%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM606+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 : n013.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 26.16s 4.72s
% Output : CNFRefutation 26.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 38 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 31 ( 9 ~; 5 |; 12 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xS) ),
file('theBenchmark.p',m__3435) ).
fof(m__4998,axiom,
( aSubsetOf0(xO,xS)
& ! [W0] :
( aElementOf0(W0,xO)
=> aElementOf0(W0,xS) ) ),
file('theBenchmark.p',m__4998) ).
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__,conjecture,
( aSubsetOf0(xQ,szNzAzT0)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aSubsetOf0(xQ,szNzAzT0)
| ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,szNzAzT0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_510,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS) ),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_948,plain,
( aElementOf0(A,xS)
| ~ aElementOf0(A,xO) ),
inference(clausify,[status(thm)],[m__4998]) ).
cnf(c_951,plain,
( aElementOf0(A,xO)
| ~ aElementOf0(A,xQ) ),
inference(clausify,[status(thm)],[m__5078]) ).
fof(nnf_95,plain,
( ~ aSubsetOf0(xQ,szNzAzT0)
& ? [W0] :
( ~ aElementOf0(W0,szNzAzT0)
& aElementOf0(W0,xQ) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( ~ aSubsetOf0(xQ,szNzAzT0)
& ~ aElementOf0(sK0,szNzAzT0)
& aElementOf0(sK0,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_95]) ).
cnf(c_957,negated_conjecture,
aElementOf0(sK0,xQ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_958,negated_conjecture,
~ aElementOf0(sK0,szNzAzT0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_5949,plain,
aElementOf0(sK0,xO),
inference(resolve,[status(thm)],[c_957,c_951]) ).
cnf(c_6305,plain,
aElementOf0(sK0,xS),
inference(resolve,[status(thm)],[c_5949,c_948]) ).
cnf(c_6434,plain,
aElementOf0(sK0,szNzAzT0),
inference(resolve,[status(thm)],[c_6305,c_510]) ).
cnf(c_6433,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_958,c_6434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM606+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.64 % Computer : n013.cluster.edu
% 0.18/0.64 % Model : x86_64 x86_64
% 0.18/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.64 % Memory : 8046.5625MB
% 0.18/0.64 % OS : Linux 6.8.0-71-generic
% 0.18/0.64 % CPULimit : 300
% 0.18/0.64 % WCLimit : 300
% 0.18/0.64 % DateTime : Sat Sep 26 03:25:21 UTC 2026
% 0.18/0.65 % CPUTime :
% 0.18/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.65 % Process 1832566 was started by sandbox2 on n013,
% 0.18/0.65 % Sat Sep 26 03:25:21 2026
% 0.18/0.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.98
% 0.22/0.98 % From the command line: assign(max_seconds, 300).
% 26.16/4.72
% 26.16/4.72 % given #500 (I,wt=37): 894 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 26.16/4.72
% 26.16/4.72 % given #1000 (I,wt=61): 1596 -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) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | aElementOf0(f27(A,B,C),xT). [resolve(287,a,159,e)].
% 26.16/4.72
% 26.16/4.72 % given #1500 (I,wt=65): 2432 -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) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | isCountable0(f28(A,B,C)). [resolve(291,a,155,e)].
% 26.16/4.72
% 26.16/4.72 % given #2000 (I,wt=80): 3153 -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) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aElementOf0(D,slbdtsldtrb0(f28(A,B,C),A)) | f27(A,B,C) = sdtlpdtrp0(C,D). [copy(3152),flip(m)].
% 26.16/4.72
% 26.16/4.72 % given #2500 (I,wt=90): 3665 -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(f26(A,B,C),sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aElementOf0(f29(A,B,C,f23(A,B,C)),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(1922,a,l),merge(m)].
% 26.16/4.72
% 26.16/4.72 % given #3000 (I,wt=80): 4175 -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) | -aElementOf0(D,f28(A,B,C)). [factor(2486,e,p)].
% 26.16/4.72
% 26.16/4.72 % given #3500 (I,wt=84): 4686 -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) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aSubsetOf0(f23(A,B,C),f28(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(3155,c,m)].
% 26.16/4.72
% 26.16/4.72 % given #4000 (I,wt=152): 5192 -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(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) | sdtlpdtrp0(B,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != f22(A,sdtlcdtrc0(B,szDzozmdt0(B))) | -iLess0(A,xK) | -aElementOf0(f29(A,sdtlcdtrc0(B,szDzozmdt0(B)),B,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)),f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) = sdtlpdtrp0(B,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)). [factor(5120,g,j)].
% 26.16/4.72
% 26.16/4.72 % SZS status Theorem for theBenchmark
% 26.16/4.72
% 26.16/4.72 % Proof 1 at 3.50 (+ 0.16) seconds.
% 26.16/4.72 % Length of proof is 12.
% 26.16/4.72 % Level of proof is 4.
% 26.16/4.72 % Maximum clause weight is 11.000.
% 26.16/4.72 % Given clauses 4054.
% 26.16/4.72
% 26.16/4.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------