%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG124+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 08:26:43 AM UTC 2026
% Result : Theorem 2.21s 0.75s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 56 ( 19 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 56 ( 19 ~; 16 |; 20 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 1 !; 8 ?)
% 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__2666,axiom,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ),
file('theBenchmark.p',m__2666) ).
fof(m__2729,axiom,
( aElementOf0(xr,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('theBenchmark.p',m__2729) ).
cnf(c_241,plain,
( ~ iLess0(sbrdtbr0(C),sbrdtbr0(xu))
| sz00 = C
| sdtpldt0(A,B) != C
| ~ aElementOf0(B,slsdtgt0(xb))
| ~ aElementOf0(A,slsdtgt0(xa)) ),
inference(clausify,[status(thm)],[m__2273]) ).
cnf(c_263,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 ),
inference(clausify,[status(thm)],[m__2666]) ).
fof(m__2673,axiom,
xr != sz00,
file('theBenchmark.p',m__2673) ).
cnf(c_264,plain,
xr != sz00,
inference(clausify,[status(thm)],[m__2673]) ).
fof(nnf_49,plain,
( aElementOf0(xr,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xr
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(fof_nnf,[status(thm)],[m__2729]) ).
fof(sk_m__2729,plain,
( aElementOf0(xr,xI)
& sdtpldt0(sK0,sK1) = xr
& aElementOf0(sK1,slsdtgt0(xb))
& aElementOf0(sK0,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(W0,sK0),skolemize(W1,sK1)],[nnf_49]) ).
cnf(c_278,plain,
aElementOf0(sK0,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[sk_m__2729]) ).
cnf(c_279,plain,
aElementOf0(sK1,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[sk_m__2729]) ).
cnf(c_280,plain,
sdtpldt0(sK0,sK1) = xr,
inference(split_conjunct,[status(thm)],[sk_m__2729]) ).
cnf(c_382,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(resolve,[status(thm)],[c_264,c_263]) ).
cnf(c_3955,plain,
( ~ iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| sz00 = xr
| ~ aElementOf0(sK1,slsdtgt0(xb))
| ~ aElementOf0(sK0,slsdtgt0(xa)) ),
inference(resolve,[status(thm)],[c_280,c_241]) ).
cnf(c_3956,plain,
( ~ iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00
| ~ aElementOf0(sK1,slsdtgt0(xb))
| ~ aElementOf0(sK0,slsdtgt0(xa)) ),
inference(copy,[status(thm)],[c_3955]) ).
cnf(c_3957,plain,
( ~ iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00
| ~ aElementOf0(sK1,slsdtgt0(xb)) ),
inference(resolve,[status(thm)],[c_278,c_3956]) ).
cnf(c_3958,plain,
( ~ iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 ),
inference(resolve,[status(thm)],[c_279,c_3957]) ).
cnf(c_3959,plain,
~ iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(resolve,[status(thm)],[c_264,c_3958]) ).
cnf(c_3954,plain,
$false,
inference(resolve,[status(thm)],[c_382,c_3959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG124+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 06:11:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 574220 was started by sandbox on n019,
% 0.08/0.36 % Sat Sep 26 06:11:50 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 2.21/0.75
% 2.21/0.75 % SZS status Theorem for theBenchmark
% 2.21/0.75
% 2.21/0.75 % Proof 1 at 0.25 (+ 0.06) seconds.
% 2.21/0.75 % Length of proof is 11.
% 2.21/0.75 % Level of proof is 3.
% 2.21/0.75 % Maximum clause weight is 31.000.
% 2.21/0.75 % Given clauses 186.
% 2.21/0.75
% 2.21/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------