%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG116+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 : 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 08:26:41 AM UTC 2026
% Result : Theorem 7.43s 1.63s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 43 ( 20 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 37 ( 11 ~; 4 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 0 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2456,axiom,
( xu = sdtpldt0(xk,xl)
& aElementOf0(xl,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xl
& aElement0(W0) )
& aElementOf0(xk,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xk
& aElement0(W0) ) ),
file('theBenchmark.p',m__2456) ).
fof(m__,conjecture,
? [W0,W1] :
( xu = sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
& aElement0(W1)
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0,W1] :
( xu = sdtpldt0(sdtasdt0(xa,W0),sdtasdt0(xb,W1))
& aElement0(W1)
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_43,plain,
( sdtpldt0(xk,xl) = xu
& aElementOf0(xl,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xl
& aElement0(W0) )
& aElementOf0(xk,slsdtgt0(xa))
& ? [X0] :
( sdtasdt0(xa,X0) = xk
& aElement0(X0) ) ),
inference(fof_nnf,[status(thm)],[m__2456]) ).
fof(sk_m__2456,plain,
( sdtpldt0(xk,xl) = xu
& aElementOf0(xl,slsdtgt0(xb))
& sdtasdt0(xb,sK1) = xl
& aElement0(sK1)
& aElementOf0(xk,slsdtgt0(xa))
& sdtasdt0(xa,sK0) = xk
& aElement0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(W0,sK1)],[nnf_43]) ).
cnf(c_244,plain,
aElement0(sK0),
inference(split_conjunct,[status(thm)],[sk_m__2456]) ).
cnf(c_245,plain,
sdtasdt0(xa,sK0) = xk,
inference(split_conjunct,[status(thm)],[sk_m__2456]) ).
cnf(c_247,plain,
aElement0(sK1),
inference(split_conjunct,[status(thm)],[sk_m__2456]) ).
cnf(c_248,plain,
sdtasdt0(xb,sK1) = xl,
inference(split_conjunct,[status(thm)],[sk_m__2456]) ).
cnf(c_250,plain,
sdtpldt0(xk,xl) = xu,
inference(split_conjunct,[status(thm)],[sk_m__2456]) ).
cnf(c_251,negated_conjecture,
( sdtpldt0(sdtasdt0(xa,A),sdtasdt0(xb,B)) != xu
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_4207,negated_conjecture,
( sdtpldt0(sdtasdt0(xa,sK0),sdtasdt0(xb,A)) != xu
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_251,c_244]) ).
cnf(c_2010,negated_conjecture,
( sdtpldt0(xk,sdtasdt0(xb,A)) != xu
| ~ aElement0(A) ),
inference(paramod,[status(thm)],[c_245,c_4207]) ).
cnf(c_4208,plain,
sdtpldt0(xk,sdtasdt0(xb,sK1)) != xu,
inference(resolve,[status(thm)],[c_2010,c_247]) ).
cnf(c_4209,plain,
sdtpldt0(xk,xl) != xu,
inference(paramod,[status(thm)],[c_248,c_4208]) ).
cnf(c_4210,plain,
xu != xu,
inference(paramod,[status(thm)],[c_250,c_4209]) ).
cnf(c_4206,plain,
$false,
inference(copy,[status(thm)],[c_4210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG116+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.63 % Computer : n006.cluster.edu
% 0.17/0.63 % Model : x86_64 x86_64
% 0.17/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.63 % Memory : 8046.5625MB
% 0.17/0.63 % OS : Linux 6.8.0-71-generic
% 0.17/0.63 % CPULimit : 300
% 0.17/0.63 % WCLimit : 300
% 0.17/0.63 % DateTime : Sat Sep 26 06:09:15 UTC 2026
% 0.17/0.64 % CPUTime :
% 0.17/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.64 % Process 529591 was started by sandbox2 on n006,
% 0.17/0.64 % Sat Sep 26 06:09:15 2026
% 0.17/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.67
% 0.21/0.67 % From the command line: assign(max_seconds, 300).
% 7.43/1.63
% 7.43/1.63 % SZS status Theorem for theBenchmark
% 7.43/1.63
% 7.43/1.63 % Proof 1 at 0.72 (+ 0.19) seconds.
% 7.43/1.63 % Length of proof is 10.
% 7.43/1.63 % Level of proof is 3.
% 7.43/1.63 % Maximum clause weight is 13.000.
% 7.43/1.63 % Given clauses 331.
% 7.43/1.63
% 7.43/1.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------