0.00/0.02	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.03	% Command  : tptp4X_and_run_prover9 1440 /export/starexec/sandbox/benchmark/theBenchmark.p
0.10/0.35	% Computer : n009.cluster.edu
0.10/0.35	% Model    : x86_64 x86_64
0.10/0.35	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.35	% Memory   : 8046.5625MB
0.10/0.35	% OS       : Linux 6.8.0-71-generic
0.10/0.36	% CPULimit : 1440
0.10/0.36	% WCLimit  : 180
0.10/0.36	% DateTime : Mon Jul 27 08:58:58 UTC 2026
0.10/0.36	% CPUTime  : 
0.10/0.36	Running tptp4X_and_run_prover9 1440 /export/starexec/sandbox/benchmark/theBenchmark.p
0.13/0.41	============================== Prover9 ===============================
0.13/0.41	Prover9 (64) version 2009-11A, November 2009.
0.13/0.41	Process 908552 was started by sandbox on n009,
0.13/0.41	Mon Jul 27 08:58:58 2026
0.13/0.41	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_908544_n009".
0.13/0.41	============================== end of head ===========================
0.13/0.41	
0.13/0.41	
0.13/0.41	% Starting search at 0.01 seconds.
0.13/0.41	
0.13/0.41	============================== PROOF =================================
0.13/0.41	% SZS status Theorem
0.13/0.41	% SZS output start Refutation
0.13/0.41	
0.13/0.41	% Proof 1 at 0.01 (+ 0.00) seconds.
0.13/0.41	% Length of proof is 12.
0.13/0.41	% Level of proof is 4.
0.13/0.41	% Maximum clause weight is 9.000.
0.13/0.41	% Given clauses 13.
0.13/0.41	
0.13/0.41	2 -(exists Xs exists Ys -(ord(Xs) -> (-ord(Ys) -> ord(merge(Xs,Ys))))) # label(non_clause).  [assumption].
0.13/0.41	7 (all Z -leqNat(s(Z),z)) # label(non_clause).  [assumption].
0.13/0.41	12 (all Y Y = merge(nil,Y)) # label(non_clause).  [assumption].
0.13/0.41	14 (all Y all Y2 all Xs (ord(cons(Y,cons(Y2,Xs))) <-> leqNat(Y,Y2) & ord(cons(Y2,Xs)))) # label(non_clause).  [assumption].
0.13/0.41	16 ord(nil).  [assumption].
0.13/0.41	19 merge(nil,A) = A.  [clausify(12)].
0.13/0.41	25 -leqNat(s(A),z).  [clausify(7)].
0.13/0.41	28 -ord(A) | ord(B) | ord(merge(A,B)).  [clausify(2)].
0.13/0.41	31 -ord(cons(A,cons(B,C))) | leqNat(A,B).  [clausify(14)].
0.13/0.41	37 ord(A).  [resolve(28,a,16,a),rewrite([19(3)]),merge(b)].
0.13/0.41	38 leqNat(A,B).  [back_unit_del(31),unit_del(a,37)].
0.13/0.41	39 $F.  [resolve(38,a,25,a)].
0.13/0.41	
0.13/0.41	% SZS output end Refutation
0.13/0.41	============================== end of proof ==========================
0.13/0.41	
0.13/0.41	
0.13/0.41	THEOREM PROVED
0.13/0.41	% SZS status Theorem
0.13/0.41	
0.13/0.41	Exiting with 1 proof.
0.13/0.41	
0.13/0.41	Process 908552 exit (max_proofs) Mon Jul 27 08:58:58 2026
0.13/0.42	Prover9 ended
0.13/0.42	EOF