%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM525+3 : 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 : n014.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 08:17:17 AM UTC 2026
% Result : Theorem 1.59s 1.00s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 22 unt; 0 def)
% Number of atoms : 62 ( 34 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 49 ( 22 ~; 15 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
fof(m__2987,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__2987) ).
fof(m__3059,axiom,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('theBenchmark.p',m__3059) ).
fof(m__,conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_98,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_100,plain,
sdtasdt0(xp,xq) = xn,
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_101,plain,
aNaturalNumber0(xq),
inference(clausify,[status(thm)],[m__3059]) ).
fof(m__3014,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('theBenchmark.p',m__3014) ).
cnf(c_111,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausify,[status(thm)],[m__3014]) ).
cnf(c_127,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_129,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_183,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_184,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_238,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xn,xn),
inference(paramod,[status(thm)],[c_111,c_98]) ).
cnf(c_1236,plain,
( sdtasdt0(sdtasdt0(xn,A),B) = sdtasdt0(xn,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_183,c_129]) ).
cnf(c_1237,plain,
( sdtasdt0(sdtasdt0(xn,xp),A) = sdtasdt0(xn,sdtasdt0(xp,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_1236,c_127]) ).
cnf(c_1238,plain,
sdtasdt0(sdtasdt0(xn,xp),xq) = sdtasdt0(xn,sdtasdt0(xp,xq)),
inference(resolve,[status(thm)],[c_1237,c_101]) ).
cnf(c_1059,plain,
sdtasdt0(sdtasdt0(xn,xp),xq) = sdtasdt0(xn,xn),
inference(paramod,[status(thm)],[c_100,c_1238]) ).
cnf(c_1239,plain,
( sdtasdt0(sdtasdt0(xp,A),B) = sdtasdt0(xp,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_183,c_127]) ).
cnf(c_1240,plain,
( sdtasdt0(sdtasdt0(xp,xn),A) = sdtasdt0(xp,sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_1239,c_129]) ).
cnf(c_1099,plain,
sdtasdt0(sdtasdt0(xp,xn),xq) = sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(resolve,[status(thm)],[c_1240,c_101]) ).
cnf(c_1241,plain,
( sdtasdt0(sdtasdt0(xp,A),B) = sdtasdt0(xp,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_183,c_127]) ).
cnf(c_1242,plain,
( sdtasdt0(sdtasdt0(xp,xq),A) = sdtasdt0(xp,sdtasdt0(xq,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_1241,c_101]) ).
cnf(c_1243,plain,
sdtasdt0(sdtasdt0(xp,xq),xq) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(resolve,[status(thm)],[c_1242,c_101]) ).
cnf(c_1244,plain,
sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(paramod,[status(thm)],[c_100,c_1243]) ).
cnf(c_1119,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xn,xq),
inference(copy,[status(thm)],[c_1244]) ).
cnf(c_1185,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xn,xq)) != sdtasdt0(xn,xn),
inference(paramod,[status(thm)],[c_1119,c_238]) ).
cnf(c_1245,plain,
( sdtasdt0(A,xn) = sdtasdt0(xn,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_184,c_129]) ).
cnf(c_1192,plain,
sdtasdt0(xp,xn) = sdtasdt0(xn,xp),
inference(resolve,[status(thm)],[c_1245,c_127]) ).
cnf(c_1246,plain,
sdtasdt0(sdtasdt0(xn,xp),xq) = sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(paramod,[status(thm)],[c_1192,c_1099]) ).
cnf(c_1247,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(paramod,[status(thm)],[c_1059,c_1246]) ).
cnf(c_1248,plain,
sdtasdt0(xp,sdtasdt0(xn,xq)) = sdtasdt0(xn,xn),
inference(copy,[status(thm)],[c_1247]) ).
cnf(c_1235,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1185,c_1248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM525+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.42 % Computer : n014.cluster.edu
% 0.07/0.42 % Model : x86_64 x86_64
% 0.07/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.42 % Memory : 8046.5625MB
% 0.07/0.42 % OS : Linux 6.8.0-71-generic
% 0.07/0.42 % CPULimit : 300
% 0.07/0.42 % WCLimit : 300
% 0.07/0.42 % DateTime : Sat Sep 26 03:06:01 UTC 2026
% 0.07/0.42 % CPUTime :
% 0.07/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.43 % Process 2005125 was started by sandbox on n014,
% 0.07/0.43 % Sat Sep 26 03:06:01 2026
% 0.07/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.44
% 0.07/0.44 % From the command line: assign(max_seconds, 300).
% 1.59/1.00
% 1.59/1.00 % SZS status Theorem for theBenchmark
% 1.59/1.00
% 1.59/1.00 % Proof 1 at 0.17 (+ 0.04) seconds.
% 1.59/1.00 % Length of proof is 20.
% 1.59/1.00 % Level of proof is 4.
% 1.59/1.00 % Maximum clause weight is 48.000.
% 1.59/1.00 % Given clauses 88.
% 1.59/1.00
% 1.59/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------