%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM620+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 : 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 08:17:36 AM UTC 2026
% Result : Theorem 139.53s 24.58s
% Output : CNFRefutation 139.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 28 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 19 ( 4 ~; 2 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4660,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
& aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('theBenchmark.p',m__4660) ).
fof(m__5389,axiom,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('theBenchmark.p',m__5389) ).
fof(m__,conjecture,
( ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_931,plain,
( aElementOf0(sdtlpdtrp0(xe,A),sdtlpdtrp0(xN,A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__4660]) ).
cnf(c_1028,plain,
aElementOf0(xm,szNzAzT0),
inference(clausify,[status(thm)],[m__5389]) ).
cnf(c_1029,plain,
sdtlpdtrp0(xe,xm) = xx,
inference(clausify,[status(thm)],[m__5389]) ).
cnf(c_1031,negated_conjecture,
( aElementOf0(A,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(A,sdtlpdtrp0(xN,xm)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_1033,negated_conjecture,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_22118,plain,
aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)),
inference(resolve,[status(thm)],[c_1028,c_931]) ).
cnf(c_7557,plain,
aElementOf0(xx,sdtlpdtrp0(xN,xm)),
inference(paramod,[status(thm)],[c_1029,c_22118]) ).
cnf(c_22119,negated_conjecture,
aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(resolve,[status(thm)],[c_7557,c_1031]) ).
cnf(c_22117,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1033,c_22119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM620+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n003.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 03:30:13 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 1928628 was started by sandbox on n003,
% 0.10/5.37 % Sat Sep 26 03:30:13 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.70
% 0.14/5.70 % From the command line: assign(max_seconds, 300).
% 139.53/24.58
% 139.53/24.58 % given #500 (I,wt=17): 917 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 139.53/24.58
% 139.53/24.58 % given #1000 (I,wt=66): 1620 -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))) | -aElementOf0(F,szDzozmdt0(C)) | sdtlpdtrp0(C,F) != E | -iLess0(A,xK) | -aElementOf0(V6,slbdtsldtrb0(f28(A,B,C),A)) | f27(A,B,C) = sdtlpdtrp0(C,V6). [copy(1619),flip(n)].
% 139.53/24.58
% 139.53/24.58 % given #1500 (I,wt=55): 2455 -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(f26(A,B,C),sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | aSubsetOf0(f28(A,B,C),B). [resolve(303,a,132,e)].
% 139.53/24.58
% 139.53/24.58 % given #2000 (I,wt=71): 3177 -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(f26(A,B,C),sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aSubsetOf0(D,f28(A,B,C)) | sbrdtbr0(D) != A | f27(A,B,C) = sdtlpdtrp0(C,D). [copy(3176),flip(n)].
% 139.53/24.58
% 139.53/24.58 % given #2500 (I,wt=56): 3781 -aSubsetOf0(f23(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(D,sdtlcdtrc0(C,szDzozmdt0(C))) | sdtlpdtrp0(C,f23(A,B,C)) != D | -iLess0(A,xK) | aSet0(f28(A,B,C)). [factor(1448,c,j)].
% 139.53/24.58
% 139.53/24.58 % given #3000 (I,wt=71): 4288 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | 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) | -aSubsetOf0(sdtlcdtrc0(C,szDzozmdt0(C)),xT) | -iLess0(A,xK) | aElementOf0(f29(A,B,C,f23(A,B,C)),f23(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(2336,a,l),merge(m)].
% 139.53/24.58
% 139.53/24.58 % given #3500 (I,wt=75): 4809 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | 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) | -aSubsetOf0(sdtlcdtrc0(C,szDzozmdt0(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(2789,a,l),merge(m)].
% 139.53/24.58
% 139.53/24.58 % given #4000 (I,wt=85): 5328 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | -aElementOf0(E,sdtlcdtrc0(C,szDzozmdt0(C))) | aElementOf0(f25(A,B,C,E),szDzozmdt0(C)) | -iLess0(A,xK) | aElementOf0(f29(A,B,C,f23(A,B,C)),f23(A,B,C)) | f27(A,B,C) = sdtlpdtrp0(C,f23(A,B,C)). [factor(3493,a,n),merge(o)].
% 139.53/24.58
% 139.53/24.58 % given #4500 (I,wt=126): 5836 -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(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(f26(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))),szNzAzT0) | -isCountable0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aFunction0(B) | -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(5132,g,l)].
% 139.53/24.58
% 139.53/24.58 % given #5000 (T,wt=4): 7215 iLess0(xn,szszuzczcdt0(xn)). [resolve(1014,a,610,a)].
% 139.53/24.58
% 139.53/24.58 % given #5500 (F,wt=7): 20695 sdtmndt0(f39(szszuzczcdt0(xp)),sz00) != szNzAzT0. [resolve(17918,a,12647,a)].
% 139.53/24.58
% 139.53/24.58 % SZS status Theorem for theBenchmark
% 139.53/24.58
% 139.53/24.58 % Proof 1 at 17.86 (+ 0.81) seconds.
% 139.53/24.58 % Length of proof is 10.
% 139.53/24.58 % Level of proof is 3.
% 139.53/24.58 % Maximum clause weight is 11.000.
% 139.53/24.58 % Given clauses 5578.
% 139.53/24.58
% 139.53/24.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------