%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG121+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 : n011.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 6.23s 1.26s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 44 ( 15 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 38 ( 8 ~; 8 |; 21 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 1 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',mAddZero) ).
fof(m__2091,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__2203,axiom,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
file('theBenchmark.p',m__2203) ).
fof(m__,conjecture,
( 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__) ).
fof(m___neg,negated_conjecture,
~ ( 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)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_81,plain,
( sdtpldt0(sz00,A) = A
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mAddZero]) ).
cnf(c_157,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_212,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_221,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(clausify,[status(thm)],[m__2203]) ).
cnf(c_265,negated_conjecture,
( sdtpldt0(A,B) != xb
| ~ aElementOf0(B,slsdtgt0(xb))
| ~ aElementOf0(A,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_605,plain,
sdtpldt0(sz00,xb) = xb,
inference(resolve,[status(thm)],[c_157,c_81]) ).
cnf(c_2306,plain,
( sdtpldt0(sz00,A) != xb
| ~ aElementOf0(A,slsdtgt0(xb)) ),
inference(resolve,[status(thm)],[c_265,c_212]) ).
cnf(c_10183,plain,
sdtpldt0(sz00,xb) != xb,
inference(resolve,[status(thm)],[c_2306,c_221]) ).
cnf(c_10182,plain,
$false,
inference(resolve,[status(thm)],[c_605,c_10183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG121+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:11:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3953933 was started by sandbox2 on n011,
% 0.09/0.37 % Sat Sep 26 06:11:14 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 6.23/1.26
% 6.23/1.26 % SZS status Theorem for theBenchmark
% 6.23/1.26
% 6.23/1.26 % Proof 1 at 0.70 (+ 0.15) seconds.
% 6.23/1.26 % Length of proof is 12.
% 6.23/1.26 % Level of proof is 3.
% 6.23/1.26 % Maximum clause weight is 23.000.
% 6.23/1.26 % Given clauses 465.
% 6.23/1.26
% 6.23/1.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------