%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG123+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 : n006.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 08:26:42 AM UTC 2026
% Result : Theorem 6.05s 6.50s
% Output : CNFRefutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 32 ( 4 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 21 ( 8 ~; 6 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 4 !; 0 ?)
% 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__2174,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('theBenchmark.p',m__2174) ).
fof(m__,conjecture,
aElementOf0(xr,xI),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xr,xI),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_119,plain,
( aElementOf0(sdtpldt0(B,C),A)
| ~ aElementOf0(C,A)
| ~ aElementOf0(B,A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_156,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__2174]) ).
fof(m__2690,axiom,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('theBenchmark.p',m__2690) ).
cnf(c_180,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(clausify,[status(thm)],[m__2690]) ).
fof(m__2699,axiom,
aElementOf0(xb,xI),
file('theBenchmark.p',m__2699) ).
cnf(c_181,plain,
aElementOf0(xb,xI),
inference(clausify,[status(thm)],[m__2699]) ).
fof(m__2718,axiom,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('theBenchmark.p',m__2718) ).
cnf(c_182,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(clausify,[status(thm)],[m__2718]) ).
cnf(c_183,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = xr,
inference(copy,[status(thm)],[c_182]) ).
cnf(c_184,negated_conjecture,
~ aElementOf0(xr,xI),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_3910,plain,
( aElementOf0(sdtpldt0(A,B),xI)
| ~ aElementOf0(B,xI)
| ~ aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_119,c_156]) ).
cnf(c_3911,plain,
( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),A),xI)
| ~ aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_3910,c_180]) ).
cnf(c_3912,plain,
aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),xI),
inference(resolve,[status(thm)],[c_3911,c_181]) ).
cnf(c_3913,plain,
aElementOf0(xr,xI),
inference(paramod,[status(thm)],[c_183,c_3912]) ).
cnf(c_3909,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_184,c_3913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG123+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.60 % Computer : n006.cluster.edu
% 0.12/5.60 % Model : x86_64 x86_64
% 0.12/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.60 % Memory : 8046.5625MB
% 0.12/5.60 % OS : Linux 6.8.0-71-generic
% 0.12/5.61 % CPULimit : 300
% 0.12/5.61 % WCLimit : 300
% 0.12/5.61 % DateTime : Sat Sep 26 06:11:09 UTC 2026
% 0.12/5.61 % CPUTime :
% 0.12/5.61 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.61 % Process 532452 was started by sandbox2 on n006,
% 0.12/5.61 % Sat Sep 26 06:11:09 2026
% 0.12/5.61 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/5.64
% 0.12/5.64 % From the command line: assign(max_seconds, 300).
% 6.05/6.50
% 6.05/6.50 % SZS status Theorem for theBenchmark
% 6.05/6.50
% 6.05/6.50 % Proof 1 at 0.63 (+ 0.21) seconds.
% 6.05/6.50 % Length of proof is 11.
% 6.05/6.50 % Level of proof is 2.
% 6.05/6.50 % Maximum clause weight is 28.000.
% 6.05/6.50 % Given clauses 103.
% 6.05/6.50
% 6.05/6.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------