%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM603+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 : n006.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 08:17:32 AM UTC 2026
% Result : Theorem 38.33s 10.71s
% Output : CNFRefutation 38.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 60 ( 5 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 53 ( 12 ~; 12 |; 17 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mZeroLess,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('theBenchmark.p',mZeroLess) ).
fof(m__3623,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,W0))
& ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
| ( ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,W0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0))
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& aElement0(W1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('theBenchmark.p',m__3623) ).
fof(m__3754,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
& ! [W2] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) ),
file('theBenchmark.p',m__3754) ).
fof(m__5034,axiom,
( sdtlpdtrp0(xe,xi) = xx
& aElementOf0(xi,szNzAzT0) ),
file('theBenchmark.p',m__5034) ).
fof(m__,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,xS) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_598,plain,
( sdtlseqdt0(sz00,A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mZeroLess]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_605,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_660,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(clausify,[status(thm)],[m__3623]) ).
cnf(c_699,plain,
( aSubsetOf0(sdtlpdtrp0(xN,A),sdtlpdtrp0(xN,B))
| ~ sdtlseqdt0(B,A)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__3754]) ).
cnf(c_965,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__5034]) ).
cnf(c_969,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_4433,plain,
sdtlseqdt0(sz00,xi),
inference(resolve,[status(thm)],[c_965,c_598]) ).
cnf(c_7127,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_4433,c_699]) ).
cnf(c_7128,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(paramod,[status(thm)],[c_660,c_7127]) ).
cnf(c_7129,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolve,[status(thm)],[c_965,c_7128]) ).
cnf(c_7130,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(resolve,[status(thm)],[c_605,c_7129]) ).
cnf(c_7126,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_969,c_7130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM603+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 03:25:10 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 271709 was started by sandbox on n006,
% 0.11/0.36 % Sat Sep 26 03:25:10 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.47
% 0.14/0.47 % From the command line: assign(max_seconds, 300).
% 38.33/10.71
% 38.33/10.71 % given #500 (I,wt=17): 900 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 38.33/10.71
% 38.33/10.71 % given #1000 (I,wt=58): 1670 -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) | -aSubsetOf0(sdtlcdtrc0(C,szDzozmdt0(C)),xT) | -iLess0(A,xK) | -aSet0(D) | aElementOf0(f29(A,B,C,D),D) | sbrdtbr0(D) != A | f27(A,B,C) = sdtlpdtrp0(C,D). [copy(1669),flip(m)].
% 38.33/10.71
% 38.33/10.71 % given #1500 (I,wt=23): 2418 -aSet0(A) | -aElementOf0(B,szNzAzT0) | slbdtsldtrb0(A,B) = A | aElementOf0(f11(A,B,A),A) | sbrdtbr0(f11(A,B,A)) = B. [factor(546,a,d)].
% 38.33/10.71
% 38.33/10.71 % given #2000 (I,wt=72): 2927 -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),B) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(f26(A,B,C),xT) | -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(2010,a,l),merge(m)].
% 38.33/10.71
% 38.33/10.71 % given #2500 (F,wt=3): 3582 xS != slcrc0. [resolve(640,b,501,a),flip(b),unit_del(a,504)].
% 38.33/10.71
% 38.33/10.71 % SZS status Theorem for theBenchmark
% 38.33/10.71
% 38.33/10.71 % Proof 1 at 4.74 (+ 0.25) seconds.
% 38.33/10.71 % Length of proof is 13.
% 38.33/10.71 % Level of proof is 3.
% 38.33/10.71 % Maximum clause weight is 16.000.
% 38.33/10.71 % Given clauses 2582.
% 38.33/10.71
% 38.33/10.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------