%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG095+2 : 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 : n010.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 08:26:37 AM UTC 2026
% Result : Theorem 1.98s 0.80s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 47 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 45 ( 16 ~; 12 |; 16 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 7 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1205_03,axiom,
! [W0] :
( aElement0(W0)
=> ( aElementOf0(W0,sdtpldt1(xI,xJ))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,xJ)
& aElementOf0(W1,xI) ) ) ),
file('theBenchmark.p',m__1205_03) ).
fof(m__,conjecture,
? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0,W1] :
( sdtpldt0(W0,W1) = sz10
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_31,negated_conjecture,
( sdtpldt0(A,B) != sz10
| ~ aElementOf0(B,xJ)
| ~ aElementOf0(A,xI) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_26,plain,
! [W0] :
( ( aElementOf0(W0,sdtpldt1(xI,xJ))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,xJ)
& aElementOf0(W1,xI) ) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[m__1205_03]) ).
fof(sk_m__1205_03_sk,plain,
! [W0] :
( ( aElementOf0(W0,sdtpldt1(xI,xJ))
& sdtpldt0(sK0(W0),sK1(W0)) = W0
& aElementOf0(sK1(W0),xJ)
& aElementOf0(sK0(W0),xI) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(W1,sK0(W0)),skolemize(W2,sK1(W0))],[nnf_26]) ).
fof(sk_m__1205_03,plain,
( ! [VAR_0] :
( aElementOf0(VAR_0,sdtpldt1(xI,xJ))
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( sdtpldt0(sK0(VAR_0),sK1(VAR_0)) = VAR_0
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(sK1(VAR_0),xJ)
| ~ aElement0(VAR_0) )
& ! [VAR_0] :
( aElementOf0(sK0(VAR_0),xI)
| ~ aElement0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_m__1205_03_sk]) ).
cnf(c_35,plain,
( sdtpldt0(sK0(A),sK1(A)) = A
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m__1205_03]) ).
cnf(c_36,plain,
( aElementOf0(sK1(A),xJ)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m__1205_03]) ).
cnf(c_37,plain,
( aElementOf0(sK0(A),xI)
| ~ aElement0(A) ),
inference(split_conjunct,[status(thm)],[sk_m__1205_03]) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('theBenchmark.p',mSortsC_01) ).
cnf(c_102,plain,
aElement0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
cnf(c_375,plain,
aElementOf0(sK0(sz10),xI),
inference(resolve,[status(thm)],[c_102,c_37]) ).
cnf(c_376,plain,
aElementOf0(sK1(sz10),xJ),
inference(resolve,[status(thm)],[c_102,c_36]) ).
cnf(c_377,plain,
sdtpldt0(sK0(sz10),sK1(sz10)) = sz10,
inference(resolve,[status(thm)],[c_102,c_35]) ).
cnf(c_1451,negated_conjecture,
( sdtpldt0(sK0(sz10),A) != sz10
| ~ aElementOf0(A,xJ) ),
inference(resolve,[status(thm)],[c_31,c_375]) ).
cnf(c_1452,negated_conjecture,
sdtpldt0(sK0(sz10),sK1(sz10)) != sz10,
inference(resolve,[status(thm)],[c_1451,c_376]) ).
cnf(c_1450,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_377,c_1452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG095+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n010.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 06:03:59 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 2648428 was started by sandbox2 on n010,
% 0.20/0.46 % Sat Sep 26 06:03:59 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 1.98/0.80
% 1.98/0.80 % SZS status Theorem for theBenchmark
% 1.98/0.80
% 1.98/0.80 % Proof 1 at 0.26 (+ 0.04) seconds.
% 1.98/0.80 % Length of proof is 11.
% 1.98/0.80 % Level of proof is 3.
% 1.98/0.80 % Maximum clause weight is 24.000.
% 1.98/0.80 % Given clauses 164.
% 1.98/0.80
% 1.98/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------