%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG115+4 : 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 : n019.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 0.14s 10.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 70 ( 25 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 86 ( 29 ~; 22 |; 34 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 11 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2273,axiom,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('theBenchmark.p',m__2273) ).
fof(m__,conjecture,
? [W0,W1] :
( xu = sdtpldt0(W0,W1)
& ( aElementOf0(W1,slsdtgt0(xb))
| ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ( aElementOf0(W0,slsdtgt0(xa))
| ? [W2] :
( sdtasdt0(xa,W2) = W0
& aElement0(W2) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0,W1] :
( xu = sdtpldt0(W0,W1)
& ( aElementOf0(W1,slsdtgt0(xb))
| ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ( aElementOf0(W0,slsdtgt0(xa))
| ? [W2] :
( sdtasdt0(xa,W2) = W0
& aElement0(W2) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_41,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| sz00 = W0
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(fof_nnf,[status(thm)],[m__2273]) ).
fof(sk_m__2273_sk,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| sz00 = W0
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sK0,sK1) = xu
& aElementOf0(sK1,slsdtgt0(xb))
& aElementOf0(sK0,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_41]) ).
fof(sk_m__2273,plain,
( ! [VAR_0] :
( ~ iLess0(sbrdtbr0(VAR_0),sbrdtbr0(xu))
| sz00 = VAR_0
| ~ aElementOf0(VAR_0,xI) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ iLess0(sbrdtbr0(VAR_2),sbrdtbr0(xu))
| sz00 = VAR_2
| sdtpldt0(VAR_0,VAR_1) != VAR_2
| ~ aElementOf0(VAR_1,slsdtgt0(xb))
| ~ aElementOf0(VAR_0,slsdtgt0(xa)) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sK0,sK1) = xu
& aElementOf0(sK1,slsdtgt0(xb))
& aElementOf0(sK0,slsdtgt0(xa)) ),
inference(cnf_transformation,[status(thm)],[sk_m__2273_sk]) ).
cnf(c_227,plain,
aElementOf0(sK0,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[sk_m__2273]) ).
cnf(c_228,plain,
aElementOf0(sK1,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[sk_m__2273]) ).
cnf(c_229,plain,
sdtpldt0(sK0,sK1) = xu,
inference(split_conjunct,[status(thm)],[sk_m__2273]) ).
cnf(c_246,negated_conjecture,
( sdtpldt0(A,B) != xu
| ~ aElementOf0(B,slsdtgt0(xb))
| ~ aElementOf0(A,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_2835,negated_conjecture,
( ~ aElementOf0(sK1,slsdtgt0(xb))
| ~ aElementOf0(sK0,slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_246,c_229]) ).
cnf(c_2836,negated_conjecture,
~ aElementOf0(sK1,slsdtgt0(xb)),
inference(resolve,[status(thm)],[c_227,c_2835]) ).
cnf(c_2834,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_228,c_2836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG115+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.37 % Computer : n019.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Sat Sep 26 06:09:30 UTC 2026
% 0.11/10.37 % CPUTime :
% 0.11/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.38 % Process 572157 was started by sandbox on n019,
% 0.11/10.38 % Sat Sep 26 06:09:30 2026
% 0.11/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/10.39
% 0.11/10.39 % From the command line: assign(max_seconds, 300).
% 0.14/10.61
% 0.14/10.61 % SZS status Theorem for theBenchmark
% 0.14/10.61
% 0.14/10.61 % Proof 1 at 0.15 (+ 0.05) seconds.
% 0.14/10.61 % Length of proof is 7.
% 0.14/10.61 % Level of proof is 2.
% 0.14/10.61 % Maximum clause weight is 23.000.
% 0.14/10.61 % Given clauses 172.
% 0.14/10.61
% 0.14/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------