%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG102+1 : 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 : n002.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 08:26:38 AM UTC 2026
% Result : Theorem 81.75s 11.91s
% Output : CNFRefutation 81.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 106 ( 36 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 140 ( 55 ~; 58 |; 24 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPrIdeal,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefPrIdeal) ).
fof(m__1933,axiom,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
file('theBenchmark.p',m__1933) ).
fof(m__,conjecture,
? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xc,W0) = xy
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_66,negated_conjecture,
( sdtasdt0(xc,A) != xy
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_70,plain,
aElementOf0(xy,slsdtgt0(xc)),
inference(clausify,[status(thm)],[m__1933]) ).
fof(m__1905,axiom,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
cnf(c_72,plain,
aElement0(xc),
inference(clausify,[status(thm)],[m__1905]) ).
fof(nnf_34,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) )
& ( ? [X3] :
( sdtasdt0(W0,X3) = W2
& aElement0(X3) )
| aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| slsdtgt0(W0) = W1 )
& ( ( ! [X0] :
( ( ! [X2] :
( sdtasdt0(W0,X2) != X0
| ~ aElement0(X2) )
| aElementOf0(X0,W1) )
& ( ? [X1] :
( sdtasdt0(W0,X1) = X0
& aElement0(X1) )
| ~ aElementOf0(X0,W1) ) )
& aSet0(W1) )
| slsdtgt0(W0) != W1 ) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefPrIdeal]) ).
fof(sk_mDefPrIdeal_sk,plain,
! [W0] :
( ! [W1] :
( ( ( ( ! [W3] :
( sdtasdt0(W0,W3) != sK1(W0,W1)
| ~ aElement0(W3) )
| ~ aElementOf0(sK1(W0,W1),W1) )
& ( ( sdtasdt0(W0,sK2(W0,W1)) = sK1(W0,W1)
& aElement0(sK2(W0,W1)) )
| aElementOf0(sK1(W0,W1),W1) ) )
| ~ aSet0(W1)
| slsdtgt0(W0) = W1 )
& ( ( ! [X0] :
( ( ! [X2] :
( sdtasdt0(W0,X2) != X0
| ~ aElement0(X2) )
| aElementOf0(X0,W1) )
& ( ( sdtasdt0(W0,sK0(W0,W1,X0)) = X0
& aElement0(sK0(W0,W1,X0)) )
| ~ aElementOf0(X0,W1) ) )
& aSet0(W1) )
| slsdtgt0(W0) != W1 ) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(W0,W1,X0)),skolemize(W2,sK1(W0,W1)),skolemize(X3,sK2(W0,W1))],[nnf_34]) ).
fof(sk_mDefPrIdeal,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sdtasdt0(VAR_0,VAR_2) != sK1(VAR_0,VAR_1)
| ~ aElement0(VAR_2)
| ~ aElementOf0(sK1(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| slsdtgt0(VAR_0) = VAR_1
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( sdtasdt0(VAR_0,sK2(VAR_0,VAR_1)) = sK1(VAR_0,VAR_1)
| aElementOf0(sK1(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| slsdtgt0(VAR_0) = VAR_1
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aElement0(sK2(VAR_0,VAR_1))
| aElementOf0(sK1(VAR_0,VAR_1),VAR_1)
| ~ aSet0(VAR_1)
| slsdtgt0(VAR_0) = VAR_1
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sdtasdt0(VAR_0,VAR_3) != VAR_2
| ~ aElement0(VAR_3)
| aElementOf0(VAR_2,VAR_1)
| slsdtgt0(VAR_0) != VAR_1
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( sdtasdt0(VAR_0,sK0(VAR_0,VAR_1,VAR_2)) = VAR_2
| ~ aElementOf0(VAR_2,VAR_1)
| slsdtgt0(VAR_0) != VAR_1
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( aElement0(sK0(VAR_0,VAR_1,VAR_2))
| ~ aElementOf0(VAR_2,VAR_1)
| slsdtgt0(VAR_0) != VAR_1
| ~ aElement0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aSet0(VAR_1)
| slsdtgt0(VAR_0) != VAR_1
| ~ aElement0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefPrIdeal_sk]) ).
cnf(c_78,plain,
( sdtasdt0(A,sK0(A,B,C)) = C
| ~ aElementOf0(C,B)
| slsdtgt0(A) != B
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefPrIdeal]) ).
cnf(c_79,plain,
( aElement0(sK0(A,B,C))
| ~ aElementOf0(C,B)
| slsdtgt0(A) != B
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefPrIdeal]) ).
cnf(c_15887,plain,
( sdtasdt0(xc,sK0(xc,A,B)) = B
| ~ aElementOf0(B,A)
| slsdtgt0(xc) != A ),
inference(resolve,[status(thm)],[c_78,c_72]) ).
cnf(c_15888,plain,
( sdtasdt0(xc,sK0(xc,slsdtgt0(xc),A)) = A
| ~ aElementOf0(A,slsdtgt0(xc)) ),
inference(xxres,[status(thm)],[c_15887]) ).
cnf(c_271,plain,
sdtasdt0(xc,sK0(xc,slsdtgt0(xc),xy)) = xy,
inference(resolve,[status(thm)],[c_15888,c_70]) ).
cnf(c_15889,plain,
( aElement0(sK0(xc,A,B))
| ~ aElementOf0(B,A)
| slsdtgt0(xc) != A ),
inference(resolve,[status(thm)],[c_79,c_72]) ).
cnf(c_15890,plain,
( aElement0(sK0(xc,slsdtgt0(xc),A))
| ~ aElementOf0(A,slsdtgt0(xc)) ),
inference(xxres,[status(thm)],[c_15889]) ).
cnf(c_275,plain,
aElement0(sK0(xc,slsdtgt0(xc),xy)),
inference(resolve,[status(thm)],[c_15890,c_70]) ).
cnf(c_15891,negated_conjecture,
~ aElement0(sK0(xc,slsdtgt0(xc),xy)),
inference(resolve,[status(thm)],[c_66,c_271]) ).
cnf(c_15886,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_275,c_15891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG102+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 06:08:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1001269 was started by sandbox2 on n002,
% 0.10/0.36 % Sat Sep 26 06:08:20 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 81.75/11.91
% 81.75/11.91 % SZS status Theorem for theBenchmark
% 81.75/11.91
% 81.75/11.91 % Proof 1 at 2.79 (+ 0.67) seconds.
% 81.75/11.91 % Length of proof is 11.
% 81.75/11.91 % Level of proof is 3.
% 81.75/11.91 % Maximum clause weight is 23.000.
% 81.75/11.91 % Given clauses 237.
% 81.75/11.91
% 81.75/11.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------