%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM592+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 : n007.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 08:17:30 AM UTC 2026
% Result : Theorem 74.56s 10.93s
% Output : CNFRefutation 74.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 102 ( 19 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 128 ( 58 ~; 48 |; 19 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4448_02,axiom,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) ),
file('theBenchmark.p',m__4448_02) ).
fof(m__4545,axiom,
( ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xX,xk))
& aSet0(W0) )
=> sdtlpdtrp0(xd,W0) = xu )
& isCountable0(xX)
& aSubsetOf0(xX,xY)
& aElementOf0(xu,xT) ),
file('theBenchmark.p',m__4545) ).
fof(m__,conjecture,
? [W0] :
( ? [W1] :
( ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aSet0(W2) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 )
& isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aElementOf0(W0,xT) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( ? [W1] :
( ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aSet0(W2) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 )
& isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aElementOf0(W0,xT) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_265,plain,
sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) = xY,
inference(clausify,[status(thm)],[m__4448_02]) ).
cnf(c_266,plain,
sdtlpdtrp0(xC,xi) = xd,
inference(clausify,[status(thm)],[m__4448_02]) ).
cnf(c_273,plain,
aElementOf0(xu,xT),
inference(clausify,[status(thm)],[m__4545]) ).
cnf(c_274,plain,
aSubsetOf0(xX,xY),
inference(clausify,[status(thm)],[m__4545]) ).
cnf(c_275,plain,
isCountable0(xX),
inference(clausify,[status(thm)],[m__4545]) ).
cnf(c_276,plain,
( sdtlpdtrp0(xd,A) = xu
| ~ aElementOf0(A,slbdtsldtrb0(xX,xk))
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[m__4545]) ).
fof(nnf_86,plain,
! [W0] :
( ! [W1] :
( ? [W2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) != W0
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aSet0(W2) )
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(W0,xT) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg_sk,plain,
! [W0] :
( ! [W1] :
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK0(W0,W1)) != W0
& aElementOf0(sK0(W0,W1),slbdtsldtrb0(W1,xk))
& aSet0(sK0(W0,W1)) )
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ aElementOf0(W0,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W2,sK0(W0,W1))],[nnf_86]) ).
fof(sk_m___neg,plain,
( ! [VAR_0,VAR_1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK0(VAR_0,VAR_1)) != VAR_0
| ~ isCountable0(VAR_1)
| ~ aSubsetOf0(VAR_1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(VAR_0,xT) )
& ! [VAR_0,VAR_1] :
( aElementOf0(sK0(VAR_0,VAR_1),slbdtsldtrb0(VAR_1,xk))
| ~ isCountable0(VAR_1)
| ~ aSubsetOf0(VAR_1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(VAR_0,xT) )
& ! [VAR_0,VAR_1] :
( aSet0(sK0(VAR_0,VAR_1))
| ~ isCountable0(VAR_1)
| ~ aSubsetOf0(VAR_1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(VAR_0,xT) ) ),
inference(cnf_transformation,[status(thm)],[sk_m___neg_sk]) ).
cnf(c_277,negated_conjecture,
( aSet0(sK0(A,B))
| ~ isCountable0(B)
| ~ aSubsetOf0(B,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(A,xT) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_278,negated_conjecture,
( aSet0(sK0(A,B))
| ~ isCountable0(B)
| ~ aSubsetOf0(B,xY)
| ~ aElementOf0(A,xT) ),
inference(paramod,[status(thm)],[c_265,c_277]) ).
cnf(c_279,negated_conjecture,
( aElementOf0(sK0(A,B),slbdtsldtrb0(B,xk))
| ~ isCountable0(B)
| ~ aSubsetOf0(B,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(A,xT) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_280,negated_conjecture,
( aElementOf0(sK0(A,B),slbdtsldtrb0(B,xk))
| ~ isCountable0(B)
| ~ aSubsetOf0(B,xY)
| ~ aElementOf0(A,xT) ),
inference(paramod,[status(thm)],[c_265,c_279]) ).
cnf(c_281,negated_conjecture,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK0(A,B)) != A
| ~ isCountable0(B)
| ~ aSubsetOf0(B,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(A,xT) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_12732,negated_conjecture,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK0(A,B)) != A
| ~ isCountable0(B)
| ~ aSubsetOf0(B,xY)
| ~ aElementOf0(A,xT) ),
inference(paramod,[status(thm)],[c_265,c_281]) ).
cnf(c_282,negated_conjecture,
( sdtlpdtrp0(xd,sK0(A,B)) != A
| ~ isCountable0(B)
| ~ aSubsetOf0(B,xY)
| ~ aElementOf0(A,xT) ),
inference(paramod,[status(thm)],[c_266,c_12732]) ).
cnf(c_12733,negated_conjecture,
( aSet0(sK0(A,xX))
| ~ isCountable0(xX)
| ~ aElementOf0(A,xT) ),
inference(resolve,[status(thm)],[c_278,c_274]) ).
cnf(c_696,negated_conjecture,
( aSet0(sK0(A,xX))
| ~ aElementOf0(A,xT) ),
inference(resolve,[status(thm)],[c_275,c_12733]) ).
cnf(c_12734,negated_conjecture,
( aElementOf0(sK0(A,xX),slbdtsldtrb0(xX,xk))
| ~ isCountable0(xX)
| ~ aElementOf0(A,xT) ),
inference(resolve,[status(thm)],[c_280,c_274]) ).
cnf(c_697,negated_conjecture,
( aElementOf0(sK0(A,xX),slbdtsldtrb0(xX,xk))
| ~ aElementOf0(A,xT) ),
inference(resolve,[status(thm)],[c_275,c_12734]) ).
cnf(c_12735,negated_conjecture,
( sdtlpdtrp0(xd,sK0(A,xX)) != A
| ~ isCountable0(xX)
| ~ aElementOf0(A,xT) ),
inference(resolve,[status(thm)],[c_282,c_274]) ).
cnf(c_698,negated_conjecture,
( sdtlpdtrp0(xd,sK0(A,xX)) != A
| ~ aElementOf0(A,xT) ),
inference(resolve,[status(thm)],[c_275,c_12735]) ).
cnf(c_7303,plain,
aSet0(sK0(xu,xX)),
inference(resolve,[status(thm)],[c_696,c_273]) ).
cnf(c_10599,plain,
aElementOf0(sK0(xu,xX),slbdtsldtrb0(xX,xk)),
inference(resolve,[status(thm)],[c_697,c_273]) ).
cnf(c_10602,plain,
sdtlpdtrp0(xd,sK0(xu,xX)) != xu,
inference(resolve,[status(thm)],[c_698,c_273]) ).
cnf(c_12736,plain,
( sdtlpdtrp0(xd,sK0(xu,xX)) = xu
| ~ aSet0(sK0(xu,xX)) ),
inference(resolve,[status(thm)],[c_10599,c_276]) ).
cnf(c_12737,plain,
sdtlpdtrp0(xd,sK0(xu,xX)) = xu,
inference(resolve,[status(thm)],[c_7303,c_12736]) ).
cnf(c_12731,plain,
$false,
inference(resolve,[status(thm)],[c_10602,c_12737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM592+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:19:23 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2678598 was started by sandbox on n007,
% 0.09/0.36 % Sat Sep 26 03:19:23 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 74.56/10.93
% 74.56/10.93 % given #500 (F,wt=14): 2508 -sdtlseqdt0(szszuzczcdt0(xi),sz00). [resolve(1779,a,141,d),flip(d),unit_del(a,594),unit_del(b,128),unit_del(d,593)].
% 74.56/10.93
% 74.56/10.93 % given #1000 (T,wt=14): 8411 aSet0(slbdtsldtrb0(xS,sz00)). [xx_res(1482,a)].
% 74.56/10.93
% 74.56/10.93 % SZS status Theorem for theBenchmark
% 74.56/10.93
% 74.56/10.93 % Proof 1 at 1.70 (+ 0.63) seconds.
% 74.56/10.93 % Length of proof is 22.
% 74.56/10.93 % Level of proof is 5.
% 74.56/10.93 % Maximum clause weight is 30.000.
% 74.56/10.93 % Given clauses 1470.
% 74.56/10.93
% 74.56/10.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------