%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM613+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 : n019.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 08:17:34 AM UTC 2026
% Result : Theorem 109.63s 20.97s
% Output : CNFRefutation 109.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 41 ( 26 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 31 ( 12 ~; 8 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSuccEquSucc,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ),
file('theBenchmark.p',mSuccEquSucc) ).
fof(m__3533,axiom,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('theBenchmark.p',m__3533) ).
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__5255,axiom,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ),
file('theBenchmark.p',m__5255) ).
fof(m__,conjecture,
sbrdtbr0(xP) = xk,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_617,plain,
( B = A
| szszuzczcdt0(B) != szszuzczcdt0(A)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mSuccEquSucc]) ).
cnf(c_668,plain,
aElementOf0(xk,szNzAzT0),
inference(clausify,[status(thm)],[m__3533]) ).
cnf(c_669,plain,
szszuzczcdt0(xk) = xK,
inference(clausify,[status(thm)],[m__3533]) ).
cnf(c_961,plain,
sbrdtbr0(xQ) = xK,
inference(clausify,[status(thm)],[m__5078]) ).
cnf(c_987,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(xP)),
inference(clausify,[status(thm)],[m__5255]) ).
cnf(c_988,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(copy,[status(thm)],[c_987]) ).
cnf(c_989,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(clausify,[status(thm)],[m__5255]) ).
cnf(c_990,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_5418,plain,
( xk = A
| szszuzczcdt0(xk) != szszuzczcdt0(A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_668,c_617]) ).
cnf(c_5794,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(paramod,[status(thm)],[c_961,c_988]) ).
cnf(c_14271,plain,
( xk = sbrdtbr0(xP)
| szszuzczcdt0(xk) != szszuzczcdt0(sbrdtbr0(xP)) ),
inference(resolve,[status(thm)],[c_5418,c_989]) ).
cnf(c_14272,plain,
( xk = sbrdtbr0(xP)
| szszuzczcdt0(sbrdtbr0(xP)) != szszuzczcdt0(xk) ),
inference(copy,[status(thm)],[c_14271]) ).
cnf(c_14273,plain,
( sbrdtbr0(xP) = xk
| szszuzczcdt0(sbrdtbr0(xP)) != szszuzczcdt0(xk) ),
inference(copy,[status(thm)],[c_14272]) ).
cnf(c_13200,negated_conjecture,
szszuzczcdt0(sbrdtbr0(xP)) != szszuzczcdt0(xk),
inference(resolve,[status(thm)],[c_990,c_14273]) ).
cnf(c_14274,plain,
szszuzczcdt0(sbrdtbr0(xP)) != xK,
inference(paramod,[status(thm)],[c_669,c_13200]) ).
cnf(c_14270,plain,
$false,
inference(resolve,[status(thm)],[c_5794,c_14274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.59 % Computer : n019.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Sat Sep 26 03:27:25 UTC 2026
% 0.11/5.60 % CPUTime :
% 0.16/5.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.60 % Process 293029 was started by sandbox2 on n019,
% 0.16/5.60 % Sat Sep 26 03:27:25 2026
% 0.16/5.60 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.85
% 0.16/5.85 % From the command line: assign(max_seconds, 300).
% 109.63/20.97
% 109.63/20.97 % given #500 (I,wt=25): 902 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 109.63/20.97
% 109.63/20.97 % given #1000 (I,wt=62): 1598 -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) | aSubsetOf0(f28(A,B,C),B). [resolve(295,a,146,e)].
% 109.63/20.97
% 109.63/20.97 % given #1500 (I,wt=79): 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) | -aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f25(A,B,C,E)) = E | -iLess0(A,xK) | -aSubsetOf0(F,f28(A,B,C)) | sbrdtbr0(F) != A | f27(A,B,C) = sdtlpdtrp0(C,F). [copy(2431),flip(o)].
% 109.63/20.97
% 109.63/20.97 % given #2000 (I,wt=74): 3154 -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))) | -aElementOf0(E,szDzozmdt0(C)) | sdtlpdtrp0(C,E) != D | -iLess0(A,xK) | -aElementOf0(F,f28(A,B,C)) | aElementOf0(F,B). [resolve(301,a,264,f)].
% 109.63/20.97
% 109.63/20.97 % given #2500 (I,wt=113): 3675 -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) | -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(1903,b,i)].
% 109.63/20.97
% 109.63/20.97 % given #3000 (I,wt=94): 4185 -aSet0(f23(A,szDzozmdt0(B),B)) | -aElementOf0(f24(A,szDzozmdt0(B),B),szDzozmdt0(B)) | sbrdtbr0(f23(A,szDzozmdt0(B),B)) != A | -aElementOf0(C,f23(A,szDzozmdt0(B),B)) | aElementOf0(C,szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(szDzozmdt0(B)) | -aElementOf0(f22(A,szDzozmdt0(B)),szNzAzT0) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | aElementOf0(D,sdtlcdtrc0(B,szDzozmdt0(B))) | sdtlpdtrp0(B,f24(A,szDzozmdt0(B),B)) != D | -iLess0(A,xK) | -aElementOf0(E,slbdtsldtrb0(f28(A,szDzozmdt0(B),B),A)) | f27(A,szDzozmdt0(B),B) = sdtlpdtrp0(B,E). [factor(2508,b,l)].
% 109.63/20.97
% 109.63/20.97 % given #3500 (I,wt=104): 4696 -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(f29(A,B,C,sdtlcdtrc0(C,szDzozmdt0(C))),sdtlcdtrc0(C,szDzozmdt0(C))) | -aElementOf0(D,szDzozmdt0(C)) | f29(A,B,C,sdtlcdtrc0(C,szDzozmdt0(C))) != sdtlpdtrp0(C,D) | -iLess0(A,xK) | -aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | sbrdtbr0(sdtlcdtrc0(C,szDzozmdt0(C))) != A | f27(A,B,C) = sdtlpdtrp0(C,sdtlcdtrc0(C,szDzozmdt0(C))). [factor(3151,j,o),flip(l)].
% 109.63/20.97
% 109.63/20.97 % given #4000 (I,wt=137): 5200 -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))),f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | sbrdtbr0(sdtlcdtrc0(B,szDzozmdt0(B))) != A | f27(A,sdtlcdtrc0(B,szDzozmdt0(B)),B) = sdtlpdtrp0(B,sdtlcdtrc0(B,szDzozmdt0(B))). [factor(5036,g,m)].
% 109.63/20.97
% 109.63/20.97 % given #4500 (F,wt=11): 10423 szszuzczcdt0(f10(xQ)) != sz00. [resolve(9572,a,618,a)].
% 109.63/20.97
% 109.63/20.97 % SZS status Theorem for theBenchmark
% 109.63/20.97
% 109.63/20.97 % Proof 1 at 6.02 (+ 0.41) seconds.
% 109.63/20.97 % Length of proof is 17.
% 109.63/20.97 % Level of proof is 4.
% 109.63/20.97 % Maximum clause weight is 18.000.
% 109.63/20.97 % Given clauses 4836.
% 109.63/20.97
% 109.63/20.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------