%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM627+1 : 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 : n003.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 08:17:37 AM UTC 2026
% Result : Theorem 54.25s 15.86s
% Output : CNFRefutation 54.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 55 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 18 ~; 20 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSuccNum,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('theBenchmark.p',mSuccNum) ).
fof(mLessTotal,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLessTotal) ).
fof(m__3754,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
file('theBenchmark.p',m__3754) ).
fof(m__5309,axiom,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('theBenchmark.p',m__5309) ).
fof(m__5389,axiom,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('theBenchmark.p',m__5389) ).
cnf(c_139,plain,
( aElementOf0(szszuzczcdt0(A),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mSuccNum]) ).
cnf(c_153,plain,
( sdtlseqdt0(szszuzczcdt0(B),A)
| sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessTotal]) ).
cnf(c_260,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_314,plain,
aElementOf0(xn,szNzAzT0),
inference(clausify,[status(thm)],[m__5309]) ).
cnf(c_320,plain,
aElementOf0(xm,szNzAzT0),
inference(clausify,[status(thm)],[m__5389]) ).
fof(m__5442,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('theBenchmark.p',m__5442) ).
cnf(c_324,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(clausify,[status(thm)],[m__5442]) ).
fof(m__5461,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
file('theBenchmark.p',m__5461) ).
cnf(c_325,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(clausify,[status(thm)],[m__5461]) ).
cnf(c_878,plain,
( sdtlseqdt0(szszuzczcdt0(xn),A)
| sdtlseqdt0(A,xn)
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_314,c_153]) ).
cnf(c_888,plain,
aElementOf0(szszuzczcdt0(xn),szNzAzT0),
inference(resolve,[status(thm)],[c_314,c_139]) ).
cnf(c_15542,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_878,c_320]) ).
cnf(c_25293,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_15542,c_260]) ).
cnf(c_25294,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_320,c_25293]) ).
cnf(c_25295,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlseqdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_888,c_25294]) ).
cnf(c_25282,plain,
sdtlseqdt0(xm,xn),
inference(resolve,[status(thm)],[c_324,c_25295]) ).
cnf(c_25296,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolve,[status(thm)],[c_25282,c_260]) ).
cnf(c_25297,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolve,[status(thm)],[c_314,c_25296]) ).
cnf(c_25298,plain,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(resolve,[status(thm)],[c_320,c_25297]) ).
cnf(c_25292,plain,
$false,
inference(resolve,[status(thm)],[c_325,c_25298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM627+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.40 % Computer : n003.cluster.edu
% 0.07/0.40 % Model : x86_64 x86_64
% 0.07/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.40 % Memory : 8046.5625MB
% 0.07/0.40 % OS : Linux 6.8.0-71-generic
% 0.07/0.40 % CPULimit : 300
% 0.07/0.40 % WCLimit : 300
% 0.07/0.40 % DateTime : Sat Sep 26 03:31:53 UTC 2026
% 0.07/0.41 % CPUTime :
% 0.07/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.41 % Process 1931874 was started by sandbox on n003,
% 0.07/0.41 % Sat Sep 26 03:31:53 2026
% 0.07/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.45
% 0.07/0.45 % From the command line: assign(max_seconds, 300).
% 54.25/15.86
% 54.25/15.86 % given #500 (T,wt=14): 448 iLess0(xK,szszuzczcdt0(xK)). [resolve(238,a,154,a)].
% 54.25/15.86
% 54.25/15.86 % given #1000 (A,wt=29): 623 -aElementOf0(A,szNzAzT0) | xK = A | szmzizndt0(sdtlpdtrp0(xN,A)) != sdtlpdtrp0(xe,xK). [back_rewrite(582),rewrite([616(8)]),flip(c)].
% 54.25/15.86
% 54.25/15.86 % given #1500 (T,wt=16): 4834 aSubsetOf0(sdtlbdtrb0(xc,xx),szDzozmdt0(xc)). [resolve(506,a,921,a)].
% 54.25/15.86
% 54.25/15.86 % given #2000 (A,wt=23): 991 -aSet0(A) | -aElementOf0(B,szNzAzT0) | slbdtsldtrb0(A,B) != xO | aSubsetOf0(xx,A). [resolve(319,a,193,d)].
% 54.25/15.86
% 54.25/15.86 % given #2500 (T,wt=17): 7440 sdtlseqdt0(xk,xx) | -aElementOf0(A,szNzAzT0) | -sdtlseqdt0(A,xp) | sdtlseqdt0(A,xk). [resolve(7428,b,152,e),unit_del(c,1516),unit_del(d,251)].
% 54.25/15.86
% 54.25/15.86 % SZS status Theorem for theBenchmark
% 54.25/15.86
% 54.25/15.86 % Proof 1 at 2.63 (+ 0.95) seconds.
% 54.25/15.86 % Length of proof is 17.
% 54.25/15.86 % Level of proof is 5.
% 54.25/15.86 % Maximum clause weight is 26.000.
% 54.25/15.86 % Given clauses 2931.
% 54.25/15.86
% 54.25/15.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------