%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG089+2 : 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 : n004.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 08:26:36 AM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 62 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 54 ( 13 ~; 10 |; 21 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefIdeal,axiom,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(m__870,axiom,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('theBenchmark.p',m__870) ).
fof(m__901,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xx
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ),
file('theBenchmark.p',m__901) ).
fof(m__934,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('theBenchmark.p',m__934) ).
fof(m__,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_29,plain,
( aElementOf0(sdtasdt0(C,B),A)
| ~ aElement0(C)
| ~ aElementOf0(B,A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_36,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__870]) ).
cnf(c_37,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[m__870]) ).
cnf(c_40,plain,
( aElementOf0(sdtasdt0(B,A),xJ)
| ~ aElement0(B)
| ~ aElementOf0(A,xJ) ),
inference(resolve,[status(thm)],[c_37,c_29]) ).
cnf(c_43,plain,
( aElementOf0(sdtasdt0(B,A),xI)
| ~ aElement0(B)
| ~ aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_36,c_29]) ).
cnf(c_54,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_61,plain,
aElementOf0(xl,xJ),
inference(clausify,[status(thm)],[m__934]) ).
cnf(c_62,plain,
aElementOf0(xk,xI),
inference(clausify,[status(thm)],[m__934]) ).
cnf(c_63,plain,
aElement0(xz),
inference(clausify,[status(thm)],[m__901]) ).
cnf(c_380,plain,
( aElementOf0(sdtasdt0(A,xk),xI)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_43,c_62]) ).
cnf(c_373,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(resolve,[status(thm)],[c_380,c_63]) ).
cnf(c_381,plain,
( aElementOf0(sdtasdt0(A,xl),xJ)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_40,c_61]) ).
cnf(c_376,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(resolve,[status(thm)],[c_381,c_63]) ).
cnf(c_382,negated_conjecture,
~ aElementOf0(sdtasdt0(xz,xl),xJ),
inference(resolve,[status(thm)],[c_373,c_54]) ).
cnf(c_379,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_376,c_382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 06:02:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 969132 was started by sandbox on n004,
% 0.11/0.37 % Sat Sep 26 06:02:06 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.42
% 0.11/0.42 % SZS status Theorem for theBenchmark
% 0.11/0.42
% 0.11/0.42 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.11/0.42 % Length of proof is 17.
% 0.11/0.42 % Level of proof is 4.
% 0.11/0.42 % Maximum clause weight is 20.000.
% 0.11/0.42 % Given clauses 26.
% 0.11/0.42
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------