%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM520+3 : 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 : n001.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 08:17:15 AM UTC 2026
% Result : Theorem 3.35s 0.90s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 53 ( 39 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 46 ( 16 ~; 6 |; 24 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 0 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2287,axiom,
( sdtlseqdt0(xm,xp)
& ? [W0] :
( sdtpldt0(xm,W0) = xp
& aNaturalNumber0(W0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [W0] :
( sdtpldt0(xn,W0) = xp
& aNaturalNumber0(W0) )
& xn != xp ),
file('theBenchmark.p',m__2287) ).
fof(m__2306,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('theBenchmark.p',m__2306) ).
fof(m__2315,axiom,
~ ( xk = sz10
| xk = sz00 ),
file('theBenchmark.p',m__2315) ).
fof(m__2327,axiom,
~ ( xk != sz10
& xk != sz00 ),
file('theBenchmark.p',m__2327) ).
cnf(c_277,plain,
( xk = sz10
| xk = sz00 ),
inference(clausify,[status(thm)],[m__2327]) ).
cnf(c_278,plain,
xk != sz10,
inference(clausify,[status(thm)],[m__2315]) ).
cnf(c_279,plain,
xk != sz00,
inference(clausify,[status(thm)],[m__2315]) ).
cnf(c_280,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(clausify,[status(thm)],[m__2306]) ).
cnf(c_281,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(copy,[status(thm)],[c_280]) ).
fof(nnf_43,plain,
( sdtlseqdt0(xm,xp)
& ? [W0] :
( sdtpldt0(xm,W0) = xp
& aNaturalNumber0(W0) )
& xp != xm
& sdtlseqdt0(xn,xp)
& ? [X0] :
( sdtpldt0(xn,X0) = xp
& aNaturalNumber0(X0) )
& xp != xn ),
inference(fof_nnf,[status(thm)],[m__2287]) ).
fof(sk_m__2287,plain,
( sdtlseqdt0(xm,xp)
& sdtpldt0(xm,sK0) = xp
& aNaturalNumber0(sK0)
& xp != xm
& sdtlseqdt0(xn,xp)
& sdtpldt0(xn,sK1) = xp
& aNaturalNumber0(sK1)
& xp != xn ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(W0,sK0)],[nnf_43]) ).
cnf(c_287,plain,
sdtpldt0(xm,sK0) = xp,
inference(split_conjunct,[status(thm)],[sk_m__2287]) ).
cnf(c_288,plain,
xp = sdtpldt0(xm,sK0),
inference(copy,[status(thm)],[c_287]) ).
cnf(c_2173,plain,
( xk = sz10
| sdtsldt0(sdtasdt0(xn,xm),xp) = sz00 ),
inference(paramod,[status(thm)],[c_281,c_277]) ).
cnf(c_2174,plain,
( xk = sz10
| sdtsldt0(sdtasdt0(xn,xm),sdtpldt0(xm,sK0)) = sz00 ),
inference(paramod,[status(thm)],[c_288,c_2173]) ).
cnf(c_2175,plain,
( sdtsldt0(sdtasdt0(xn,xm),xp) = sz10
| sdtsldt0(sdtasdt0(xn,xm),sdtpldt0(xm,sK0)) = sz00 ),
inference(paramod,[status(thm)],[c_281,c_2174]) ).
cnf(c_1089,plain,
( sdtsldt0(sdtasdt0(xn,xm),sdtpldt0(xm,sK0)) = sz10
| sdtsldt0(sdtasdt0(xn,xm),sdtpldt0(xm,sK0)) = sz00 ),
inference(paramod,[status(thm)],[c_288,c_2175]) ).
cnf(c_2176,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) != sz00,
inference(paramod,[status(thm)],[c_281,c_279]) ).
cnf(c_1090,plain,
sdtsldt0(sdtasdt0(xn,xm),sdtpldt0(xm,sK0)) != sz00,
inference(paramod,[status(thm)],[c_288,c_2176]) ).
cnf(c_2177,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) != sz10,
inference(paramod,[status(thm)],[c_281,c_278]) ).
cnf(c_1091,plain,
sdtsldt0(sdtasdt0(xn,xm),sdtpldt0(xm,sK0)) != sz10,
inference(paramod,[status(thm)],[c_288,c_2177]) ).
cnf(c_2178,plain,
sdtsldt0(sdtasdt0(xn,xm),sdtpldt0(xm,sK0)) = sz10,
inference(resolve,[status(thm)],[c_1090,c_1089]) ).
cnf(c_2172,plain,
$false,
inference(resolve,[status(thm)],[c_1091,c_2178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM520+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 03:11:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 760162 was started by sandbox2 on n001,
% 0.11/0.37 % Sat Sep 26 03:11:26 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 3.35/0.90
% 3.35/0.90 % SZS status Theorem for theBenchmark
% 3.35/0.90
% 3.35/0.90 % Proof 1 at 0.45 (+ 0.03) seconds.
% 3.35/0.90 % Length of proof is 15.
% 3.35/0.90 % Level of proof is 4.
% 3.35/0.90 % Maximum clause weight is 33.000.
% 3.35/0.90 % Given clauses 0.
% 3.35/0.90
% 3.35/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------