%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG123+4 : 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 : n016.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 08:26:43 AM UTC 2026
% Result : Theorem 44.30s 6.84s
% Output : CNFRefutation 44.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 63 ( 17 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 46 ( 5 ~; 5 |; 30 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 6 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2174,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& 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__2174) ).
fof(m__2690,axiom,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('theBenchmark.p',m__2690) ).
fof(m__2699,axiom,
( aElementOf0(xb,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xb
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) )
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xb
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('theBenchmark.p',m__2699) ).
fof(m__,conjecture,
( aElementOf0(xr,xI)
| ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aElementOf0(xr,xI)
| ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_198,plain,
( aElementOf0(sdtpldt0(A,B),xI)
| ~ aElementOf0(B,xI)
| ~ aElementOf0(A,xI) ),
inference(clausify,[status(thm)],[m__2174]) ).
fof(nnf_47,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(fof_nnf,[status(thm)],[m__2690]) ).
fof(sk_m__2690,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& sdtpldt0(sK0,sK1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(sK1,slsdtgt0(xb))
& aElementOf0(sK0,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(W0,sK0),skolemize(W1,sK1)],[nnf_47]) ).
cnf(c_267,plain,
sdtpldt0(sK0,sK1) = smndt0(sdtasdt0(xq,xu)),
inference(split_conjunct,[status(thm)],[sk_m__2690]) ).
cnf(c_268,plain,
smndt0(sdtasdt0(xq,xu)) = sdtpldt0(sK0,sK1),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_269,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[sk_m__2690]) ).
cnf(c_270,plain,
aElementOf0(sdtpldt0(sK0,sK1),xI),
inference(paramod,[status(thm)],[c_268,c_269]) ).
cnf(c_277,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_278,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(clausify,[status(thm)],[m__2718]) ).
cnf(c_22760,plain,
xr = sdtpldt0(sdtpldt0(sK0,sK1),xb),
inference(paramod,[status(thm)],[c_268,c_278]) ).
cnf(c_279,plain,
sdtpldt0(sdtpldt0(sK0,sK1),xb) = xr,
inference(copy,[status(thm)],[c_22760]) ).
cnf(c_281,negated_conjecture,
~ aElementOf0(xr,xI),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_22761,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sK0,sK1),A),xI)
| ~ aElementOf0(A,xI) ),
inference(resolve,[status(thm)],[c_198,c_270]) ).
cnf(c_22762,plain,
aElementOf0(sdtpldt0(sdtpldt0(sK0,sK1),xb),xI),
inference(resolve,[status(thm)],[c_22761,c_277]) ).
cnf(c_22763,plain,
aElementOf0(xr,xI),
inference(paramod,[status(thm)],[c_279,c_22762]) ).
cnf(c_22759,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_281,c_22763]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.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 06:16:44 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 176733 was started by sandbox2 on n016,
% 0.10/0.36 % Sat Sep 26 06:16:44 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.40
% 0.15/0.40 % From the command line: assign(max_seconds, 300).
% 44.30/6.84
% 44.30/6.84 % SZS status Theorem for theBenchmark
% 44.30/6.84
% 44.30/6.84 % Proof 1 at 5.04 (+ 1.31) seconds.
% 44.30/6.84 % Length of proof is 14.
% 44.30/6.84 % Level of proof is 4.
% 44.30/6.84 % Maximum clause weight is 27.000.
% 44.30/6.84 % Given clauses 182.
% 44.30/6.84
% 44.30/6.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------