
& aElementOf0(sK0,xP) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_101]) ).
cnf(c_981,negated_conjecture,
aElementOf0(sK0,xP),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_982,negated_conjecture,
~ aElementOf0(sK0,xO),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_6161,plain,
aElementOf0(sK0,xQ),
inference(resolve,[status(thm)],[c_981,c_974]) ).
cnf(c_7122,plain,
aElementOf0(sK0,xO),
inference(resolve,[status(thm)],[c_6161,c_957]) ).
cnf(c_7121,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_982,c_7122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM610+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 03:29:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4180607 was started by sandbox2 on n026,
% 0.10/0.37 % Sat Sep 26 03:29:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.48
% 0.21/0.48 % From the command line: assign(max_seconds, 300).
% 30.96/5.10
% 30.96/5.10 % given #500 (I,wt=37): 900 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 30.96/5.10
% 30.96/5.10 % given #1000 (I,wt=71): 1594 -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(E,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f25(A,B,C,E)) = E | -iLess0(A,xK) | aElementOf0(f27(A,B,C),xT). [resolve(293,a,147,e)].
% 30.96/5.10
% 30.96/5.10 % given #1500 (I,wt=75): 2430 -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(E,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f25(A,B,C,E)) = E | -iLess0(A,xK) | isCountable0(f28(A,B,C)). [resolve(297,a,143,e)].
% 30.96/5.10
% 30.96/5.10 % given #2000 (I,wt=90): 3151 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | aSubsetOf0(f23(A,B,C),B) | -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) | -aElementOf0(E,slbdtsldtrb0(f28(A,B,C),A)) | f27(A,B,C) = sdtlpdtrp0(C,E). [copy(3150),flip(n)].
% 30.96/5.10
% 30.96/5.10 % given #2500 (I,wt=116): 3671 -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) | -aSubsetOf0(sdtlcdtrc0(B,szDzozmdt0(B)),szNzAzT0) | -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(C,f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(C,sdtlcdtrc0(B,szDzozmdt0(B))). [factor(1899,b,i)].
% 30.96/5.10
% 30.96/5.10 % given #3000 (I,wt=94): 4181 -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(E,sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(F,szDzozmdt0(C)) | sdtlpdtrp0(C,F) != E | -iLess0(A,xK) | -aSubsetOf0(f23(A,B,C),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(2503,c,p)].
% 30.96/5.10
% 30.96/5.10 % given #3500 (I,wt=128): 4692 -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 | 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(C,szDzozmdt0(B)) | f22(A,sdtlcdtrc0(B,szDzozmdt0(B))) != sdtlpdtrp0(B,C) | -iLess0(A,xK) | -aElementOf0(D,f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(D,sdtlcdtrc0(B,szDzozmdt0(B))). [factor(3147,g,j),flip(k)].
% 30.96/5.10
% 30.96/5.10 % given #4000 (I,wt=149): 5198 -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(f22(A,sdtlcdtrc0(B,szDzozmdt0(B))),f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(f22(A,sdtlcdtrc0(B,szDzozmdt0(B))),sdtlcdtrc0(B,szDzozmdt0(B))) | -aElementOf0(A,szNzAzT0) | -aSet0(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) | aElementOf0(f29(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,sdtlcdtrc0(B,szDzozmdt0(B))),sdtlcdtrc0(B,szDzozmdt0(B))) | sbrdtbr0(sdtlcdtrc0(B,szDzozmdt0(B))) != A | f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) = sdtlpdtrp0(B,sdtlcdtrc0(B,szDzozmdt0(B))). [factor(5041,g,m)].
% 30.96/5.10
% 30.96/5.10 % SZS status Theorem for theBenchmark
% 30.96/5.10
% 30.96/5.10 % Proof 1 at 4.31 (+ 0.22) seconds.
% 30.96/5.10 % Length of proof is 9.
% 30.96/5.10 % Level of proof is 3.
% 30.96/5.10 % Maximum clause weight is 11.000.
% 30.96/5.10 % Given clauses 4087.
% 30.96/5.10
% 30.96/5.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------